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motion

motion

motion Sentence Examples

  • She shook her head and the motion brought on a dizzy spell.

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  • Raindrops fell as if in slow motion, and lightning stayed, brighter than the midday sun.

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  • Absolute continuity of motion is not comprehensible to the human mind.

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  • She tried to sit up, but the motion created a nauseating pain in her shoulder.

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  • The man reached down with one hand and pulled his partner to a standing position and nudged Dean forward all in one motion, burying his gun in the detective's side.

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  • If nothing else, we can bury motion sensors a few feet away, if you think the Others will sense anything close to the portal.

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  • You've set in motion a course which cannot be altered.

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  • It is continually receiving new life and motion from above.

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  • The zipper opened in one motion to reveal the lighted face of Fred O'Connor.

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  • She follows with her hands every motion you make, and she knew that I was looking for the doll.

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  • My hands felt every object and observed every motion, and in this way I learned to know many things.

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  • In one fluid motion, he mounted Ed.

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  • The slow motion world around them snapped into real time, throwing them against a wall.

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  • It is splendid to feel the wind blowing in my face and the springy motion of my iron steed.

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  • The later English artists have somewhat changed the mode of communicating motion to the slides, by attaching the screws pdrmanently to the micrometer head and tapping each micrometer screw into its slide.

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  • I was never still a moment; my life was as full of motion as those little insects that crowd a whole existence into one brief day.

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  • Sensing motion, she opened her eyes to find Alex leaning across her, placing a long stemmed glass on the window sill beside her.

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  • Just as in a clock, the result of the complicated motion of innumerable wheels and pulleys is merely a slow and regular movement of the hands which show the time, so the result of all the complicated human activities of 160,000 Russians and French--all their passions, desires, remorse, humiliations, sufferings, outbursts of pride, fear, and enthusiasm--was only the loss of the battle of Austerlitz, the so-called battle of the three Emperors--that is to say, a slow movement of the hand on the dial of human history.

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  • He kicked Ed into motion and headed for the house.

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  • In a single motion, she tugged open her robe and nightgown, baring both breasts, pressing Claire to her right side.

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  • Surprised by the intimate motion that seemed meant to comfort her, Deidre glanced up at him before nuzzling his neck.

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  • The bullet of your thought must have overcome its lateral and ricochet motion and fallen into its last and steady course before it reaches the ear of the hearer, else it may plow out again through the side of his head.

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  • I do remember some theories concerning relativity suggesting some sort of motion in space might allow time travel if space-time geometrics are possible.

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  • A languor of motion and speech, resulting from weakness, gave her a distinguished air which inspired respect.

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  • By adopting smaller and smaller elements of motion we only approach a solution of the problem, but never reach it.

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  • The ship moves independently with its own enormous motion, the boat hook no longer reaches the moving vessel, and suddenly the administrator, instead of appearing a ruler and a source of power, becomes an insignificant, useless, feeble man.

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  • As Dean watched, scarcely breathing, she lifted the ancient white dress above her head in one motion and dropped it to the floor.

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  • They were a soft, sable brown with specs of black that seemed to swirl in motion around her pupils like two tiny solar systems.

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  • Darkyn glanced at the sand in the hourglass.  He had one more chain of events to set in motion.

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  • I would cling to my mother's dress as she went about her household duties, and my little hands felt every object and observed every motion, and in this way I learned a great many things.

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  • The top of the buggy caught the air like a parachute or an umbrella filled with wind, and held them back so that they floated downward with a gentle motion that was not so very disagreeable to bear.

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  • Thus the smallest rotation of either head communicates to the corresponding slide motion, which, if the screws are accurate, is proportional to the amount through which the head is turned.

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  • With a swift motion, she sent the combination skyward where tack and bill joined the hundreds of others while she deftly caught the falling quarter to the cheers of the dinners.

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  • Her first strike might as well have been in slow motion; no one moved like he did with brute strength that flattened her after a particularly harsh block.

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  • The world moved like it was in slow motion, giving him time to react with unnatural agility.

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  • (2) Time is infinite motion without a moment of rest and is unthinkable otherwise.

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  • Together they watched as Alex put the horse down the hill, his body moving gracefully with the motion of the horse.

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  • Having looked at Natasha he approached his sister, laid his well gloved hand on the edge of her box, nodded to her, and leaning forward asked a question, with a motion toward Natasha.

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  • She laughed merrily and raised her arms in one motion, pulling up her t-shirt.

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  • Yesterday I thought for the first time what a beautiful thing motion was, and it seemed to me that everything was trying to get near to God, does it seem that way to you?

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  • Momentum (quantity of motion) is the product of mass and velocity.

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  • The front door was in continual motion with guests coming and going, amid laughter and boisterous conversation.

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  • The old man grabbed a metal trashcan from the curb and in one motion swung it at the car, scoring a direct hit on the windshield.

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  • Whenever it was possible, I touched the machinery while it was in motion, so as to get a clearer idea how the stones were weighed, cut, and polished.

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  • He nudged Random into motion and Carmen stepped back.

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  • He could feel the tremor of movement in his hand, the result of some motion far below.

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  • The only motion in the air was that of the dripping, microscopic particles of drizzling mist.

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  • She responds quickly to the gentle pressure of affection, the pat of approval, the jerk of impatience, the firm motion of command, and to the many other variations of the almost infinite language of the feelings; and she has become so expert in interpreting this unconscious language of the emotions that she is often able to divine our very thoughts.

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  • Few know what joy it is to feel the roses pressing softly into the hand, or the beautiful motion of the lilies as they sway in the morning breeze.

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  • How full of life and motion it was!

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  • I made her go through the motion of knocking the doll's head on the table and spelled to her: No, no, Helen is naughty.

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  • In the middle of one of the longest sentences, he stopped the rotary motion of the snuffbox, raised his head, and with inimical politeness lurking in the corners of his thin lips interrupted Weyrother, wishing to say something.

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  • A man in motion always devises an aim for that motion.

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  • He swept his hand to motion her through the doorway, then walked to the desk and the only chair in the room.

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  • The more this field of motion spreads out before our eyes, the more evident are the laws of that movement.

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  • The discovery of these laws is only possible when we have quite abandoned the attempt to find the cause in the will of some one man, just as the discovery of the laws of the motion of the planets was possible only when men abandoned the conception of the fixity of the earth.

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  • No spotting or cramps, but she did have motion sickness.

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  • We set this chain of events in motion before the Schism.

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  • This rock was separate from the rest of the mountain and was in motion, turning slowly around and around as if upon a pivot.

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  • The buoyant motion of the water filled me with an exquisite, quivering joy.

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  • She turned to see him motion her towards the jungle surrounding the lake.  His clothing was torn, and blood stained his skin.  He appeared to have been running; his boots were covered in mud that had splashed to his thighs, and his face was flushed.

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  • She turned to see him motion her towards the jungle surrounding the lake.  His clothing was torn, and blood stained his skin.  He appeared to have been running; his boots were covered in mud that had splashed to his thighs, and his face was flushed.

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  • But the mysterious forces that move humanity (mysterious because the laws of their motion are unknown to us) continued to operate.

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  • Wheels creak on their axles as the cogs engage one another and the revolving pulleys whirr with the rapidity of their movement, but a neighboring wheel is as quiet and motionless as though it were prepared to remain so for a hundred years; but the moment comes when the lever catches it and obeying the impulse that wheel begins to creak and joins in the common motion the result and aim of which are beyond its ken.

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  • A modern branch of mathematics having achieved the art of dealing with the infinitely small can now yield solutions in other more complex problems of motion which used to appear insoluble.

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  • It takes time for me to establish motion and I got a late start.

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  • Finally she got up from the table and went through the motion of picking seaweed and shells, and splashing in the water, holding up her skirts higher than was proper under the circumstances.

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  • On the motion of Cabanis he was named associate of the Institute in the class of the moral and political sciences.

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  • On one occasion Dundas carried a motion in the House of Commons, censuring Hastings and demanding his recall.

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  • Wrapping the rope around the saddle horn, he nudged Ed into motion, tugging the fallen tree downstream.

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  • It was like walking in water and I almost lost my balance but after a few steps, I could control my motion pretty well.

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  • Even with the particles retarding the motion of the aether, the same will be true if, to counterbalance the increased inertia, suitable forces are caused to act on the aether at all points where the inertia is altered.

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  • Motion is communicated to the forks by female screws tapped in the heads m and n acting on the screws o and p respectively.

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  • She made a choking, gagging motion at her throat in answer to Donnie's written question.

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  • With one motion he struck downward with his right arm and swung his left elbow with all his might on a level line at the man's jaw.

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  • How strange, how extraordinary, how joyful it seemed, that her son, the scarcely perceptible motion of whose tiny limbs she had felt twenty years ago within her, that son about whom she used to have quarrels with the too indulgent count, that son who had first learned to say "pear" and then "granny," that this son should now be away in a foreign land amid strange surroundings, a manly warrior doing some kind of man's work of his own, without help or guidance.

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  • Natasha threw off the shawl from her shoulders, ran forward to face "Uncle," and setting her arms akimbo also made a motion with her shoulders and struck an attitude.

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  • A still further facility was given to the use of the filar micrometer by the introduction of clockwork, which caused the telescope automatically to follow the diurnal motion of a star, and left the observer's hands entirely at liberty.'

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  • "Motion sensors there," Chapo added.

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  • It looked as if by that slight motion the army itself was expressing its joy at the approach of the Emperors.

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  • She turned and in one motion straddled him, pinning his arms above his head, the heat of her body pressed against him.

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  • He held that every fermentation consisted of molecular motion which is transmitted from a substance in a state of chemical motion - that is, of decomposition - to other substances, the elements of which are loosely held together.

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  • What's been set into motion can't be stopped, but you at least have a chance if you have her.

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  • Time slowed down, and it was as if everything was in slow motion.

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  • True to his word, when informed of our decision, he immediately put the gears in motion.

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  • She snapped into motion, but he deflected her next strike as easily as he had those of the vamps he killed.

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  • The magic took hold of her, and she danced away from his strikes as if they were in slow motion.

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  • The wheels were already in motion.

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  • I'm still not certain it'll work, but that chain of events is in motion.

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  • "Stay close to me," he said as he kicked Ed into motion.

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  • I was running as fast as I could, but it was like I was running in slow motion.

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  • Deidre couldn't move as they fell in slow motion.

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  • Burgess stepped back, holding up his hand in a halting motion.

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  • She obeyed and lowered herself to the floor a moment before the wagon jarred into motion.

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  • When she woke again, her body was in motion.

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  • She sighed and shrugged, wincing at the pain caused by the motion.

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  • C is the clamp and M the slow motion in position angle.

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  • I, 2 and 3), used to bolt the head of one of the screws, and the instrument was provided with a slipping piece, giving motion to the micrometer by screws acting on two slides, one in right ascension, the other in declination, so that " either of the, webs can be placed upon either component of a double star with ease and certainty (Mem.

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  • The pitch of the screw is the same as that of the measuring screw (50 threads to the inch), and its motion can be limited by a stop to half a revolution.

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  • Quick motion in position-angle for rough setting or for the measurement of close double stars is given by the large ring R.

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  • For accurate measurement of the displacements of lines of stellar spectra which are produced by the relative motion of star and observer in the line of sight, a very beautiful instrument has been devised by Dr J.

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  • At the meeting of parliament on the 8th of January 1674, he carried a motion for a proclamation banishing Catholics to a distance of 10 m.

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  • The force of the universe is swept up and gathered in God, who communicates motion to the parts of extension, and sustains that motion from moment to moment; and in the same way the force of mind has really been concentrated in God.

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  • The true physical conception is motion, the ultimate ground of which is to be sought in God's infinite power.

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  • Man himself cannot increase the sum of motion; he can only alter its direction.

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  • The whole conception of force may disappear from a theory of the universe; and we can adopt a geometrical definition of motion as the shifting of one body from the neighbourhood of those bodies which immediately touch it, and which are assumed to be at rest, to the neighbourhood of other bodies.

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  • Motion, in short, is strictly locomotion, and nothing else.

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  • The first law affirms that every body, so far as it is altogether unaffected by extraneous causes, always perseveres in the same state of motion or of rest; and the second law that simple or elementary motion is always in a straight line.'

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  • We have then to think of a full universe of matter (and matter = extension) divided and figured with endless variety, and set (and kept) in motion by God; and any sort of division, figure and motion will serve the purposes of our supposition as well as another.

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  • The defects of Descartes lie rather in his apparently imperfect apprehension of the principle of movements uniformly accelerated which his contemporary Galileo had illustrated and insisted upon, and in the indistinctness which attaches to his views of the transmission of motion in cases of impact.

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  • Lucas brought in a bill in his first session to effect this reform, but was defeated on the motion to have the bill sent to England for approval by the privy council; and he insisted upon the independent.

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  • materia, matter), in philosophy, the theory which regards all the facts of the universe as explainable in terms of matter and motion, and in particular explains all psychical processes by physical and chemical changes in the nervous system.

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  • He showed that the heat motion of particles, which is too small to be perceptible when these particles are large, and which cannot be observed in molecules since these themselves are too small, must be perceptible when the particles are just large enough to be visible and gave complete equations which enable the masses themselves to be deduced from the motions of these particles.

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  • On the 6th of November he carried a motion entrusting the train-bands south of the Trent to the command of the earl of Essex.

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  • A distinction was formerly made between double stars of which the components were in revolution around each other, and those in which no relative motion was observed; but it is now considered that all double stars must really be binary systems.

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  • In cases where the direction of the air motion is always the same, as in the ventilating shafts of mines and buildings for instance, these anemometers, known, however, as air meters, are employed, and give most satisfactory results.

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  • To make matters worse, the pen which records the motion of the plate is often connected with it by an extensive system of chains and levers.

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  • A violent gust strikes the plate, which is driven back and carried by its own momentum far past the position in which a steady wind of the same force would place it; by the time the motion has reached the pen it has been greatly exaggerated by the springiness of the connexion, and not only is the plate itself driven too far back, but also its position is wrongly recorded by the pen; the combined errors act the same way, and more than double the real maximum pressure may be indicated on the chart.

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  • In most mechanical systems the working stresses acting between the parts can be determined when the relative positions of all the parts are known; and the energy which a system possesses in virtue of the relative positions of its parts, or its configuration, is classified as "potential energy," to distinguish it from energy of motion which we shall presently consider.

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  • Energy of motion is usually called "kinetic energy."

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  • Available kinetic energy is possessed by a system of two or more bodies in virtue of the relative motion of its parts.

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  • Since our conception of velocity is essentially relative, it is plain that any property possessed by a body in virtue of its motion can be effectively possessed by it only in relation to those bodies with respect to which it is moving.

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  • But there are stresses which depend on the relative motion of the visible bodies between which they appear to act.

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  • When work is done against these forces no full equivalent of potential energy may be produced; this applies especially to frictional forces, for if the motion of the system be reversed the forces will be also reversed and will still oppose the motion.

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  • Francis Bacon expressed his conviction that heat consists of a kind of motion or "brisk agitation" of the particles of matter.

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  • It must not be thought that heat generates motion or motion heat (though in some respects this is true), but the very essence of heat, or the substantial self of heat, is motion and nothing else."

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  • "It is hardly necessary to add," he remarks, "that anything which any insulated body or system of bodies can continue to furnish without limitation cannot possibly be a material substance; and it appears to me to be extremely difficult, if not quite impossible, to form any distinct idea of anything capable of being excited and communicated in the manner that heat was excited and communicated in these experiments, except it be motion."

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  • Though we may allow that the results obtained by Rumford and Davy demonstrate satisfactorily that heat is in some way due to motion, yet they do not tell us to what particular dynamical quantity heat corresponds.

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  • In the second class there are, in addition to the lifting motion, two horizontal movements at right angles to one another.

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  • The principal motion in a crane is naturally the hoisting or lifting motion.

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  • It has the horizontal racking motion mentioned FIG.

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  • setting concrete blocks in courses, this motion is almost a necessity.

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  • When the cross traverse motion of a traveller crab is suppressed, and the longitudinal travelling motion is increased in importance we come to a type of crane, the use of which is rapidly increasing; it goes by the name of " transporter."

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  • Transporters can only move the load to any point on a vertical surface (generally a plane surface); they have a lifting Trans- motion and a movement of translation.

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  • In depths beyond the reach of wave motion, and apart from suspension across a submarine gully, which will sooner or later result in a rupture of the cable, the most frequent cause of interruption is seismic or other shifting of the ocean bed, while in shallower waters and near the shore the dragging of anchors or 40 fishing trawls has been mostly responsible.

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  • When one of a series of keys (each corresponding to a letter) arranged round a pointer is depressed, the motion of the pointer, which is geared to the shuttle armature, is arrested on coming opposite that particular key, and the transmission of the currents to line is stopped, though the armature itself can continue to rotate.

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  • The arm which moves round over the segments rotates at the rate of three revolutions per second, and is kept in motion by means of an iron toothed wheel, the rim of which is set in close proximity to the poles of an electromagnet.

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  • One diaphragm gives the mirror a movement in a vertical direction while the other gives it a horizontal motion.

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  • A ray of light is directed upon the mirror, and the motion of the latter, due to the varying strengths and direction of the received currents, is made to write the transmitted signals upon a strip of bromide photographic paper about three inches wide.

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  • The telautograph is on a similar principle to the Cowper apparatus, the motion of the transmitting pencil or stylus used in writing being resolved by a system of levers into two component rectilinear motions, which are used to control and vary the currents in two distinct electrical circuits.

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  • The motion communicated to rollers by the pencil serves to cut resistance in or out of the two line circuits which are connected to the rollers, and thus two independent variable line currents are obtained.

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  • indicator, suitably supported, a to-and-fro motion was recorder given by the electromagnetic actions due to the electric currents constituting the signals.

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  • The indicator was connected with a Ruhmkorff coil or other equivalent apparatus, designed to cause a continual succession of sparks to pass between the indicator and a metal plate situated beneath it and having a plane surface parallel to its line of motion.

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  • Over the surface of the plate and between it and the indicator there was passed, at a regularly uniform speed, in a direction perpendicular to the line of motion of the indicator, a material capable of being acted on physically by the sparks, through either their chemical action, their heat, or their perforating force.

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  • When therefore the signalcoil moves in obedience to the electric signal-currents passed through it, the motion communicated to the siphon is recorded on the moving slip of paper by a wavy line of ink-marks very close together.

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  • When electric oscillations are set up in an open or closed electric circuit having capacity and inductance, and left to themselves, they die away in amplitude, either because they dissipate their energy as heat in overcoming the resistance of the circuit, or because they radiate it by imparting wave motion to the surrounding ether.

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  • Owing to hysteresis the part of the band magnetized is not symmetrically placed with regard to the magnetic poles, but advanced in the direction of motion of the band.

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  • The process of reflection in the case of a wave motion involves the condition that the wave-length shall be small compared with the dimensions of the mirror, and hence the attempt to reflect and converge electric waves loon ft.

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  • In all cases of wave motion the wave-length is connected with the velocity of propagation of the radiation by the relation v=nX, where n is the frequency of the oscillations and X is the wave-length.

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  • The receiver was based on the change of friction produced by the passage of an electric current through the point of contact of certain substances in relative motion.

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  • Her ancient prestige, her geographical position and the intellectual primacy of her most noble children rendered Italy the battleground of principles that set all Christendom in motion, and by the clash of which she found herself for ever afterwards divided.

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  • A motion presented by the Socialists in the Chamber for the immediate discussion of a bill to prevent the massacres of the proletariate having been rejected by an enormous majority, the 28 Socialist deputies resigned their seats; on presenting themselves for re-election their number was reduced to 25.

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  • A motion was passed for his committal by the Lords, who, as in Clarendon's case, voted his banishment.

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  • In 1705 he supported a motion that the church was in danger, and in 1710 in Sacheverell's case spoke in defence of hereditary right.'

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  • The element of naturalism stands for science with a leaning towards materialism (" explanation in terms of matter and motion ").

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  • Polyp 7 has proof sense, 1 o c oduced as its first bud, 8; as its second bud, a7, motion and nutriwhich starts a uniserial pinnule; and as a third t i on, until its bud I', which starts a biserial branch (I I'-VI') medusoid nature that repeats the structure of the main stem and and organization gives off pinnules.

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  • Their fundamental conception is that of Democritus; they seek to account for the formation of the cosmos, with its order and regularity, by setting out with the idea of an original (vertical) motion of the atoms, which somehow or other results in movements towards and from one another.

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  • The speaker seeks to make intelligible the appearance of art and contrivance in the world as a result of a natural settlement of the universe (which passes through a succession of chaotic conditions) into a stable condition, having a constancy in its forms, yet without its several parts losing their motion and fluctuation.

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  • They do not, of course, deny the co-operation of the other forces which have been suggested, except so far as these are inconsistent with the motion of the water in the form of separate columns rather than a flowing stream.

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  • Sir George Darwin finds a possible explanation of these in the screwing motion which the earth would suffer in its plastic state.

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  • The quadrate muscle adjusts the motion, and prevents pressure upon the optic nerve; during the state of relaxation of both muscles the nictitans withdraws through its own elasticity.

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  • Cuculus canorus and trogons, is often lined with the broken-off hairs of these caterpillars, which, penetrating the cuticle, assume a regular spiral arrangement, due to the rotatory motion of the muscles of the gizzard.

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  • Eight times the mean motion of Venus is so nearly equal to thirteen times that of the earth that the difference amounts to only the 2.

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  • Hansen of two new inequalities in the moon's motion.

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  • "Just as a steamengine," he says in Kraft and Stoff (7th ed., p. 130), "produces motion, so the intricate organic complex of force-bearing substance in an animal organism produces a total sum of certain effects, which, when bound together in a unity, are called by us mind, soul, thought."

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  • In 1744 Alembert applied this principle to the theory of the equilibrium and the motion of fluids (Trcite de l'equilibre et du mouvement des fluides), and all the problems before solved by geometricians became in some measure its corollaries.

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  • In 1749 he furnished a method of applying his principles to the motion of any body of a given figure; and in 1754 he solved the problem of the precession of the equinoxes, determined its quantity and explained the phenomenon of the nutation of the earth's axis.

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  • He maintained that the laws of motion were necessary, not contingent.

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  • They are flattened oval in form, circling with gliding motion over the surface film of the water, and occasionally diving, when they carry down with them a bubble of air.

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  • The former presents an intimate mixture of boulders brought from Finland and Olonets (with an addition of local boulders) with small gravel, coarse sand and the finest glacial mud, - the whole bearing no trace of ever having been washed up and sorted by water in motion, except in subordinate layers of glacial sand and gravel; the size of the boulders decreases on the whole from N.

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  • and central Russia, often takes the shape of ridges parallel to the direction of the motion of the boulders.

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  • Goremykin, who had succeeded Witte at the head of the government, met these preposterous demands with a flat refusal, the House voted, on the motion of M.

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  • From falling off trains, engines, &c., in motion io.

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  • While attending to the machinery, &c., of " engines in motion.

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  • Of these there are two main systems: (1) a continuous cable is carried over two main drums at each end of the line, and the motion is derived either (a) from the weight of the descending load or (b) from a motor acting on one of the main drums; (2) each end of the cable is attached to wagons, one set of which accordingly ascends as the other descends.

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  • The weight required to cause the downward motion is obtained either by means of the material which has to be transported to the bottom of the hill or by water ballast, while to aid and regulate the motion generally steam or electric motors are arranged to act on the main drums, round which the cable is passed with a sufficient number of turns to prevent slipping.

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  • If the total resistance against which the train is maintained in motion with an instantaneous velocity of V feet per second is R, the rate at which energy is expended in moving the train is represented by the product RV, and this must be the rate at which energy is supplied to the train after deducting all losses due to transmission from the source of power.

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  • In whatever form energy is produced and distributed to the train it ultimately appears as mechanical energy applied to turn one or more axles against the resistance to their rotation imposed by the weight on the wheels and the motion of the train.

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  • The resistance to motion round a curve has not been so systematically studied that any definite rule can be formulated applicable to all classes of rolling stock and all radii of curves.

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  • This is the horse-power, therefore, which must be developed in the cylinders to maintain the train in motion at a uniform speed of 40 m.

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  • All types of valves are with few exceptions operated by a link motion, generally of the Stephenson type, occasionally of the Allan type or the Gooch type, or with some form of radial gear as the Joy gear or the Walschaert gear, though the latter gear has characteristics which ally it with the link motions.

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  • The Stephenson link motion is used almost universally in England and America, but it has gradually been displaced by the Walschaert gear on the continent of Europe, and to some extent in England by the Joy gear.

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  • The lead is variable in the Stephenson link motion, whilst in the Walschaert and the Joy gears it is constant.

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  • The distribution of steam to both cylinders is effected by one piston-valve operated by a link motion, so that there is considerable mechanical simplicity in the arrangement.

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  • A considerable amount of standing room is then available, and those who have to occupy it have been nicknamed " straphangers," from the fact that they steady themselves against the motion of the train by the aid of leather straps fixed from the roof for that purpose.

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  • Their use secures a continuous passage-way through the train, but is attended with some discomfort and risk when the train is in motion.

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  • As it was, although Parker said that Grindal "was not resolute and severe enough for the government of London," his attempts to enforce the use of the surplice evoked angry protests, especially in 1565, when considerable numbers of the nonconformists were suspended; and Grindal of his own motion denounced Cartwright to the Council in 1570.

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  • Another of Roberval's discoveries was a very general method of drawing tangents, by considering a curve as described by a moving point whose motion is the resultant of several simpler motions.

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  • On the 6th of December he protested with three other peers against the measure sent up from the Commons enforcing the disarming of all convicted recusants and taking bail from them to keep the peace; he was the only peer to dissent from the motion declaring the existence of an Irish plot; and though believing in the guilt and voting for the death of Lord Stafford, he interceded, according to his own account, 3 with the king for him as well as for Langhorne and Plunket.

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  • There is no difficulty in conceiving how a nebula, quite independently of any internal motion of its parts, shall also have had as a whole a movement of rotation.

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  • He wrote an admirable textbook of the Theory of Heat (1871), and a very excellent elementary treatise on Matter and Motion (1876).

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  • But this was based upon the assumption of a distance-action between electric particles, the intensity of which depended on their relative motion as well as on their position.

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  • After three months' tenure of this office he was returned by the department to the Constituent Assembly, where he voted with the Mountain, and brought forward the celebrated motion for the abolition of the presidential office.

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  • In this Assembly he proposed that " a confession of faith, a catechism, a directory for all the parts of the public worship, and a platform of government, wherein possibly England and we might agree," should be drawn up. This was unanimously approved of, and the laborious undertaking was left in Henderson's hands; but the " notable motion " did not lead to any immediate results.

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  • The soul is in turn the image or product of the vas, and the soul by its motion begets corporeal matter..

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  • is a form of motion, and the desire of the soul is for the motionless rest which belongs to the One.

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  • The necessary and immediate results of such periodical changes of pressure are winds, which, speaking generally, blow from the area of greatest to that of least pressure - subject, however, to certain modifications of direction, arising from the absolute motion of the whole body of the air due to the revolution of the earth on its axis from west to east.

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  • In 1780 and 1781 he took an active part in opposition to Lord North's American policy, and it was largely as the result of his motion on the 22nd of February in the latter year, demanding the cessation of the war against the colonies, when the ministerial majority was reduced to one, that Lord North resigned office.

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  • Russell resigned; and on the 29th of January 1855 a motion by J.

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  • Let AB be the major axis of the orbit, B the pericentre, F the focus or centre of motion, P the position of the body.

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  • Though for the present the Sultan regained his hold upon Egypt, yet in reality Bonaparte set in motion forces which could not be stayed until the ascendancy of one or other of the western maritime powers in that land was definitely decided.

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  • The fact that the three new consuls had entered upon office and set the constitutional machinery in motion fully six weeks before the completion of the plebiscite, detracts somewhat from the impressiveness of the vox populi on that occasion.

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  • He also shows how his method may be used to determine some curious and long-discussed problems, such as the light of the stars, the ebb and flow of the tide, the motion of the balance.

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  • They are in almost continuous motion, their power of endurance being equal to the rapidity of their motions.

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  • The samson-post is placed flush with one side of the main sill, the band-wheel jack-post being flush with the other side, so that the walking-beam, which imparts motion to the string of tools, works parallel with the main sill.

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  • The engine, which is provided with reversing gear, is of 12 or 15 horse-power and motion is communicated through a belt to the band-wheel, which operates the walking-beam by means of a crank.

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  • The band-wheel communicates motion to the walking-beam, while drilling is in progress, through the crank and a connectingrod known as the pitman; to the bull-wheels, while the tools are being raised, by the bull-rope; and to the sand-pump reel, by a friction pulley, while the sand-pump is being used.

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  • The sand-pump reel is set in motion by pressing a lever, the reel being then brought into contact with the face of the band-wheel.

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  • The adoption of a different arrangement for transmitting motion.

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  • In 1100, indeed, it might appear that a new Crusade from the West, which the capture of Antioch in 1098 had begun, and the conquest of Jerusalem in 1099 had finally set in motion, was destined to achieve great things for the nascent kingdom.

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  • He was said to be the inventor of a kind of flying-machine, a wooden pigeon balanced by a weight suspended from a pulley, and set in motion by compressed air escaping from a valve.'

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  • We begin by considering the laws of motion in the orbit itself, regardless of the position of the latter.

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  • Another curious theorem proposed by Bouilland in 1625 as a substitute for Kepler's second law is that the angular motion of the body as measured around the empty focus F' is (approximately) uniform.

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  • From the law of angular motion of the latter its radius vector will run ahead of PQ near A, PQ will overtake and pass it at apocentre, and the two will again coincide at pericentre when the revolution is completed.

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  • Instead of the period it is common in astronomical practice to use the mean angular speed, called the mean motion of the body.

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  • This is defined as the speed of revolution of the fictitious body already described, revolving with a uniform angular motion and the same periodic time as the planet.

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  • It follows that putting n for the mean motion and T for the period of revolution we shall have in degrees nT=3600.

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  • In these cases therefore the mean distance and mean motion are regarded as different elements, and the whole number of the latter is seven.

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  • In 1798 he presented to the Royal Society his "Enquiry concerning the Source of Heat which is excited by Friction," in which he combated the current view that heat was a material substance, and regarded it as a mode of motion.

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  • At the end of each twig is a membrane pierced by pores, and a number of cilia depend into the lumen of the tube; these cilia maintain a constant motion.

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  • In 1776 it was moved in the House of Commons by David Hartley, son of the author of Observations on Man, that " the slave trade was contrary to the laws of God and the rights of men "; but this motion - the first which was made on the subject - failed.

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  • Wilberforce's first motion for a committee of the whole House upon the question was made on the 19th of March 1789, and this committee proceeded to business on the 12th of May of the same year.

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  • After an admirable speech, Wilberforce laid on the table twelve resolutions which were intended as the basis of a future motion for the abolition of the trade.

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  • At length, on the 18th of April of the latter year, a motion was made for the introduction of a bill to prevent the further importation of slaves into the British colonies in the West Indies.

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  • Opinion had been prejudiced by the insurrections in St Domingo and Martinique, and in the British island of Dominica; and the motion was defeated by 163 votes against 88.

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  • When a similar motion was brought forward in the Lords the consideration of it was postponed to the following year, in order to give time for the examination of witnesses by a committee of the House.

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  • When the news of this reached Paris, it created a strong feeling against the planters; and on the motion of the Abbe Gregoire it was resolved by the assembly on the 15th of May 1791 " that the people of colour resident in the French colonies, born of free parents, were entitled to, as of right, and should be allowed, the enjoyment of all the privileges of French citizens, and among others those of being eligible to seats both in the parochial and colonial assemblies."

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  • Canning carried against Buxton and his friends a motion to the effect that the desired ameliorations in the condition and treatment of the slaves should be recommended by the home government to the colonial legislatures, and enforced only in case of their resistance, direct action being taken in the single instance of Trinidad, which, being a crown colony, had no legislature of its own.

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  • His most interesting paper is "On the Proper Motion of the Solar System," and was published in the Phil.

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  • For the subjects of this general heading see the articles Mechanics; Dynamics, Analytical; Gyroscope; Harmonic Analysis; Wave; HYDROMechanics; Elasticity; Motion, Laws Of; Energy; Energetics; Astronomy (Celestial Mechanics); Tide.

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  • The mutual slaughter of barbarians in the Levant seemed, even to George Canning, a lesser evil than a renewed Armageddon in Europe; and all the resources of diplomacy were set in motion to heal the rupture between Turkey and Russia.

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  • Scarcely leaving his troops time to restore their worn-out footgear, or for the cavalry to replace their jaded horses from captured Prussian resources, he set Davout in motion towards Warsaw on the 2nd of November, and the remainder of the army followed in successive echelons as rapidly as they could be despatched.

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  • His work is an attack on Toland's Letters to Serena (1704), which argued that motion is essential to matter, and on Locke and Berkeley.

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  • Near its margin the surface of the inland ice is broken up by numerous large crevasses, formed by the outward motion of the glacier covering the underlying land.

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  • The steep icewalls at the margin of the inland ice show, especially where the motion of the ice is slow, a distinct striation, which indicates the strata of annual precipitation with the intervening thin seams of dust (Nordenskidld's kryokonite).

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  • In the rapidly moving glaciers of the icefjords this striation is not distinctly visible, being evidently obliterated by the strong motion of the ice masses.

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  • The motion of the outwardscreeping inland ice will naturally be more independent of the configurations of the underlying land in the interior, where its thickness is so enormous, than near the margin where it is thinner.

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  • In 1657 he advised his father not to accept the office of king, although in 1654 he had supported a motion to this effect; 8 See Hugo Goldschmidt, "Das Orchester der italienischen Oper im 17.

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  • ELONGATION, strictly "lengthening"; in astronomy, the apparent angular distance of a heavenly body from its centre of motion, as seen from the earth; designating especially the angular distance of the planet Mercury or Venus from the sun, or the apparent angle between a satellite and its primary.

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  • As the rock was highly viscous and the surface over which it moved was often irregular the motion was disturbed and fluctuating; hence the sinuous and contorted appearance frequently assumed by the banding.

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  • According to the molecular theory, diffusion is due to the motion of the molecules of the dissolved substance through the liquid.

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  • This result revolted public opinion; the bishops acquired the habit (rendered easier by the personal expense involved in setting the law in motion) of vetoing, under the power given to them in the act, all prosecutions; and the act became a dead letter.

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  • Utilizing this principle he constructed the radiometer, which he was at first disposed to regard as a machine that directly transformed light into motion, but which was afterwards perceived to depend on thermal action.

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  • Direct motion >>

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  • But his old rivalry with Nordin was resumed at the same time, and when the latter defeated a motion of the bishop's in the Estate of Clergy, at the diet of Norrkoping, Wallqvist from sheer vexation had a stroke of apoplexy and died the same day (30th of April 1800).

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  • From this the distance of the sun can be at once determined by a fundamental equation of planetary motion.

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  • The fourth method is through the parallactic inequality in the moon's motion.

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  • The fifth method consists in observing the displacement in the direction of the sun, or of one of the nearer planets, due to the motion of the earth round the common centre of gravity of the earth and moon.

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  • From the meridian observations of the same planets made for the purpose of controlling the elements of motion of the planets Auwers found it = 8.806".

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  • The indirect method is based upon the observed constant of aberration or the displacement of the stars due to the earth's motion.

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  • The motion of the node of this plane is found with great exactness from observaMass, of the g tions of the transits of Venus.

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  • Its weak point is that the apparent motion of the node depends partly upon the motion of the ecliptic, which cannot be determined with equal precision.

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  • From the observed motion of the node of Venus, as shown by the four transits of 1761, 1769, 1874 and 1882, is found Mass of (earth +moon) _Mass of sun 332600 In gravitational units of mass, based on the metre and second as units of length and time, Log.

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  • Putting a for the mean distance of the earth from the sun, and n for its mean motion in one second, we use the fundamental equation a3 n2 = Mo-1-M', Mo being the sun's mass, and M' the combined masses of the earth and moon, which are, however, too small to affect the result.

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  • For the mean motion of the earth in one second in circular measure, we have n 8149' l o g.

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  • The determination of the solar parallax through the parallactic inequality of the moon's motion also involves two elements - one of observation, the other of purely mathematical theory.

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  • An electrically neutral atom is believed to be constituted in part, or perhaps entirely, of a definite number of electrons in rapid motion within a " sphere of uniform positive electrification " not yet explained.

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  • Thus a universal science of matter and motion was derived, by an unbroken sequence of deduction, from one radical principle; and analytical mechanics assumed the clear and complete form of logical perfection which it now wears.

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  • Instead of following the motion of each individual part of a material system, he showed that, if we determine its configuration by a sufficient number of variables, whose number is that of the degrees of freedom to move (there being as many equations as the system has degrees of freedom), the kinetic and potential energies of the system can be expressed in terms of these, and the differential equations of motion thence deduced by simple differentiation.

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  • His speech in 1835 in support of the motion for inquiry into the Irish Church temporalities with a view to their partial appropriation for national purposes (for disestablishment was not then dreamed of as possible) contains much terse argument, and no doubt contributed to the fall of Peel and the formation of the Melbourne cabinet.

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  • The next year Campbell had a fierce encounter with Lord Stanley in the debate which followed the motion of T.

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  • He protests in favour of Lord Monteagle's motion for inquiry into the sliding scale of corn duties; of Lord Normanby's motion on the queen's speech in 1843, for inquiry into the state of Ireland (then wholly under military occupation); of Lord Radnor's bill to define the constitutional powers of the home secretary, when Sir James Graham opened Mazzini's letters.

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  • Chase and Judge John C. Underwood constituted the United States circuit court sitting for Virginia before which the case was brought in December 1868; the court was divided, the chief justice voting to sustain the motion and Underwood to overrule it.

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  • But at the close of 1906 the Cape ministry formally reopened the question of federation, and at a railway conference held in Pretoria in May 1908 the Natal delegates agreed to a motion affirming the desirability of the early union of the self-governing colonies.

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  • In 1849 he brought forward a proposal in parliament in favour of international arbitration, and in 1851 a motion for mutual reduction of armaments.

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  • He brought forward a motion in parliament to this effect, which led to a long and memorable debate, lasting over four nights, in which he was supported by Sydney Herbert, Sir James Graham, Gladstone, Lord John Russell and Disraeli, and which ended in the defeat of Lord Palmerston by a majority of sixteen.

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  • of March Kossuth's motion for the appointment of an independent, responsible ministry was accepted by the Lower House.

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  • The moderates, alarmed not so much by the motion itself as by its tone, again tried to intervene; but on the 13th of March the Vienna revolution broke out, and the king, yielding to pressure or panic, appointed Count Louis Batthyany premier of the first Hungarian responsible ministry, which included Kossuth, Szechenyi and Deak.

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  • At his instance the diet not only refused to vote supplies for the troops of the ban of Croatia, but only consented to pass a motion for sending reinforcements to the army in Italy on condition that the anti-Magyar races in Hungary should be first disarmed.

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  • On the 1 ith, on his motion, a decree was passed by acclamation for a levy of 200,000 men and the raising of £4,500,000 for the defence of the independence of the country.

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  • Unhappily, however, when Lamberg arrived in Pest, Batthyany had not yet returned; the diet, on Kossuth's motion, called on the army not to obey the new commander-in-chief, on the ground that his commission had not been countersigned by a minister at Pest.

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  • The news of this manifesto, arriving as it did simultaneously with that of Gdrgei's successes, destroyed the last vestiges of a desire of the Hungarian revolutionists to compromise, and on the 14th of April, on the motion of Kossuth, the diet proclaimed the independence of Hungary, declared the house of Habsburg as false and perjured, for ever excluded from the throne, and elected Kossuth president of the Hungarian Republic. This was an execrable blunder in the circumstances, and the results were fatal to the national cause.

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  • After 1872, in addition to its regular organs, it issued Hungarian translations of several popular scientific English works, as, for instance, Darwin's Origin of Species; Huxley's Lessons in Physiology; Lubbock's Prehistoric Times; Proctor's Other Worlds than Ours; Tyndall's Heat as a Mode of Motion, &c. Versions were also made of Cotta's Geologie der Gegenwart and Helmholtz's Populcire Vorlesungen.

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  • If round the origin of waves an ideal closed surface be drawn, the whole action of the waves in the region beyond may be regarded as due to the motion continually propagated across the various elements of this surface.

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  • The wave motion due to any element of the surface is called a secondary wave, and in estimating the total effect regard must be paid to the phases as well as the amplitudes of the components.

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  • The,ideal surface of resolution may be there regarded as a flexible lamina; and we know that, if by forces locally applied every element of the lamina be made to move normally to itself exactly as the air at that place does, the external aerial motion is fully determined.

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  • Then the first of the equations of motion may be put under the form dt ?

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  • According to this notation, the three equations of motion are dt2 = b2v2E + (a2 - b2) d.s dt =b2v2rj+(a2 - b2) dy d2 CIF - b2p2+(a2_b2)dz It is to be observed that denotes the dilatation of volume of the element situated at (x, y, z).

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  • At every point the motion of the lamina will be the same as would have occurred in its absence, the pressure of the waves impinging from behind being just what is required to generate the waves in front.

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  • Now it is evident that the aerial motion in front of the lamina is determined by what happens at the lamina without regard to the cause of the motion there existing.

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  • The conception of the lamina leads immediately to two schemes, according to which a primary wave may be supposed to be broken up. In the first of these the element dS, the effect of which is to be estimated, is supposed to execute its actual motion, while every other element of the plane lamina is maintained at rest.

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  • When the secondary disturbance thus obtained is integrated with respect to dS over the entire plane of the lamina, the result is necessarily the same as would have been obtained had the primary wave been supposed to pass on without resolution, for this is precisely the motion generated when every element of the lamina vibrates with a common motion, equal to that attributed to dS.

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  • The only assumption here involved is the evidently legitimate one that, when two systems of variously distributed motion at the lamina are superposed, the corresponding motions in front are superposed also.

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  • If, instead of supposing the motion at dS to be that of the primary wave, and to be zero elsewhere, we suppose the force operative over the element dS of the lamina to be that corresponding to the primary wave, and to vanish elsewhere, we obtain a secondary wave following quite a different law.

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  • In this case the motion in different directions varies as cos°, vanishing at right angles to the direction of propagation of the primary wave.

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  • The force operative upon the positive half is parallel to OZ, and of amount per unit of area equal to - b 2 D = b 2 kD cos nt; and to this force acting over the whole of the plane the actual motion on the positive side may be conceived to be due.

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  • Thus, to refer again to the acoustical analogue in which plane waves are incident upon a perforated rigid screen, the circumstances of the case are best represented by the first method of resolution, leading to symmetrical secondary waves, in which the normal motion is supposed to be zero over the unperforated parts.

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  • 1 Hostilities were still proceeding, but in the areas under control Lord Milner (who was raised to the peerage in May) speedily set the machinery of government in motion.

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  • iii., with a short appendix `On the Motion of the Sun' " (Wright).

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  • The manakins are peculiar to the Neotropical Region and have many of the habits of the titmouse family (Paridae), living in deep forests, associating in small bands, and keeping continually in motion, but feeding almost wholly on the large soft berries of the different kinds of Melastoma.

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  • The principal symptons of chronic ether-drinking are a weakening of the activity of the special senses, and notably sight and hearing, a lowering of the intelligence and a degree of general paresis (partial paralysis) of motion.

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  • If a point be in motion in any orbit and with any velocity, and if, at each instant, a line be drawn from a fixed point parallel and equal to the velocity of the moving point at that instant, the extremities of these lines will lie on a curve called the hodograph.

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  • Every orbit must clearly have a hodograph, and, conversely, every hodograph a corresponding orbit; and, theoretically speaking, it is possible to deduce the one from the other, having given the other circumstances of the motion.

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  • The motion was lost but the House resolved to bring in a bill for repealing the Corporation Act, and ten years later (March 5) the Grand Committee of Grievances reported to the House its opinion (I) that the rights of the City of London in the election of sheriffs in the year 1682 were invaded and that such invasion was illegal and a grievance, and (2) that the judgment given upon the Quo Warranto against the city was illegal and a grievance.

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  • The line is double track and the rope constantly in motion, the cars being attached at intervals through its length by clips or clutches; the loaded cars move in one direction, the empties in the other.

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  • Entente troops had already before March 18 been set in motion for the Aegean, and some were in Lemnos.

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  • As a matter of fact, the Suvla troops had afforded the Anzac columns no assistance at all beyond occupying the attention of one of the two Turkish divisions which Liman von Sanders set in motion south-westwards from about Gallipoli as soon as he had satisfied himself as to where danger lay, and the doings of this newly landed force had now to be recorded.

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  • On reversing the motion the valve E closes and the liquid is forced through the valve F to the upper part of the cylinder.

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  • On reversing the motion the - I valve E closes and the liquid is IL driven past the valve F.

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  • u3po ajXavuta), the science of the mechanics of water and fluids in general, including hydrostatics or the mathematical theory of fluids in equilibrium, and hydromechanics, the theory of fluids in motion.

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  • Notwithstanding these inventions of the Alexandrian school, its attention does not seem to have been directed to the motion of fluids; and the first attempt to investigate this subject was made by Sextus Julius Frontinus, inspector of the public fountains at Rome in the reigns of Nerva and Trajan.

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  • In 1628 Castelli published a small work, Della misura dell' acque correnti, in which he satisfactorily explained several phenomena in the motion of fluids in rivers and canals; but he committed a great paralogism in supposing the velocity of the water proportional to the depth of the orifice below the surface of the vessel.

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  • The theorem of Torricelli was employed by many succeeding writers, but particularly by Edme Mariotte (1620-1684), whose Traite du mouvement des eaux, published after his death in the year 1686, is founded on a great variety of well-conducted experiments on the motion of fluids, performed at Versailles and Chantilly.

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  • He considered the horizontal strata of this hyperboloid as always in motion, while the remainder of the water was in a state of rest, and imagined that there was a kind of cataract in the middle of the fluid.

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  • Newton was also the first to investigate the difficult subject of the motion of waves (q.v.).

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  • In order to determine the motion of each stratum, he employed the principle of the conservatio virium vivarum, and obtained very elegant solutions.

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  • He applied this principle to the motion of fluids, and gave a specimen of its application at the end of his Dynamics in 1743.

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  • It was more fully developed in his Traite des fluides, published in 1744, in which he gave simple and elegant solutions of problems relating to the equilibrium and motion of fluids.

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  • He considered, at every instant, the actual motion of a stratum as composed of a motion which it had in the preceding instant and of a motion which it had lost; and the laws of equilibrium between the motions lost furnished him with equations representing the motion of the fluid.

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  • It remained a desideratum to express by equations the motion of a particle of the fluid in any assigned direction.

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  • The resolution of the questions concerning the motion of fluids was effected by means of Euler's partial differential coefficients.

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  • This calculus was first applied to the motion of water by d'Alembert, and enabled both him and Euler to represent the theory of fluids in formulae restricted by no particular hypothesis.

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  • Following in the steps of the Abbe Charles Bossut (Nouvelles Experiences sur la resistance des fluides, 1777), he published, in 1786, a revised edition of his Principes d'hydraulique, which contains a satisfactory theory of the motion of fluids, founded solely upon experiments.

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  • Dubuat considered that if water were a perfect fluid, and the channels in which it flowed infinitely smooth, its motion would be continually accelerated, like that of bodies descending in an inclined plane.

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  • But as the motion of rivers is not continually accelerated,and soon arrives at a state of uniformity,it is evident that the viscosity of the water, and the friction of the channel in which it descends, must equal the accelerating force.

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  • Assoc. Report., 1869), and stream line motion was studied by Professor Osborne Reynolds and by Professor H.

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  • In considering the motion of a fluid we shall suppose it non-viscous, so that whatever the state of motion the stress across any section is normal, and the principle of the normality and thence of the equality of fluid pressure can be employed, as in hydrostatics.

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  • The practical problems of fluid motion, which are amenable to mathematical analysis when viscosity is taken into account, are excluded from treatment here, as constituting a separate branch called "hydraulics" (q.v.).

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  • In the Eulerian method the attention is fixed on a particular point of space, and the change is observed there of pressure, density and velocity, which takes place during the motion; but in the Lagrangian method we follow up a particle of fluid and observe how it changes.

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  • The Eulerian Form of the Equations of Motion.

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  • The equations of motion can be established in a similar way by considering the rate of increase of momentum in a fixed direction of the fluid inside the surface, and equating it to the momentum generated by the force acting throughout the space 5, and by the pressure acting over the surface S.

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  • The time rate of increase of momentum of the fluid inside S is )dxdydz; (5) and (5) is the sum of (I), (2), (3), (4), so that /if (dpu+dpu2+dpuv +dpuw_ +d p j d xdyd z = o, (b)` dt dx dy dz dx / leading to the differential equation of motion dpu dpu 2 dpuv dpuv _ X_ (7) dt + dx + dy + dz with two similar equations.

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  • dp dpu dpv dpw -z)' reducing to the first line, the second line vanishing in consequence of the equation of continuity; and so the equation of motion may be written in the more usual form du du du du d dt +udx+vdy +wdz =X -n dx' with the two others dv dv dv dv i dp dt +u dx +v dy +w dz - Y -P d y' dw dw dw Z w dw i d p dt +u dx +v dy +wd - -P dz.

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  • (5) (8) (I) The components of acceleration of a particle of fluid are consequently Du dudu du du dt = dt +u dx +v dy + wdz' Dr dv dv dv dv dt -dt+udx+vdy+wdz' dt v = dtJ+udx+vdy +w dx' leading to the equations of motion above.

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  • But turbulence in the motion will vitiate the principle that a bounding surface will always consist of the same fluid particles, as we see on the surface of turbulent water.

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  • = dx dy dz the equations of motion may be Written du - 2v?

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  • If w vanishes throughout the fluid at any instant, equation (I I) shows that it will always be zero, and the fluid motion is then called irrotational; and a function 4) exists, called the velocity function, such that udx+vdy-{-wdz =-d, (13) and then the velocity in any direction is the space-decrease or downward gradient of cp.

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  • Putting do dipdp _ Hdt - dt -K, the equations of motion (4), (5), (6) § 24 can be written -2u +2wn - d(x',t))o,...,.

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  • and as we prove subsequently (§ 37) that the vortex lines are composed of the same fluid particles throughout the motion, the surface m and satisfies the condition of (6) § 23; so that K is uniform throughout the fluid at any instant, and changes with the time only, and so may be replaced by F(t).

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  • When the motion is steady, that is, when the velocity at any point of space does not change with the time, dK dx-2v{ +2wn = o, ..

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  • d - K dK dK _ dK dK dK ?dx n dyd °, udx dz - ° and K=fdp/o+V+2q 2 =H (3) is constant along a vortex line, and a stream line, the path of a fluid particle, so that the fluid is traversed by a series of H surfaces, each covered by a network of stream lines and vortex lines; and if the motion is irrotational H is a constant throughout the fluid.

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  • Taking the axis of x for an instant in the normal through a point on the surface H = constant, this makes u = o, = o; and in steady motion the equations reduce to dH/dv=2q-2wn = 2gco sin e, (4) where B is the angle between the stream line and vortex line; and this holds for their projection on any plane to which dv is drawn perpendicular.

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  • In plane motion (4) reduces to dH = 2q"= q /av q?

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  • If homogeneous liquid is drawn off from a vessel so large that the motion at the free surface at a distance may be neglected, then Bernoulli's equation may be written H = PIP--z - F4 2 / 2g = P/ p +h, (8) where P denotes the atmospheric pressure and h the height of the free surface, a fundamental equation in hydraulics; a return has been made here to the gravitation unit of hydrostatics, and Oz is taken vertically upward.

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  • Uniplanar Motion.

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  • - In the uniplanar motion of a homogeneous liquid the equation of continuity reduces to du dv dx' dy-O' u= -d,y/dy, v = d i t/dx, (2) surface containing so that we can put _ (6) (9) we have (I) (2) (5) (I) where 4 is a function of x, y, called the streamor current-function; interpreted physically, 4-4c, the difference of the value of 4, at a fixed point A and a variable point P is the flow, in ft.

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  • In the equations of uniplanar motion = dx - du = dx + dy = -v 2 ?, suppose, so that in steady motion dx I +v24 ' x = ?'

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  • The curves 0 = constant and 4, = constant form an orthogonal system; and the interchange of 0 and 4, will give a new state of uniplanar motion, in which the velocity at every point is turned through a right angle without alteration of magnitude.

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  • (7) Interchanging these values =m log r, 4, = mO, 4,+4,i =m log rei e (8) gives a state of vortex motion, circulating round Oz, called a straight or columnar vortex.

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  • When the liquid is bounded by a cylindrical surface, the motion of a vortex inside may be determined as due to a series of vorteximages, so arranged as to make the flow zero across the boundary.

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  • (22) Conjugate functions can be employed also for the motion of liquid in a thin sheet between two concentric spherical surfaces; the components of velocity along the meridian and parallel in colatitude 0 and longitude A can be written d¢_ i _ d4, I dip _ dy (13) d8 sin - 0 dX' sin 0 dX de' and then = F (tan O.

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  • Uniplanar Motion of a Liquid due to the Passage of a Cylinder through it.-A stream-function 4, must be determined to satisfy the conditions v24 =o, throughout the liquid; (I) I =constant, over any fixed boundary; (2) d,t/ds = normal velocity reversed over a solid boundary, (3) so that, if the solid is moving with velocity U in the direction Ox, d4y1ds=-Udy/ds, or 0 +Uy =constant over the moving cylinder; and 4,+Uy=41' is the stream function of the relative motion of the liquid past the cylinder, and similarly 4,-Vx for the component velocity V along Oy; and generally 1,1'= +Uy -Vx (4) is the relative stream-function, constant over a solid boundary moving with components U and V of velocity.

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  • If the liquid is stirred up by the rotation R of a cylindrical body, d4lds = normal velocity reversed dy = - Rx- Ry ds (5) ds 4' + 2 R (x2 + y2) = Y, (6) a constant over the boundary; and 4,' is the current-function of the relative motion past the cylinder, but now V 2 4,'+2R =o, (7) throughout the liquid.

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  • Example z.-Liquid motion past a circular cylinder.

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  • Consider the motion given by w=U(z+a2/z), (I) 4,=U(r+- r) cos 0= U + a1x, so that (2) = U (r-)sin 0= U(i -¢) y.

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  • Over a concentric cylinder, external or internal, of radius r=b, 4,'=4,+ Uly =[U I - + Ui]y, (4) and 4" is zero if U 1 /U = (a 2 - b2)/b 2; (5) so that the cylinder may swim for an instant in the liquid without distortion, with this velocity Ui; and w in (I) will give the liquid motion in the interspace between the fixed cylinder r =a and the concentric cylinder r=b, moving with velocity U1.

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  • If the liquid is reduced to rest at infinity by the superposition of an opposite stream given by w = - Uz, we are left with w = Ua2/z, (6) =U(a 2 /r) cos 0= Ua2x/(x2+y2), (7) 4, = -U(a 2 /r) sin 0= -Ua2y/( x2+y2), (8) giving the motion due to the passage of the cylinder r=a with velocity U through the origin 0 in the direction Ox.

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  • If the direction of motion makes an angle 0' with Ox, tan B' = d0 !dam _ ?xy 2 = tan 20, 0 =-10', (9) dy/ y and the velocity is Ua2/r2.

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  • When the cylinder r =a is moved with velocity U and r =b with velocity U 1 along Ox, = U b e - a,1 r +0 cos 0 - U ib2 - 2 a, (r +Q 2 ') cos 0, = - U be a2 a2 (b 2 - r) sin 0 - Uib2 b1)a, (r - ¢2 sin 0; b and similarly, with velocity components V and V 1 along Oy a 2 b2 ?= Vb,_a,(r+r) sin g -Vi b, b2 a, (r+ 2) sin 0, (17) = V b, a2 a, (b2 r) cos 0+Vi b, b, a, (r- ¢ 2) cos h; (18) and then for the resultant motion z 2zz w= (U 2 + V2)b2a a2U+Vi +b a b a2 U z Vi -(U12+V12) b2 z a2b2 Ui +VIi b 2 - a 2 U1 +Vii b 2 - a 2 z The resultant impulse of the liquid on the cylinder is given by the component, over r=a (§ 36), X =f p4 cos 0.ad0 =7rpa 2 (U b z 2 + a 2 Uib.2bz a2); (20) and over r =b Xi= fp?

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  • The expression for w in (i) § 29 may be increased by the addition of the term im log z =-m0 + im log r, (1) representing vortex motion circulating round the annulus of liquid.

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  • Consider the streaming motion given by w =m =a+si, (5) 4=m ch (n -a)cos(-0), p=m sh(n-a)sin(-13).

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  • Negative values of n must be interpreted by a streaming motion on a parallel plane at a level slightly different, as on a double Riemann sheet, the stream passing from one sheet to the other across a cut SS' joining the foci S, S'.

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  • Next consider the motion given by = m ch 2(77a)sin 2E, tii= -m sh 2(na)cos 2E; (I) in which > ' =o over the ellipse a, and =1'+IR(x2+y2) =[ -m sh 2(7 7 -a)+4Rc 2 ]cos 4Rc2 ch 2n, (2) which is constant over the ellipse n if 4Rc 2.

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  • In a similar way the more general state of motion may be analysed, given by w =r ch2('-y), y =a+, i, (26) as giving a homogeneous strain velocity to the confocal system; to which may be added a circulation, represented by an additional term in w.

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  • x+yi =c1,1 [sin(+ 7 ni)] (17) i ' =Qc sh((n-a)sin((E-,6) (18) 'will give motion streaming past the fixed cylinder n = a, and dividing along t =43; and then x 2 -3/ 2 = c 2 sin ch n, 2xy = c 2 cos sh n.

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  • Motion symmetrical about an Axis.-When the motion of a liquid is the same for any plane passing through Ox, and lies in the plane, a function ' can be found analogous to that employed in plane motion, such that the flux across the surface generated by the revolution of any curve AP from A to P is the same, and represented by 2s-4 -11'o); and, as before, if d is the increase in due to a displacement of P to P', then k the component of velocity normal to the surface swept out by PP' is such that 274=2.7ryk.PP'; and taking PP' parallel to Oy and Ox, u= -d/ydy, v=dl,t'/ydx, (I) and 1P is called after the inventor, " Stokes's stream or current function," as it is constant along a stream line (Trans.

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  • In this symmetrical motion =o, n=O' 2s,=27c dx) d (?'

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  • 1 = yv24, (2) y 2 y y y suppose; and in steady motion, + y 2 dx v-t ' = o, dH +y 2dy0 2P = o, so that 2 "/ y = - y2, 7 2 1,G = dH/d is a function of 1,G, say f'(> '), and constant along a stream line; dH/dv = 2qi', H -f (1/.) = constant, throughout the liquid.

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  • When the motion is irrotational, dq_ _I d deId> G =o, a=-dxy dy, v dy ydx' v 21, ' = o, or dx + dy -y chi, '1/4724, 4 1 1+1 Rx2 = $Rc 2 (ch 2 a1 +I), +h+I Ry2 = 8Rc 2 (ch 2a 1 - I), (6) (7) b2)2/(a2 + b2).

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  • 0, 1, = -ZUa 3 sin e B/r; (13) and then =Ux(I+1a3/r2), 4=ZUa 3 cos 0/r2, -d r = Ua3 cos B, -d9=ZUa3 sin 0, so that, if the direction of motion makes an angle >G with Ox, tan (4y-0) =Z tan 0, tan =3 tan 0/(2-tan 2 e).

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  • With n =2, a state of motion is given by ty = - ZUy 2 a 4 µ/r 4, ' _ 0' = Ux+.4), 4'--3U(a 4 /r 3) P 2, P2 = Aµ 2 2, (23) representing a stream past the surface r4=a4µ.

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  • 35 A circular vortex, such as a smoke ring, will set up motion symmetrical about an axis, and provide an illustration; a half vortex ring can be generated in water by drawing a semicircular blade a short distance forward, the tip of a spoon for instance.

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  • The first vortex dilates and moves slower, while the second contracts and shoots through the first; after which the motion is reversed periodically, as if in a game of leap-frog.

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  • Projected perpendicularly against a plane boundary, the motion is determined by an equal opposite vortex ring, the optical image; the vortex ring spreads out and moves more slowly as it approaches the wall; at the same time the molecular rotation, inversely as the cross-section of the vortex, is seen to increase.

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  • Irrotational Motion in General.-Liquid originally at rest in a singly-connected space cannot be set in motion by a field of force due to a single-valued potential function; any motion set up in the liquid must be due to a movement of the boundary, and the motion will be irrotational; for any small spherical element of the liquid may be considered a smooth solid sphere for a moment, and the normal pressure of the surrounding liquid cannot impart to it any rotation.

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  • (2) If the actual motion at any instant is supposed to be generated instantaneously from rest by the application of pressure impulse over the surface, or suddenly reduced to rest again, then, since no natural forces can act impulsively throughout the liquid, the pressure impulse W satisfies the equations I do = I d i dos - ax -u, - - y = -v, Pdz = -t, a =p4)-}-a constant, (4) and the constant may be ignored; and Green's transformation of the energy T amounts to the theorem that the work done by an impulse is the product of the impulse and average velocity, or half the velocity from rest.

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  • In a multiply connected space, like a ring, with a multiply valued velocity function ¢, the liquid can circulate in the circuits independently of any motion of the surface; thus, for example, 4) =mB=m tan - l y/x (5) will give motion to the liquid, circulating in any ring-shaped figure of revolution round Oz.

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  • In plane motion the kinetic energy per unit length parallel to Oz T 2p J J [(d4)) 2+ (d dy (P)1dxdy=lpfl[ a) 2+ (=zp 4d ds=zp f, ydvds.

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  • Again, since d4)/dv =d /ds, d4)/ds= - d4y/dv, (13) T = 1 p f(1 9 d = - 2 p f4' d (14) With the Stokes' function, y for motion symmetrical about an axis.

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  • So far these theorems on vortex motion are kinematical; but introducing the equations of motion of § 22, Du + dQ =o, Dv+dQ =o, Dw + dQ dt dx dt dy dt dz and taking dx, dy, dz in the direction of u, v, w, and dx: dy: dz=u: v: w, (udx + vdy + wdz) = Du dx +u 1+..

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  • = -dQ+1dg2, and integrating round a closed curve (udx+vdy+wdz) =0, and the circulation in any circuit composed of the same fluid particles is constant; and if the motion is differential irrotational and due to a velocity function, the circulation is zero round all reconcilable paths.

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  • The circulation being always zero round a small plane curve passing through the axis of spin in vortical motion, it follows conversely that a vortex filament is composed always of the same fluid particles; and since the circulation round a cross-section of a vortex filament is constant, not changing with the time, it follows from the previous kinematical theorem that aw is constant for all time, and the same for every cross-section of the vortex filament.

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  • Denoting the cross-section a of a filament by dS and its mass by dm, the quantity wdS/dm is called the vorticity; this is the same at all points of a filament, and it does not change during the motion; and the vorticity is given by w cos edS/dm, if dS is the oblique section of which the normal makes an angle e with the filament, while the aggregate vorticity of a mass M inside a surface S is M - l fw cos edS.

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  • .) = (X-jfidp) +m (Y-dy) +n (Zp 2), for all values of 1, m, n, leading to the equations of motion with moving axes.

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  • When the motion is such that d?

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  • I, ' 2 dx (y dx) +dy U dy) so that § 34 (4) is satisfied, with f' (W') =1.0 a2, f (Y") = 2 U'a2; and (ro) reduces to `)(() P +v-3 U j _ S = constant; (16) this gives the state of motion in M.

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  • As an application of moving axes, consider the motion of liquid filling the ellipsoidal case 2 y 2 z2 Ti + b1 +- 2 = I; (1) and first suppose the liquid be frozen, and the ellipsoid l3 (4) (I) (6) (9) (I o) (II) (12) (14) = 2 U ¢ 2, (15) rotating about the centre with components of angular velocity, 7 7, f'; then u= - y i +z'i, v = w = -x7 7 +y (2) Now suppose the liquid to be melted, and additional components of angular velocity S21, 522, S23 communicated to the ellipsoidal case; the additional velocity communicated to the liquid will be due to a velocity-function 2224_ - S2 b c 6 a 5 x b2xy, as may be verified by considering one term at a time.

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  • 3 /, with similar equations for 13 and If we can make (41 rpA + a) x2' = (4 7 P B +a) b2 = (4 7 P C +7)0, (16) the surfaces of equal pressure are similar to the external case, which can then be removed without affecting the motion, provided remain constant.

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  • In the general motion again of the liquid filling a case, when a = b, 52 3 may be replaced by zero, and the equations, hydrodynamical and dynamical, reduce to d =- 2+ 2 J, = 2 x22111, d = 2 2`2 (+/'15-Om) (1 yy y n`t dt a +c dt a +c dt a +c) dc2, a2-1-c2 d122 a2 c2 dt ="2) +a2= G2y 71' dt = 121 1 - a 2 -c 2SJ, (19) of which three integrals are e +777 r z y 2= L -?2J2, (20) (a2 + c2) 2 2 121+14 =M+ 2c2(a2-c2)1 ' (21) 121+522hN = + x24 2,2 and then (dt / 2 = (a2 + c 2) 2(° v 2 - 12171) 2 4C4 2 2 - (+ c2)2?(E+77) (?

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  • In a state of steady motion d4- 121 _S22 Tit °' - fl 4=1G = nt, suppose, S21 -F9,277 = S2co, d4 a2+c2 WI- 1 a2-c2S21' _ 2a 2 SZ dt a2+c2cos' a 2 + c 2 a, 2 a 2 S2 I- a2_c22--a2+C2,0, 1a2 c2)2 (a 2 -c 2) (9a2-c2) ?

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  • 2 2a2 c2 4 (a2+L2) ' and a state of steady motion is impossible when 3a c >a.

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  • Uniplanar motion alone is so far amenable to analysis; the velocity function 4 and stream function 1G are given as conjugate functions of the coordinates x, y by w=f(z), where z= x +yi, w=4-Plg, and then dw dod,y az = dx + i ax - -u+vi; so that, with u = q cos B, v = q sin B, the function - Q dw u_vi=g22(u-}-vi) = Q(cos 8+i sin 8), gives f' as a vector representing the reciprocal of the velocity in direction and magnitude, in terms of some standard velocity Q.

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  • To determine the motion of a jet which issues from a vessel with plane walls, the vector I must be constructed so as to have a constant (to) (II) the liquid (15) 2, integrals;, (29) (30) (I) direction 0 along a plane boundary, and to give a constant skin velocity over the surface of a jet, where the pressure is constant.

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  • The theory of conformal representation shows that the motion is given by (b-a'.u -a) +?

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  • The motion of a jet impinging on an infinite barrier is obtained by putting j = a, j' = a'; duplicated on the other side of the barrier, the motion reversed will represent the direct collision of two jets of unequal breadth and equal velocity.

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  • The Motion of a Solid through a Liquid.

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  • - An important problem in the motion of a liquid is the determination of the state of velocity set up by the passage of a solid through it; and thence of the pressure and reaction of the liquid on the surface of the solid, by which its motion is influenced when it is free.

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  • Beginning with a single body in liquid extending to infinity, and denoting by U, V, W, P, Q, R the components of linear and angular velocity with respect to axes fixed in the body, the velocity function takes the form = Ucb1+V42+W43+ P xi+Qx2+Rx3, (I) where the 0's and x's are functions of x, y, z depending on the shape of the body; interpreted dynamically, C -p0 represents the impulsive pressure required to stop the motion, or C +p4) to start it again from rest.

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  • For a cavity filled with liquid in the interior of the body, since the liquid inside moves bodily for a motion of translation only, 41 = - x, 42 = -, 43 = - z; (2) but a rotation will stir up the liquid in the cavity, so that the'x's depend on the shape of the surface.

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  • A system of confocal ellipsoids is taken y2 (3) a 2 +X b 2 +X c2 + A= I, and a velocity function of the form = x1 P, (4) where 4' is a function of X only, so that 4) is constant over an ellipsoid; and we seek to determine the motion set up, and the form of >G which will satisfy the equation of continuity.

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  • l ' so that over the surface of an ellipsoid where X and ¢ are constant, the normal velocity is the same as that of the ellipsoid itself, moving as a solid with velocity parallel to Ox U = -q, - 2 (a2+X) dtP, and so the boundary condition is satisfied; moreover, any ellipsoidal surface X may be supposed moving as if rigid with the velocity in (I I), without disturbing the liquid motion for the moment.

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  • The quiescent ellipsoidal surface, over which the motion is entirely tangential, is the one for which (a2+X)d?

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  • The impulse required to set up the motion in liquid of density p i the resultant of an impulsive pressure p4) over the surface S of th ellipsoid, and is therefore ffp4ldS = p4GoffxldS =p 40 (volume of the ellipsoid) =4)oW', (23) where W' denotes the weight of liquid displaced.

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  • ZUy2BB0 Bll; reducing, when the liquid extends to infinity and B 3 =0, to = xA o' _ - zUy 2B o so that in the relative motion past the body, as when fixed in the current U parallel to xO, A 4)'=ZUx(I+Bo), 4)'= zUy2(I-B o) (6) Changing the origin from the centre to the focus of a prolate spheroid, then putting b 2 =pa, A = A'a, and proceeding to the limit where a = oo, we find for a paraboloid of revolution P B - p (7) B = 2p +A/' Bo p+A y2 i =p+A'- 2x, (8) p+?

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  • The motion of these cylinders across the line of centres is the equivalent of a line doublet along each axis.

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  • But supposing them determined for the motion of a body through a liquid, the kinetic energy T of the system, liquid and body, is expressible as a quadratic function of the components U, V, W, P, Q, R.

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  • These theorems, which hold for the motion of a single rigid body, are true generally for a flexible system, such as considered here for a liquid, with one or more rigid bodies swimming in it; and they express the statement that the work done by an impulse is the product of the impulse and the arithmetic mean of the initial and final velocity; so that the kinetic energy is the work done by the impulse in starting the motion from rest.

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  • When no external force acts, the case which we shall consider, there are three integrals of the equations of motion (i.) T =constant, x 2 +x 2 +x 2 =F 2, a constant, (iii.) x1y1 +x2y2+x3y3 =n = GF, a constant; and the dynamical equations in (3) express the fact that x, x, xs.

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  • In the motion which can be solved by the elliptic function, the most general expression of the kinetic energy was shown by A.

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  • A number of cases are worked out in the American Journal of athematics (1907), in which the motion is made algebraical by the se of the pseudo-elliptic integral.

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  • To give a simple instance, hanging to the stereographic projection by putting tan 20=x, ill give a possible state of motion of the axis of the body; and the otion of the centre may then be inferred from (22).

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  • The theory preceding is of practical application in the vestigation of the stability of the axial motion of a submarine oat, of the elongated gas bag of an airship, or of a spinning rifled rojectile.

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  • In the steady motion under no force of such a body in medium, the centre of gravity describes a helix, while the axis escribes a cone round the direction of motion of the centre of ravity, and the couple causing precession is due to the dislacement of the medium.

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  • But the presence of the medium makes the effective inertia depend on the direction of motion with respect to the external shape of the body, and on W' the weight of fluid medium displaced.

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  • Consider, for example, a submarine boat under water; the inertia is different for axial and broadside motion, and may be represented by (1) c 1 =W+W'a, c2=W+W'/3' where a, R are numerical factors depending on the external shape; and if the C.G is moving with velocity V at an angle 4) with the axis, so that the axial and broadside component of velocity is u = V cos 0, v =V sin 4), the total momentum F of the medium, represented by the vector OF at an angle 0 with the axis, will have components, expressed in sec. Ib, F cos 0 =c 1 - = (W +W'a) V cos 43, F sin 0 = c 2.11 = (W +W'/3) V sin 4) .

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  • A rotation about the axis of a figure of revolution does not set the medium in motion, so that C 1 is.

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  • the moment of inertia of the body about the axis, denoted by But if is the moment of inertia of the body about a mean diameter, and w the angular velocity about it generated by an impluse couple M, and M' is the couple required to set the surrounding medium in motion, supposed of effective radius of gyration k', If the shot is spinning about its axis with angular velocity p, and is precessing steadily at a rate about a line parallel to the resultant momentum F at an angle 0, the velocity of the vector of angular momentum, as in the case of a top, is C i pµ sin 0- C2µ 2 sin 0 cos 0; (4) and equating this to the impressed couple (multiplied by g), that is, to gN = (c 1 -c 2)c2u 2 tan 0, (5) and dividing out sin 0, which equated to zero would imply perfect centring, we obtain C21 2 cos 0- (c 2 -c 1)c2u 2 sec 0 =o.

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  • The Motion of a Perforated Solid Liquid.

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  • the precedin investigation, the liquid stops dead when the body is brought to rest and when the body is in motion the surrounding liquid moves in uniform manner with respect to axes fixed in the body, and the force experienced by the body from the pressure of the liquid on it surface is the opposite of that required to change the motion of the liquid; this has been expressed by the dynamical equations give above.

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  • Bryan, in which the analytical equations of motion are deduced of a perforated solid in liquid, from considerations purely hydrodynamical.

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  • The effect of an external circulation of vortex motion on the motion of a cylinder has been investigated in § 29; a similar procedure will show the influence of circulation through a hole in a solid, taking as the simplest illustration a ring-shaped figure, with uniplanar motion, and denoting by the resultant axial linear momentum of the circulation.

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  • ZI /t = - (a - s) M'Q 2 sine cos ° - EQ sin() =[ - (a - (3)M'U+E]V (8) Now suppose the cylinder is free; the additional forces acting on the body are the components of kinetic reaction of the liquid - aM' (Ç_vR), - (3M' (-- E -FUR), - EC' dR, (9) so that its equations of motion are M (Ç - vR) _ - aM' (_vR) - (a - $) M'VR, (io) M (Ç+uR) = - OM' (dV+U R) - (a - ()M'UR - R, '(II) C dR = dR + (a - Q)M'UV+0V; (12) and putting as before M+aM'=ci, M+13M' = c2, C+EC'=C3, ci dU - c2VR=o, dV +(c1U+E)R=o, c 3 dR - (c 1 U+ - c 2 U)V =o; showing the modification of the equations of plane motion, due to the component E of the circulation.

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  • 192, resembling the trochoidal curves, which can be looped, investigated in § 29 for the motion of a cylinder under gravity, when surrounded by a vortex.

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  • The branch of hydrodynamics which discusses wave motion in a liquid or gas is given now in the articles Sound and Wave; while the influence of viscosity is considered under Hydraulics.

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  • Both at Euyuk and Yasili Kaya reliefs in one and the same series are widely separated in artistic conception and execution, some showing the utmost naiveté, others expressing both outline and motion with fair success.

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  • Like the rest of the Megarian school he revelled in verbal quibbles, proving that motion and existence are impossible.

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  • White Ogors, possibly the Barsileens of the Volga delta) were swept along in a flood of mixed Tatar peoples which the conquests of the Avars had set in motion.

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  • John Kepler inferred that the planets move in their orbits under some influence or force exerted by the sun; but the laws of motion were not then sufficiently developed, nor were Kepler's ideas of force sufficiently clear, to admit of a precise statement of the nature of the force.

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  • The mutual action of electrified bodies, for example, is affected by their relative or absolute motion.

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  • If not, the action would not be exactly in the line adjoining the two bodies at the instant, but would be affected by the motion of the line joining them during the time required by the force to pass from one body to the other.

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  • On the other hand the enigmatical motion of the perihelion of Mercury has not yet found any plausible explanation except on the hypothesis that the gravitation of the sun diminishes at a rate slightly greater than that of the inverse square - the most simple modification being to suppose that instead of the exponent of the distance being exactly - 2, it is - 2.000 000 161 2.

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  • From an investigation of all the observations upon Mercury and the other three interior planets, Simon Newcomb found it almost out of the question that any such mass of matter could exist without changing either the figure of the sun itself or the motion of the planes of the orbits of either Mercury or Venus.

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  • But the combination of observations and theory on which this is based is not sufficient fully to establish so slight a motion.

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  • In the case of the motion of the moon around the earth, assuming the gravitation of the latter to be subject to the modification in question, the annual motion of the moon's perigee should be greater by I 5" than the theoretical motion.

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  • Brown is the first investigator to determine the theoretical motions with this degree of precision; and he finds that there is no such divergence between the actual and the computed motion.

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  • The Perseids are visible from about the fil th of July to the 10th of August, the radiant having a daily motion of about 1° R.A.

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  • It is hardly less certain that the great achievement which he did actually perform was originally set in motion by Saint-Simon's conversation, though it was afterwards directly filiated with the fertile speculations of A.

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  • the word is found with its present meaning, the spring being considered as particularly the season of the year), a period of time, in particular, that of the four periods into which the year is divided by the changing of the temperature, rainfall, and growth and decay of vegetation due to the annual motion of the sun in declination.

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  • Divided strictly according to this motion the year falls into four nearly equal seasons, "spring" (i.e.

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  • On the division on Mr Roebuck's motion the government was beaten by the unexpected majority of 157.

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  • On the other band, the draped figure received admirable treatment from his brush, and the naturalistic school of the 17th, 18th and i9th centuries reached a high level of skill in depicting men, women and children in motion.

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  • This is illustrated by the difficulties inherent in the conception of Cause, Space, Time, Matter, Motion, the Infinite, and the Absolute, and by the" relativity of knowledge,"which precludes knowledge of the Unknowable, since" all thinking is relationing."Yet the Unknowable may exist, and we may even have an" indefinite knowledge "of it, positive, though vague and extralogical.

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  • Spencer recognizes successively likenesses and unlikenesses among phenomena (the effects of the Unknowable), which are segregated into manifestations, vivid (object, nonego) or faint (subject, ego), and then into space and time, matter and motion and force, of which the last is symbolized for us by the experience of resistance, and is that out of which our ideas of matter and motion are built.

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  • integration of matter with concomitant dissipation of motion) and.

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  • And he admits (§ 63) that if we were compelled to choose between translating mental phenomena into physical and its converse, the latter would be preferable, seeing that the ideas of matter and motion, merely symbolic of unknowable realities, are complex states of consciousness built out of units of feeling.

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  • It is clear that Swedenborg showed (150 years before any other scientist) that the motion of the brain was synchronous with the respiration and not with the action of the heart and the circulation of the blood, a discovery the full bearings of which are still far from being realized.

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  • After carrying his motion for the abolition of the slave trade on the 10th of June, he was forced to give up attendance in parliament, and he died in the house of the duke of Devonshire, at Chiswick, on the 13th of September 1806.

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  • In 336, when Ctesiphon proposed that his friend Demosthenes should be rewarded with a golden crown for his distinguished services to the state, he was accused by Aeschines of having violated the law in bringing forward the motion.

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  • with rapidity, they do not keep in motion for any length of time.

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  • It is often exserted with a rapid motion, sometimes with the object of feeling some object, sometimes under the influence of anger or fear.

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  • Electrified bodies exert mechanical forces on each other, creating or tending to create motion, and also induce electric charges on neighbouring surfaces.

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  • It is tacitly assumed that the motion is relatively so slow that the pressure and temperature of the substance are practically uniform throughout its mass at any stage of the process.

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  • If mechanical work or kinetic energy is directly converted into heat by friction, reversal of the motion does not restore the energy so converted.

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  • In this case the work of expansion, pdv, is expended in the first instance in producing kinetic energy of motion of parts of the gas.

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  • Others see in the glass coloured figures of men, women and animals in motion; while in rarer cases the ball disappears from view, and the scryer finds himself apparently looking at an actual scene.

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  • The larger stones having been removed by hand, gyratory motion is given to the pan by a combination of shaking and twisting movements so as to keep its contents suspended in the stream of water, which carries away the bulk of the lighter material, leaving the heavy minerals, together with any gold which may have been present.

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  • In the conflict between the Petitioners and the Abhorrers he supported the former, and on the 27th of October 1680 brought forward a motion asserting the right of petitioning the king to summon parliament, and proposed the impeachment of Chief Justice North as the author of the proclamation against tumultuous petitioning.

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  • The ridge was captured with little resistance, but the sound of the firing at once set all the neighbouring troops in motion, and fortunately so, for the French had immediately retaliated on von der Goltz's audacious attack.

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  • Corps, set his two divisions in motion towards La Folie and the Bois de la Cusse, and advanced to reconnoitre the French position.

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  • He was several times a successful competitor for the prizes given by the Academy of Sciences of Paris; the subjects of his essays being: - the laws of motion (Discours sur les lois de la communication du mouvement, 1727), the elliptical orbits of the planets, and the inclinations of the planetary orbits (Essai d'une nouvelle physique celeste, 1735).

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  • If the light exerted direct impulsion on the vanes, their motion would gradually drag the case round after them, by reason of the friction of the residual air in the bulb and of the pivot.

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  • On the other hand, if the effects arose from balanced stresses set up inside the globe by the radiation, the effects on the vanes and on the case would be of the nature of action and reaction, so that the establishment of motion of the vanes in one direction would involve impulsion of the case in the opposite direction; but when the motion became steady there would no longer be any torque either on the vanes or on the case, and the latter would therefore come back to its previous position of equilibrium; finally, when the light was turned off, the decay of the motion of the vanes would involve impulsion of the case in the direction of their motion until the moment of the restoring torque arising from the suspension of the case had absorbed the angular momentum in the system.

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  • As far as the order to which he carried the approximations - which, however, were based on a simplifying hypothesis that the molecules influenced each other through mutual repulsions inversely as the fifth power of their distance apart--the result was that the equations of motion of the gas, considered as subject to viscous and thermal stresses, could be satisfied by a state of equilibrium under a modified internal pressure equal in all directions.

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  • A remarkable feature of the solar system, which distinguishes it from all other known systems in the universe, is the symmetry of arrangement and motion of its greater bodies.

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  • He laboriously perfected the military machine, which when once set in motion went on to victory.

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  • But the method is not available if the separation is to be measured by screws; it is found, in that case, that the direction of the final motion of turning of the screw must always be such as to produce motion of the segment against gravity, otherwise the " loss of time " is apt to be variable.

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  • Thus the simple connexion of the two screws by cogwheels to give them automatic opposite motion is not an available method unless the separation of the segments is independently measured by scales.

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  • They provided a splendid, rigidly mounted, equatorial stand, fitted with every luxury in the way of slow motion, and scales for measuring the displacement of the segments were read by powerful micrometers from the eye-end.

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  • But it is still more curious that it was not afterwards carried out, for the communication of automatic symmetrical motion to both segments only involves a simple alteration previously described.

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  • 2 Steinheil applied such motion to a double-image micrometer made for Struve.

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  • This instrument suggested to Struve the abovementioned idea of employing a similar motion for the heliometer.

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  • means of measuring the focal point were provided; symmetrical motion was given to the slides; scales on each slide were provided instead of screws for measuring the separation of the segments, and both scales were read by the same micrometer microscope; a metallic thermometer was added to determine the temperature of the scales.

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  • k clamps the telescope in declination, n clamps it in right ascension, and the handles m and I provide slow motion in declination and right ascension respectively.

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  • The screw, turned by the wheels at g', acts in a toothed arc, whence, as shown in the figure, equal and opposite motion is communicated to the slides by the jointed rods v, v.

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  • Their slow motion in position angle, however, was not all that could be desired.

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  • Thus the slow motion would take place I the observer.

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  • The tube V, on the contrary, is attached to the cradle, and merely forms a support for the finder Q, the handles at f and p, and the moving ring P. The latter gives quick motion in position angle; the handles at p clamp and give slow motion in position angle, those at f clamp and give slow motion in right ascension and declination.

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  • (2) That an additional motion intermediate between the quick and slow motion in position angle was necessary, because, whilst the slow motion provided by Repsolds was admirably adapted for adjusting the pointings in position angle, it was too slow for causing the images to "cross through " each other in the process of measuring distances.

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  • When the heliometer-part of Lord Lindsay's heliometer was acquired by Gill in 1879, he changed the manner of imparting the motion in question.

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  • The reverse motion of P automatically moves the paper ribbon forward, ready to - 20 receive the next impression.

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  • To remedy drawback (2) Repsolds provided for the Yale heliometer an additional handle for motion in position angle, intermediate in velocity between the original quick and slow motions.

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  • heliometer, completed in 1887 for the Royal Observatory at the Cape of Good Hope, Repsolds, on Gill's suggestion, introduced the following improvements: (a) Four different speeds of motion in position angle were provided.

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  • This ring runs between friction wheels and is provided with teeth on its inner periphery, and these teeth transmit motion to a pinion on a spindle having at its other end another pinion which, through an intermediate wheel, rotates the heliometer tube.

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  • With similar bevel-gear and rods the tangent screw is connected to the hand-wheel, 79, by which the observer communicates the fourth or slowest motion in position angle.

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  • Finally the hand-wheel 80 is connected by gearing to the rod carrying the hand-wheel 79, and it can thus be used to give the latter a more rapid motion than if used direct; this constitutes the third speed of movement.

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  • 18 clamps and 19 gives slow motion in declination; 20 clamps and 21 gives slow motion in right ascension.

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  • In a direction perpendicular to that axis it must be so placed that when it is moved by rotation of the axis bb the separation of the images shall be parallel to that motion.

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  • We must remember that the ocean is a continuous sheet of water of a certain depth, and the conditions of continuity which hold good for all fluids require that there should be no vacant space within it; hence if a single water particle is set in motion, the whole ocean must respond, as Varenius pointed out in 1650.

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  • When the wind acts on the surface of the sea it drives before it the particles of the surface layer of water, and, as these cannot be parted from those immediately beneath, the internal friction of the fluid causes the propelling impulse to act through a considerable depth, and if the wind continued long enough it would ultimately set the whole mass of the ocean in motion 'right down to the bottom.

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  • Ekman shows further that in a pure drift current the mean direction of the whole mass of the current is perpendicular to the direction of the wind which sets it in motion.

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  • Such currents, due to the banking up of water, have a large share in setting the depths of the sea in motion, and so securing the vertical circulation and ventilation of the ocean.

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  • If there were strong currents at the bottom of the ocean the uniform accumulation of the deposit of minute shells of globigerina and radiolarian ooze would be impossible, the rises and ridges would necessarily be swept clear of them, and the fact that this is not the case shows that from whatever cause the waters of the depths are set in motion, that motion must be of the most deliberate and gentlest kind.

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  • He is living, active intelligence, the principle of motion and creation, realizing himself in the infinitely various forms of activity that constitute individual things.

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  • One of these projects, on which an elaborate report had actually to be submitted to the Emperor, was a device for which it was claimed that it had solved the problem of perpetual motion.

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  • per second; but, unlike the older machines, in which the cutting is done in a fixed plane, the chain with its motor is made movable, and is fed forward by a rack-and-pinion motion as the cutting advances, so that the cut is limited in breadth (31 to 4 ft.), while its depth may be varied up to the maximum travel (8 ft.) of the cutting frame.

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  • The forward motion is given by a chain winding upon a crab placed in front, by which it is hauled slowly forward.

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  • Motion is communicated to the rope by frictional contact with the drum,.

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  • Motion is obtained from a continuous-current generator driven by an alternating motor with a very heavy fly-wheel, a combination known as the Ilgner transformer, which runs continuously with a constant draught on the generating station, the extremely variable demand of the winding engine during the acceleration period being met by the energy stored in the fly-wheel, which runs at a very high speed.

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  • In 1793 he supported Grey's motion for a return to the old constitutional system of representation, and so earned the title to be regarded as one of the earliest promoters of the cause of parliamentary reform; and he was one of the founders of the "Society of the Friends of the People."

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  • The most ancient philosophers whose speculations are known to us seem to have discussed the ideas of number and of continuous magnitude, of space and time, of matter and motion, with a native power of thought which has probably never been surpassed.

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  • This was the state of opinion when the celebrated arguments against the possibility of motion, of which that of Achilles and the tortoise is a specimen, were propounded by Zeno, and such, apparently, continued to be the state of opinion till Aristotle pointed out that time is divisible without limit, in precisely the same sense that space is.

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  • If it were not so, Lucretius tells us, there could be no motion, for the atom which gives way first must have some empty place to move into.

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  • that there is no vacuum - that every part of space is full of matter, that there is a universal plenum, and that all motion is like that of a fish in the water, which yields in front of the fish because the fish leaves room for it behind.

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  • According to Boscovich matter is made up of atoms. Each atom is an indivisible point, having position in space, capable of motion in a continuous path, and possessing a certain mass, whereby a certain amount of force is required to produce a given change of motion.

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  • More than a century was required to invent methods of investigating the conditions of the motion of systems of bodies such as Descartes imagined.

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  • An essential feature of the modern view of the structure of matter is that the molecules are supposed to be in rapid motion relatively to one another.

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  • We are compelled also to suppose that the motion assumes.

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  • Roughly speaking, it is found that there are three main types of molecular motion corresponding to the three states of matter - solid, liquid and gaseous.

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  • In a gas the state of things is very different; an odour is known to spread rapidly through great distances, even in the stillest air, and a gaseous poison or corrosive will attack not only those objects which are in contact with its source but also all those which can be reached by the motion of its molecules.

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  • As a preliminary to examining further into the nature of molecular motion and the differences of character of this motion, let us try to picture the state of things which would exist in a mass of solid matter in which all the molecules are imagined to be at rest relatively to one another.

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