It is possible that tradition is right in supposing that " Judah went down from his brethren " (Gen.
Supposing the pot to be filled with melted lead to be treated, the fire is withdrawn beneath and steam introduced.
But, on his return, he forgot to hoist the white sail, and his father, supposing that his son had lost his life, threw himself from a high rock on which he was keeping watch into the sea, which was afterwards called the Aegean.
Other authorities explain the formation of the tendril and its anomalous position opposite to a leaf by supposing that the end of the stem bifurcates during growth, one division forming the shoot, the other the tendril or inflorescence.
Though people were afraid of Marya Dmitrievna she was regarded in Petersburg as a buffoon, and so of what she had said they only noticed, and repeated in a whisper, the one coarse word she had used, supposing the whole sting of her remark to lie in that word.
That same day he had learned that Prince Andrew, after surviving the battle of Borodino for more than a month had recently died in the Rostovs' house at Yaroslavl, and Denisov who told him this news also mentioned Helene's death, supposing that Pierre had heard of it long before.
Moreover, the difficulties in the way of supposing that the author of Acts could at an earlier period of his life have been a companion of St Paul do not seem to be so serious as some critics think.
He saw Karay seize the wolf, and checked his horse, supposing the affair to be over.
"Well, let her sleep," said Marya Dmitrievna as she went out of the room supposing Natasha to be asleep.
The condition of things can be imagined by supposing that in a medusa primitively of normal build, with tentacles at the margin, the umbrella has grown down past the insertion of the tentacles.
The coal has been treated and found to be of good quality, and there are grounds for supposing that there are 250,000,000 tons in the field.
Supposing, then, that these waves are moo ft.
Supposing Dekker to be chiefly responsible for the scenes dealing with the unfortunate old woman whom persecution as a witch actually drives to become one, and Ford for the domestic tragedy of the bigamist murderer, it cannot be denied that both divisions of the subject are effectively treated, while the more important part of the task fell to the share of Ford.
There is ground also for supposing that they may at first have been used with a specific or restricted local application, a more extended signification having eventually been given to them.
The creatures had sense enough to reason that way, and the only mistake they made was in supposing the earth people were unable to overcome such ordinary difficulties.
"Supposing I suddenly marry... it might happen," he added with an involuntary smile.
But while there are thus some grounds for supposing that the idea of transmutation grew out of the practical receipts of Alexandrian Egypt, the alchemy which embraced it as a leading principle was also strongly affected by Eastern influences such as magic and astrology.
Some columns, supposing they had reached their destination, halted, piled arms, and settled down on the cold ground, but the majority marched all night and arrived at places where they evidently should not have been.
Various derivations are given by the ancient grammarians - one from the town of Aegae; another from Aegea, a queen of the Amazons who perished in this sea; and a third from Aegeus, the father of Theseus, who, supposing his son dead, drowned himself in it.
S.) But there is absolutely no necessity for supposing that when the grandson of Ben Sira reached Egypt the Psalter had been translated into Greek.
Thus, supposing that moo lb of coal were required to work a single vacuum pan, evaporating, say, 6000 lb of water in a given time, then 500 lb of coal would be required for a double-effect apparatus to do the same work, 333 lb for a triple effect, 250 for a quadruple effect, and 200 lb for a quintuple effect.
Excited and vexed by the failure and supposing that someone must be responsible for it, Toll galloped up to the commander of the corps and began upbraiding him severely, saying that he ought to be shot.
We are justified in supposing that the cult of the moon-god was brought into Babylonia by the Semitic nomads from Arabia.
Besides the general arguments for supposing that the physical phenomena of spiritualism may be due to conjuring, there are two special reasons which gain in force as time goes on.
Supposing the tube to be completely introverted and to commence its eversion, we then find that eversion may take place, either by a forward movement of the side of the tube near its attached base, as in the proboscis of the Nemertine worms, the pharynx of Chaetopods and the eye-tentacle of Gastropods, or by a forward movement of the inverted apex of the tube, as in the proboscis of the Rhabdocoel Planarians, and in that of Gastropods here under consideration.
It only remains to be added that there is some ground for supposing that the language spoken in Crete before the later Doric was non-Hellenic, but Indo-European.
Of this contribution to science, as of all the rest which have since proceeded from him, may be said in the words he himself has applied (ut supra, p. 271) to the work of another labourer in a not distant field: " This is a model paper for unbiassed observation, and freedom from that pleasant mode of supposing instead of ascertaining what is the true nature of an anatomical element."
A slave, having detected her in the act of embracing it and supposing it to be a lover, informed her father, who ordered her to burn the image; whereupon she threw herself with it into the flames.
Charles, however, has given good grounds for supposing that it is merely a preface, and that the work went on to discuss grammar, logic (which Bacon thought of little service, as reasoning was innate), mathematics, general physics, metaphysics and moral philosophy.
Now, supposing dealing to be confined to experts, what effects upon the course of prices would one expect from the specialism of the cotton market and improved facilities Effect specula= for dealing, on the assumption that dealers were governed wholly in their actions by the course of prices and never tried to manipulate them?
" The whole course of nature becomes intelligible only by supposing the co-working of God, who alone carries forward the reciprocal action of the different parts of the world.
This is obviously unsymmetrical, consisting of an aliphatic and an aromatic nucleus; Claus explained the formation of the same phthalic acid from the oxidation of either nucleus by supposing that if the aromatic group be oxidized, the aliphatic residue assumes the character of a benzene nucleus.
Instead of supposing the light to fall vertically upon the surface it is often supposed to fall obliquely, generally at an angle of 45° from the upper left-hand corner.
There are reasons for supposing that the truncal coelom was at one time provided with pore-canals, but supposed vestiges of these structures have only been described for one genus, Spengelia,in which they lie near the anterior end of the truncal coelom.
For the cubic (ab) 2 axbx is a covariant because each symbol a, b occurs three times; we can first of all find its real expression as a simultaneous covariant of two cubics, and then, by supposing the two cubics to merge into identity, find the expression of the quadratic covariant, of the single cubic, commonly known as the Hessian.
Supposing a number of some species of arthropod or fish to be swept into a cavern or to be carried from less to greater depths in the sea, those individuals with perfect eyes would follow the glimmer of light and eventually escape to the outer air or the shallower depths, leaving behind those with imperfect eyes to breed in the dark place.
Journ., 18 43, 3, p. 46), determine the law of the secondary wave, by comparing the result of the integration with that obtained by supposing the primary wave to pass on to P without resolution.
Another particular case of interest is obtained by supposing a small relatively to (a+d).
We have already noticed the difficulty of supposing that the Elohistic Psalter was compiled in a place where a Jehovistic Psalter was already in use.
Nor had the Allies grounds for supposing that drift-mines would not be met with, were the attack renewed.
of the Straits connoted disembarkation in face of opposition, and, even supposing the landing to be successful, the force would start work much further from the Narrows than were either Helles or Anzac. Then again, to plant down a portion of the Allied troops on one side of the Straits, while continuing operations on the other side, would mean voluntary dispersion of resources in place of concentration.
Supposing the vessel to be exhausted to have already been securely connected to the pump, we now lower the reservoir B so as to reduce the pressure in A sufficiently below the tension in the gas to be sucked in, and, by turning the cock so as to connect A with the vessels to be exhausted, cause the gas to expand into and almost fill A.
Hence, supposing the crystals immediately after their formation to be in absolute contact with one another all round, then, in the case of Class II., such contact will be maintained on cooling, while in the case of Class I.
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.
As an example of the general equations, take the simplest case of a uniform field of gravity, with Oz directed vertically downward; employing the gravitation unit of force, 1 dp i dp t dp dp/dz = p = pzn (4) z n+I pz 1 /n p-p n-H ?t), (5) supposing p and p to vanish together.
u -b' Along a jet surface, q=Q, and ch S2= cos 0 =cos a-i sin2a(a-a')/(u-b), (5) if 0 =-a at the source x of the jet xB, where u = co; and supposing 0=0,13 at the end of the streams where u =j, j', u-b i sin 2 a u - j cos 0-cos /3 i a -a cos a sin a -cos 0' aa' - 2 (cos a -cos (3) (cos a-cos 0)' u-j' 1 2 cos 0-cos, (6) a -a' - 2 S i n a (cos a -cos (3') (cos a -cos B)' and 4' being constant along a stream line d4 - dw ds _d8 d4 _ dw du du du' d- -dud0' 7rQ ds_ it ds (cos a-cos /3) (cos a -cos (3') sin 0 m+m' dB c d0 - (cos a-cos B) (cos 0-cos /3) (cos 0 -cos /3')' _ sin 0 cos a-cos 13 sin 0 - cos a-cos B + cos 0-cos (3' cos 0-cos 13 cos a -cos $ sin 6 cos (3-cos /3' cos 0-cos 0" giving the intrinsic equation of the surface of a jet, with proper attention to the sign.
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.
Supposing the last of these preliminary distillations to have been completed, the residues left in the retorts are removed, and the retorts, as they lie in the hot furnace, are charged by mean: of semi-cylindrical shovels, and their adapters put on.
There is reason for supposing that the marble coating of the facade, and perhaps the erection of the quadrangle, also covered with marble, were the work of Herodes Atticus, and therefore just completed when Pausanias saw them.
It has now become obvious that the data afforded by the Hebrew writings should never have been regarded as sufficiently accurate for the purpose of exact historical computations: that, in short, no historian working along modern scientific lines could well have made the mistake of supposing that the genealogical lists of the Pentateuch afforded an adequate chronology of world-history.
Many authors confound the year of Rome with the civil year, supposing them both to begin on the 1st of January.
We must be careful, however, not to fall into the error of supposing that he wrote it with the sole object of meeting an occasional emergency.
Three principal patterns, those of King, Ormerod and Walker, are in use, and they are generally efficient supposing the speed of the cage at arrival is not excessive.
A simple approximate calculation of the pressure exerted by a gas on its containing vessel can be made by supposing that the molecules are so small in comparison with their distances apart that they may be treated as of infinitesimal size.
We may get some idea of the effect by supposing that for a short time the change in form is negligible.
The chief experimental basis for supposing that a train of longitudinal waves with displacement curve of this kind arouses the sensation of a pure tone is that the more nearly a source is made to vibrate with a single simple harmonic motion, and therefore, presumably, the more nearly it sends out such a harmonic train, the more nearly does the note heard approximate to a single pure tone.
We may see how this occurs by supposing that the restoring force of the receiving mechanism is represented by Ax- f-µx 2, where x is the displacement and µx 2 is very small.
On the 2nd of March 1834, Greeley and Winchester issued the first number of The New Yorker, a weekly literary and news paper, the firm then supposing itself to be worth about $3000.
In October 1904, therefore, supposing the Japanese to have used part of their forces against Port Arthur.
This argument, then, for supposing that the original writing by Mark differed widely in form and contents from the Gospel which now bears his name appears to be without force.
The process of disintegration and levelling down has reached such an advanced stage that, if ever there did exist evidences of former glaciation, they have now become entirely obliterated, even to the complete pulverization of the erratic blocks, supposing there were any.
The problem is whether we can represent the facts more simply by supposing the intervening space to be occupied by a medium which transmits physical actions, after the manner that a continuous material medium, solid or liquid, transmits mechanical disturbance.
We may, in short, put this complex matter as follows: The conditions of the problem are sufficiently satisfied by supposing a single editor, who had three works at his disposal, the Martyrdom of Isaiah, of Jewish origin, and the Testament of Hezekiah and the Vision of Isaiah, of Christian origin.
The medieval church had spanned the centuries by supposing that Christ's death was continuous down through the age in the sacrifice of the Mass; Protestant theology had nothing equivalent.
di g d tan i g dt - v cos i ' and now (53) dx d 2 y dy d2xdx Cif dt 2 dt dt2 _ - _ gdt' and this, in conjunction with (46) dy _ d y tan i = dx dt/dt' (47)di d 2 d d 2 x dx sec 2 idt = (ctt d t - at dt2) I (dt), reduces to (48) Integrating from any initial pseudo-velocity U, (60) du t _ C U uf(u) x= C cos n f u (u) y=C sin n ff (a); and supposing the inclination i to change from 0, to 8 radians over the arc.
It is found experimentally that m = 1.2 is a good average value to take for cordite; so now supposing the combustion of the charge of the 6-in.
Supposing that the scale under this wire is divided into 2000 parts and that we are in possession of a standard Clark cell, the electromotive force being known at various temperatures, and equal, say, to 1.434 volts at 15° C. The first process is to set the potentiometer.
Supposing that the potential fall down the strip is found to be.
It involves, moreover, the incongruity of supposing that thirty-seven years elapsed between Esau's marrying his Hittite wives (xxvi.
44 by supposing that he commenced reckoning a second year of his reign on Nisan I, A.D.
He was the first, in 1867, to examine the spectrum of the aurora borealis, and detected and measured the characteristic bright line in its yellow green region; but he was mistaken in supposing that this same line, which is often called by his name, is also to be seen in the zodiacal light.
This system, the Aeginetan, one of the most important to the Greek world, has been thought to be a degradation of the Phoenician (17, 21), supposing 220 grains to have been reduced in primitive Greek usage to 194.
There seems, however, no ground whatever for supposing that Briggs meant to express anything beyond his hope that the reason for the alteration would be explained in the posthumous work; and in his own account, written seven years after Napier's death and five years after the appearance of the work itself, he shows no injured feeling whatever, but even goes out of his way to explain that he abandoned his own proposed alteration in favour of Napier's, and, rejecting the tables he had already constructed, began to consider the calculation of new ones.
The remarkable phenomenon of nations so similar in bodily make but so distinct in language can hardly be met except by supposing a long period to have elapsed since the country was first inhabited by the ancestors of peoples whose language has since passed into so different forms. The original peopling of America might then well date from the time when there was continuous land between it and Asia.
Serpent cults were well known in ancient Europe; there does not, it is true, appear to be much ground for supposing that Aesculapius was a serpent-god in spite of his connexion with serpents.
He first brought the revolutions of our satellite within the domain of Kepler's laws, pointing out that her apparent irregularities could be completely accounted for by supposing her to move in an ellipse with a variable eccentricity and directly rotatory major axis, of which the earth occupied one focus.
Euhemerus of Messenia tried of old to rationalize the Greek myths by supposing that the Olympian gods were deified men.
This new faith was that of Mani, which spread with a rapidity only to be explained by supposing that Mithraism had prepared men's minds for its reception.
But even supposing $1,000,000,000 to be a juster estimate according to present-day values, it is probable that the increase of this since 1790 has been more than a hundredfold and since 1850 (since when such data have been gathered by the census) about fifteenfold.
But we may explain the share of Theodectes by supposing that he had a hand in the work (cf.
Finding then that substances are real predicates, and supposing that in that case they must be species or genera, he could not avoid the conclusion that some substances are species or genera, which were therefore called by him " secondary substances," and by his Latin followers substantiae universales.
This important difference between the De Interpretatione and the Prior Analytics can only be explained by supposing that the former is the earlier treatise.
Spengel, indeed, tries to bring the latest date in the book down to 330; but it is by absurdly supposing that the author could not have got the commonplace, " one ought to criticize not bitterly but gently," except from Demosthenes, De Corona (§ 265).
But Supposing The Instant Of The Sun'S Entering Into The Sign Libra To Be Very Near Midnight, The Small Errors Of The Solar Tables Might Render It Doubtful To Which Day The Equinox Really Belonged; And It Would Be In Vain To Have Recourse To Observation To Obviate The Difficulty.
For Example, Supposing The Date To Be 1148.
But, Supposing This Correction To Have Been Made, It Would Have Again Become Necessary, At The End Of 308 Years, To Advance Them One Line Higher, In Consequence Of The Accumulation Of The Error Of The Cycle To A Whole Day.
They Are Therefore Connected With The Golden Numbers By The Formula (I), In Which N Is Any Whole Number; Andor A Whole Lunar Cycle (Supposing The First Epact To Be 11), They Are As Follows: 11, 22, 3, 14, 25, 6, 17, 28, 9, 20, I, 12, 23, 4, 15, 26, 7, 18, 29.
In 1788 the English lieutenant Shortland coasted along the south side of the chain, and, supposing it to be a continuous land, named it New Georgia; and in 1792 Captain Edward Manning sailed through the strait which separates Ysabel from Choiseul and now bears his name.
But, in spite of these materialistic tendencies, he followed Hume in reducing matter and everything knowable to phenomena of consciousness; and, supposing that nothing is knowable beyond phenomena, concluded that we can neither affirm nor deny that anything exists beyond, but ought to take up an attitude which the ancient sceptics called Aphasia, but he dubbed by the new name of Agnosticism.
Finally, he explained the concomitance of these two series, as well as that between the perceptions of different monads, by supposing a pre-established harmony ordained by the primitive monad, God.
He suggested that this theory of the substantial unity of a body might explain transubstantiation, by supposing that, while the monads and phenomena of bread remain, the vinculum substantiale of the body of Christ is substituted.
(c) He explains the rise of consciousness by supposing that, while it requires brain as a condition, it consists in the emancipation of intelligence from will at the moment when in sensation the individual mind finds itself with an idea without will.
Lotze concluded that we have no more reason for supposing an external space like space constructed out of our perceptions, than we have for supposing an external colour like perceived colour.
The first question he answered from his imagination by supposing that, while the external world is stimulus of the nervous process, the nervous process is the immediate stimulus of the sensation, and that the sensation increases by a constant fraction of the previous stimulus in the nervous system, when Weber's law proves only that it increases by a constant fraction of the previous stimulus in the external world.
By thus supposing a psychical basis to evolution, Fechner, anticipating Wundt, substituted a psychical development of organs for Darwinian accidental variation.
In supposing a direct perception of such a nondescript thing, he shows to what straits idealists are driven in the endeavour to supplement Kant's limitation of knowledge to phenomena by some sort of knowledge of things.
(Thus, if a pain is an E-value directly dependent on a disturbance in C, and a pleasure another E-value directly dependent on a recovery of C, it will follow that a transition from pain to pleasure will be a vital series in E directly dependent on an independent vital series in C, recovering from a vital difference to its maintenance-maximum.) Lastly, supposing that all human processes can in this way be reduced to vital series in an essential co-ordination of oneself and environment, Avenarius held that this empirio-critical supposition, which according to him is also the natural view of pure experiences, contains no opposition of physical and psychical, of an outer physical and an inner psychical world - an opposition which seemed to him to be a division of the inseparable.
We can only explain it by supposing that Wundt wishes to believe that, beyond the " ideal," there really is proof of a transcendent, ideating, substance-generating will of God; and that he is approaching the noumenal voluntarism of his younger contemporary Paulsen.
He carries its operation beforereason still farther, supposing that " attuition " makes particular inferences about outside objects, and that a man, or a dog, through association " attuites " sequence and invariableness of succession, and, in fact, gets as far in the direction of causation as Hume thought it possible to go at all.
He maintained that the physical and the psychical are two orders which are parallel without interference; that the physical or objective order is merely phenomena, or groups of feelings, or " objects," while the psychical or subjective order is both a stream of feelings of which we are conscious in ourselves, and similar streams which we infer beyond ourselves, or, as he came to call them, " ejects "; that, if we accept the doctrine of evolution at all, we must carry these ejective streams of feelings through the whole organic world and beyond it to the inorganic world, as a " quasimental fact "; that at bottom both orders, the physical phenomena and the psychical streams, are reducible to feelings; and that therefore there is no reason against supposing that they are made out of the same " mind-stuff," which is the thing-in-itself.
Lastly, though the personal idealists are right in rejecting the hypothesis of one mind, they are too hasty in supposing that the hypothesis is useless for idealistic purposes.
No idealism can explain how we all know one sun, except by supposing that we all have one mind.
by supposing it to be one object of one mind, or realistically by supposing it to be one thing distinct from the many minds which think about it.
Trendelenburg (1802-1872), a formidable opponent of Hegel, tried to surmount Kant's transcendental idealism by supposing that motion, and therefore time, space and the categories, though a priori, are common to thought and being.
He vacillated a great deal about our mode of perceiving the external world; but his final view (edition of Reid's works, note D*) consisted in supposing that (1) sensation is an apprehension of secondary qualities purely as affections of the organism viewed as ego; (2) perception in general is an apprehension of primary qualities as relations of sensations in the organism viewed as non-ego; while (3) a special perception of a so-called " secundo-primary " quality consists in " the consciousness of a resisting something external to our organism."
Aristotle could not know enough, physically, about Nature to understand its matter, or its motions, or its forces; and consequently he fell into the error of supposing a primary matter with four contrary primary qualities, hot and cold, dry and moist, forming by their combinations four simple bodies, earth, water, air and fire, with natural rectilineal motions to or from the centre of the earth; to which he added a quintessence of ether composing the stars, with a natural circular motion round the earth.
One would scarcely be justified, however, in supposing that it was anything like universal; for the purchasing power of such a sum was at that time considerable, representing as it did about 16-20 oxen or 100-120 sheep. It would hardly be safe to credit men of the sixhynde class in general with more than a horse, spear and shield.
In the 11th century it was distinctly unusual for a peasant to possess a whole team of his own, and there is no reason for supposing the case to have been otherwise in early times; for though the peasant might then hold a hide, the hide itself was doubtless smaller and not commensurate in any way with the ploughland.
For ten years the marriage was barren, and the only reason for supposing that the future tsar Paul, who was born on the 2nd of October 1754, was the son of Peter, is the strong similarity of their characters.
The possibility that it had been brought to England by Cabot or some of his successors earlier in the century is not to be overlooked, and reasons will presently be assigned for supposing that one of the breeds of English turkeys may have had a northern origin;' but the of tenquoted distich first given in Baker's Chronicle (p. 298), asserting that turkeys came into England in the same year - and that year by reputation 2524 - as carps, pickerels and other commodities, is wholly untrustworthy, for we know that both these fishes lived in the country long before, if indeed they were not indigenous to it.
Supposing seedlings to have been developed, it is found that a large number of them present considerable variations, some being especially robust, others peculiar in size or form.
After this, supposing the work to have occupied most of the summer, the whole may be laid up in ridges, to expose as great a surface as possible to the action of the winter's frost.
distant from it, supposing there were no trees at the back.
The early history of the thesmothetae is not clear, but this much is certain that there is no adequate reason for supposing, as many historians do, that in early times, they, with the three chief archons, constituted a collective or collegiate magistracy.
On the other hand, Bramhall, supposing Hobbes privy to the publication, resented the manner of it, especially as no mention was made of his rejoinder.
The construction was, of course, utterly premature, even supposing it were inherently possible; but it is Hobbes's distinction, in his century, to have conceived it, and he is thereby lifted from among the scientific workers with whom he associated to the rank of those philosophical thinkers who have sought to order the whole domain of human knowledge.
There, and there only, one seems to find a common and a satisfactory ground, supposing always that all men's feelings give the same answer.
The high road from Kabul to Kandahar passes this way (another reason for supposing the Tarnak to be Arachotus), and the people live off the road to avoid the onerous duties of hospitality.
Harris is followed by Harnack and others in supposing that it was only through a careless reading of this inscription that the work was supposed to have been addressed to Hadrian.
Ultimately the Greek East was absorbed by Islam; the popular mistake lies in supposing that the Hellenistic tradition thereby came to an end.
Since Alexandria could neither have been stormed nor starved out by the Arabs, his motives for surrendering it, and with it the whole of Egypt, have been variously interpreted, some supposing him to have been secretly a convert to Islam.
This seems an unlikely limitation, throwing an impossible amount of work upon the crew, and leaving each ship terribly weak supposing a naval battle had to be undertaken - as with some rival viking fleet, even before any Christian nation possessed a fleet.
Even supposing its possibility, the Bible does not present such a revelation.
There is ground for supposing that the Phoenicians were not ignorant of the Canaries.
As the weight of bleaching-powder consumed in the world is at most one-fifth of that of alkali, calculated as Na2C03, it follows that only about one-tenth of all the alkali required could be made by electrol y sis, even supposing the Leblanc process to be entirely abolished.
1, 1), swordsmanship, and forensic argumentation, implies that they came to eristic not from the sophistry of Socrates, but from that of the later humanists, polymaths of the type of Hippias; (2) that the fifth and sixth definitions of the Sophist, in which " that branch of eristic which brings pecuniary gain to the practitioner " is opposed to the " patience-trying, purgative elenchus " of Socrates, indicate that contemporary with Socrates there were eristics whose aims were not his; (3) that, whereas the sophist of the final definition " disputes, and teaches others to dispute, about things divine, cosmical, metaphysical, legal, political, technical, in fact, about all things," we have no ground for supposing that the Megarians and the Cynics used their eristic for any purpose except the defence of their logical heresies.
The Difference From Rowland'S Value, 4.181, Could Be Explained By Supposing The E.M.F.
Supposing that the two stars are of unequal surface brilliancy, the magnitude at minimum will depend on which of the two stars is the nearer to us, accordingly there are two unequal minima in each revolution.
It was natural enough that the originators of conceptual logic, seeing that judgments can be expressed by propositions, and conceptions by terms, should fall into the error of supposing that, as propositions consist of terms, so judgments consist of conceptions, and that there is a triple mental order - conception, judgment, reasoning - parallel to the triple linguistic order - term, proposition, discourse.
But why spoil the further mental analysis of inference by supposing that conceptions are constituents of judgment and therefore of inference, which thus becomes merely a complex combination of conceptions, an extension of ideas?
Lastly, all the authors of the above-quoted theories err in supposing that all judgment requires conception; for even Mill thinks a combination of ideas necessary, and Brentano, who comes still nearer to the nature of sensory judgment when he says, " Every perception counts for a judgment," yet thinks that an idea is necessary at the same time in order to understand the thing judged.
But whether Kant be right or wrong, Wundt and his school are decidedly wrong in supposing " supplementary notions which are not contained in experience itself, but are gained by a process of logical treatment of this experience "; as if our behalf in causality could be neither a posteriori nor a priori, but beyond experience wake up in a hypothetical major premise of induction.
If we assume Regnault's formula (10) for the total heat, we have evidently the simple relation S=0.305(0'-0)/(0"-o), supposing the initial steam to be dry, or at least of the same quality as that employed by Regnault.
It is equivalent, as Callendar (loc. cit.) points out, to supposing that the variation of the specific heat is due to the formation and solution of a mass w/(v-w) of vapour molecules per unit mass of the liquid.
and Madame de Maintenon was celebrated in his presence at Versailles, but there is no reason for supposing that the subsequent coolness between him and Madame de Maintenon arose from his insistence on secrecy in this matter.
The line of resistance is a line traversing all the centres of resistance of a series of joints,its form, in the positions intermediate between the actual joints of the structure, being determined by supposing the pieces and their loads to be subdivided by the introduction of intermediate joints ad snfinstum, and finding the continuous line, curved or straight, in which the intermediate centres of resistance are all situated, however great their number.
The relative velocity pet-pendicular to P~Pi of the teeth at their point of contactthat is, their velocity of sliding on each otheris found by supposing one of the wheels, such as I, to be fixed; the line of centres CXCi to rotate backwards round C~ with the angular velocity aj, and the wheel 2 to rotate round C2 as before, with the angular velocity az relatively to the line of centres CiC2, so as to, have the same motion as if its pitch-circle rolled,on the pitch-circle of the first wheel.
Supposing all the wheels to be in outside gearing, then, as each elementary combination reverses the direction of rotation, and as the number of elementary combinations m 1 is one less than the number of axes rn it is evident that if m is odd the direction of rotation is preserved, and if even reversed.
It is seldcm that one of these effects is produced without at the same time producing the other; but the classification of Willis depends upon which of those two effects, even supposing them to occur together, is the practical object of the mechanism.
Feeling the difficulty of supposing that all the ancient minstrels sang of the " wrath of Achilles " or the " return of Ulysses " (leaving out even the capture of Troy itself), he was led to assume that two poems of no great compass dealing with these two themes became so famous at an early period as to throw other parts of the Trojan story into the background, and were then enlarged by successive generations of rhapsodists.
There are reasons for supposing that these funnels are vestiges of an ancient excretory system, which has given way by substitution to the excretory tubules described above.
Faithful to the ancient tradition of Contarini and Pole at Trent, these good men persisted in supposing that the Reformation was nothing more than a protest against practical abuses: remove the abuses, and the rest would follow of itself.
But even supposing that this method were accurate and completely unfolded, it is evident that it could only be made applicable and produce fruit when the phenomena of the universe have been very completely tabulated and arranged.
Now, supposing the forme to be dealt with consists of thirty-two pages to be printed on quad crown paper, measuring 40X30 in., on a suitable size of single cylinder machine of the Wharfedale class, it would be found, although both the machine and type were fairly new (that is, not much worn), that there was some amount of inequality in the impression given to the whole sheet.
There is at least good ground for supposing Mattioli's death to have been indicated in 1694, but nothing is known that would imply Dauger's, unless it was he who died in 1703.
This is accompanied by another statement in which the chancellor gives an estimate of what the produce of the revenue may be in the year just entered upon, supposing the taxes and duties to remain as they were in the past year, and also an estimate of what the expenditure will be in the current year.
602) is more likely to be right in supposing that the road taken by Horace ran directly from Beneventum to Trevicum and thence to Aquilonia (though the course of this road is not yet determined in detail), and that the easier, though somewhat longer, road by Aeclanum was of later date.
Supposing this could be established, the question would still remain whether the same result could not be obtained at far less expense by dispensing with the hatching operations and distributing the eggs directly after fertilization.
des Sciences, 1787, p. 506) asserted that " by supposing the adherence of the particles of a fluid to have a sensible effect only at the surface itself and in the direction of the surface it would be easy to determine the curvature of the surfaces of fluids in the neighbourhood of the solid boundaries which contain them; that these surfaces would be linteariae of which the tension, constant in all directions, would be everywhere equal to the adherence of two particles, and the phenomena of capillary tubes would then present nothing which could not be determined by analysis."
He was really a stoicizing Platonist; and this has led to the error of supposing Varro to have been a professed Stoic. The influence of Antiochus is clearly to be seen in many remains of Varro's writings.
We shall not err in supposing that we have here (what we find nowhere else) an authentic expression of the feeling entertained by a majority of the Roman senate concerning Stilicho.
Here again the inference is that the Latin treatises printed from the 15th century onwards as the work of Geber are not authentic, regarded as translations of the Arabic author Jaber, always supposing that the Arabic MSS.
There is no reason for supposing that Joinville indulged in various editions, such as those which have given Kervyn de Lettenhove and Simeon Luce so much trouble, and which make so vast a difference between the first and the last redaction of the chronicler of the Hundred Years' War.
These are - Wha.t is the general drift and purpose of Gargantua and Pantagruel, supposing there to be any?
"There is no absurdity in supposing that the deity may, for wise purposes, have chosen to open a source of contingency in the voluntary actions of his creatures, to which no prescience can possibly extend."
Latham's name for this species is " Faithful Jacana "- he supposing it to belong to the genus in which Linnaeus placed it.
But we must not fall into the error of supposing that the early progenitor of the whole Simian stock, including man, was identical with, or even closely resembled, any existing ape or monkey."
12 being of doubtful origin) for supposing that Jeremiah would have excepted Deuteronomy from his condemnation.
Certain expositors have tried to obviate the difficulty, first by supposing that the expression "son of Nebuchadrezzar" in Daniel means "descendant" or "son," a view which is rendered untenable by the facts just cited.
The amount is such that, supposing the average specific heat of the sun's body as high as that of water, there would result a general fall of temperature of 2.0° to 2.5° C. in the lapse of each year.
An equivalent statement of the same conclusion may be put thus: supposing a gaseous nebula is destined to condense into a sun, the elementary matter of which it is composed will develop in the process into our known terrestrial and solar elements, parting with energy as it does so.
It appears that Newton made the mistake of supposing that all prisms would give a spectrum of exactly the same length; the objections of his opponents led him to measure carefully the lengths of spectra formed by prisms of different angles and of different refractive indices; and it seems strange that he was not led thereby to the discovery of the different dispersive powers of different refractive substances.
Newton, by calculating from Kepler's laws, and supposing the orbits of the planets to be circles round the sun in the centre, had already proved that the force of the sun acting upon the different planets must vary as the inverse square of the distances of the planets from the sun.
Pierre Battifol' is correct in supposing that the Disciplina arcani was more or less of a makebelieve, a bit of belletristic trifling on the part of the overrhetorical Fathers of the 4th and 5th centuries.
First, whereas it has been assumed above that Xenophanes was theologian rather than philosopher, whence it would seem to follow that the philosophical doctrine of unity originated, not with him, but with Parmenides, Zeller, supposing Xenophanes to have taught, not merely the unity of God, but also the unity of Being, assigns to Parmenides no more than an exacter conception of the doctrine of the unity of Being, the justification of that doctrine, and the denial of the plurality and the mutability of things.
Secondly, whereas it has been argued 'above that " Opinion " is necessarily included in the system, Zeller, supposing Parmenides to deny the Nonent even as a matter of opinion, regards that part of the poem which has opinion for its subject as no more than a revised and improved statement of the views of opponents, introduced in order that the reader, having before him the false doctrine as well as the true one, may be led the more certainly to embrace the latter.
per annum, the simple interest on £A for n years is £nrA, and the compound interest (supposing interest payable yearly) is £[(r +r)"-- If n is large, the compound interest is most easily calculated by means of logarithms.
The resemblance of the flooring-plates to the ambulacral ossicles of a starfish is so exact that one can explain it only by supposing similar relations of the water-canals and their branches (podia).
What would have happened supposing that England had made no further stir, and had not vexed William by rebellion, it is impossible to say.
Supposing that the two curves are of the orders m, n, respectively, then the order of the resultant equation is in general and at most = mn; in particular, if the curve of the order n is an arbitrary line (n= 1), then the order of the resultant equation is = m; and the curve of the order m meets therefore the line in m points.
a property independent of the particular axes of co-ordinates used in the representation of the curve by its equation; for instance, the curve may have a node, and in order to this, a relation, say A = o, must exist between the coefficients of the equation; supposing the axes of co-ordinates altered, so that the equation becomes u' = o, and writing A' = o for the relation between the new coefficients, then the relations A = o, A' = o, as two different expressions of the same geometrical property, must each of them imply the other; this can only be the case when A, A' are functions differing only by a constant factor, or say, when A is an invariant of u.
taking P, P' as the corresponding points in an (a, a') correspondence on a curve of deficiency D, and supposing that when P is given the corresponding points P' are found as the intersections of the curve by a curve o containing the co-ordinates of P as parameters, and having with the given curve k intersections at the point P, then the number of united points is a = a+a' +2kD; and more generally, if the curve 0 intersect the given curve in a set of points P' each p times, a set of points Q' each q times, &c., in such manner that the points (P,P') the points (P, Q') &c., are pairs of points corresponding to each other according to distinct laws; then if (P, P') are points having an (a, a') correspondence with a number=a of united points, (P, Q') points having a (0,0') correspondence with a number =b of united points, and so on, the theorem is that we have p(a-a-a')+q(b-(3-(')+ ...
Supposing 0 indefinitely small, we have what may be called the penultimate curve, and when 0=o the ultimate curve.
But a serious objection to the comparison is that the development of Phylactolaemata can be explained by supposing it to be a modification of what occurs in other Polyzoa, while it appears to have no relation whatever to that of Phoronis.
He will be conscious indeed of physical appetite; but he will not be misled into supposing that its object is really a good; he cannot, therefore, hope for the attainment of this object or fear to miss it, as these states involve the conception of it as a good.
proper) by supposing some latent or antecedent voluntary sin, of which the apparently involuntary heresy was the fearful.
The latter difficulty Thomas, like many of his predecessors, avoids by supposing a " co-operation " of free-will and grace, but the former he does not fully meet.
And supposing it to be replied that the motive is really the moral uneasiness involved in choosing the selfish alternative, Godwin answers that this uneasiness, though a " constant step " in the process of volition, is a merely " accidental " step - " I feel pain in the neglect of an act of benevolence, because benevolence is judged by me to be conduct which it becomes me to adopt."
The law of this motion was such that the phenomena could be represented by supposing the motion to be actually circular and uniform, the apparent variations being explained by the hypothesis that the earth was not situated in the centre of the orbit, but was displaced by an amount about equal to one-twentieth of the radius of the orbit.
There are good reasons for supposing that the relics were origin ally in the collection of Acca, bishop of Hexham, who took them into Pictland when he was driven from Hexham (c. 732), and founded a see, not, according to tradition, in Galloway, but on the site of St Andrews.
Thus Athene is a divine name without meaning in Greek, but Max Muller advances reasons for supposing that it is identical with ahana, " the dawn," in Sanskrit.
Arago pointed out, by supposing that in passing through the plate the plane of polarization of each monochromatic constituent is rotated by an amount dependent upon the frequency - an explanation that may be at once verified either by using monochromatic light or by analysing the light with a spectroscope, the spectrum in the latter case being traversed by one or more dark bands, according to the thickness of the plate, that pass along the spectrum from end to end as the analyser is rotated.
Fresnel showed that rotary polarization could be explained kinematically by supposing that a plane-polarized stream is resolved on entering an active medium into two oppositely circularly polarized streams propagated with different speeds, the rotation being rightor left-handed according as the rightor left-handed stream travels at the greater rate: The polarization-vector of the primitive - stream being = a cos nt, the first circularly polarized stream after traversing a distance z in the medium may be represented by = a cos (nt - k i z), ni = a sin (nt - kiz), and the second b z = a cos (nt - k 2 z), n2= - a sin (nt - k2z).
He explained this effect by supposing that the Volta contact electromotive force varied with the temperature, so that the exact balance was destroyed by unequal heating.
He shows that, supposing the cloud of particles to move around the sun in nearly circular orbits immediately outside the earth, the perturbations by the earth in the motion of the particles will result in their retardation in that part of the orbit nearest the earth, and therefore in their always being more numerous in a given space in this part of the orbit Ethan in any other.
To ensure the telecentric transmission, the diaphragm in the back focus of the objective may be replaced by a diaphragm in the front focal plane of the condenser, supposing that uniformly illuminated objects are being dealt with; for in this case all the principal rays in the object-space are transmitted parallel to the axis.
The brightnesses of image points in a median section of the pencil are proportional to the aperture of the lens, supposing that the rays are completely reunited.
Supposing, however, there is oblique illumination, then formula (5) can always be applied to determine the magnifying power attainable with at least one objective.
Free central placentation, there fore, has been accounted for in two ways: either by supposing that the placentas in the early state were formed on the margins of 2 FIG.
carpellary leaves, and that in the progress of development these leaves separated from them, leaving the placentas and ovules free in the centre; or by supposing that the placentas are not marginal but axile formations, produced by an elongation of the axis, and the carpels verticillate leaves, united together around the axis.
In strictness, sense, understanding, imagination and reason ought to have had their functions defined in close relation to the elements of knowledge with which they are severally connected, and as these elements have no existence as separate facts, but only as factors in the complex organic whole, it might have been possible to avoid the error of supposing that each subjective process furnished a distinct, separately cognizable portion of a mechanical whole.
These are known as muffle or chamber furnaces; and by supposing the crucibles or retorts to represent similar chambers of only temporary duration, the ordinary pot melting air furnaces, and those for the reduction of zinc ores or the manufacture of coal gas, may be included in the same category.
And let us not fritter away the truth by supposing this reconciliation to mean a change in the sinner's heart to God.
Supposing that these arguments are sound, what conclusion does Nāgārjuna wish us to draw from our supposed inability to theorize reality?
For another popular error is that of supposing that evil spirits must be unclean spirits.
The consequences of supposing AN to be zero have already been traced.
Taking Linke's (28) figures as given in § 10, and supposing h, = o, h 2 = 15 X 10 4, we find for the charge in the unit tube between the ground and 1500 metres level, remembering that the centimetre is now the unit of length, M = (I/41r) (125-25)/100.
We learn from Ovid that Propertius was his senior, but also his friend and companion; and that he was third in the sequence of elegiac poets, following Gallus, who was born in 69 B.C., and Tibullus, and immediately preceding Ovid himself, who was born in 43 B.C. We shall not then be far wrong in supposing that he was born about 50 B.C. His early life was full of misfortune.
It -is worth while to notice that this reference occurs in a chapter "De Multiplicationis et Partitionis compendiis miscellaneis," which, supposing the treatise to have been written in Napier's younger days, may have been his earliest production on a subject over which his subsequent labours were to exert so enormous an influence.
The intercalary month being purely arbitrary may exhibit a normal arrangement, supposing that the month and the week begin together.
The occurrence of a large number of common roots proves them to be derived from one source, but the great variety of dialects - sometimes unintelligible between tribes separated by only a few miles - cannot be explained except by supposing a vast period to have elapsed since their first settlement.
The jib is usually inclined, so as to enable the travel to be performed by gravity in one direction, and the object of the transporter mechanism is to ensure that pulling in or slacking out the lifting rope shall perform the cycle of operations in the following order: - Supposing the load is ready to be lifted out of a vessel on to a quay, the pull of the lifting rope raises the load, the travelling jenny being meanwhile locked in position.
Perhaps the discrepancy is to be explained by supposing that the pious tsar did not consider all his victims as servants of the Lord, whose souls deserved the prayers of the faithful.
Thus, on the Midland railway in 1885, each third-class passenger, supposing the carriage to have its full complement, was allowed o 62 ft.
Among the educated Greeks rationalistic views of the old mythology had become so current that they could assimilate Alexander to Dionysus without supposing him to be supernatural, and to this temper the divine honours were a mere form, an elaborate sort of flattery.
Instead of supposing the light to fall vertically upon the surface it is often supposed to fall obliquely, generally at an angle of 45Ã‚° from the upper left-hand corner.
Driver prefers to bisect the dialogue by supposing i.
A simple illustration of the difference is this: a man born with four fingers only on his right hand is ascertained to be likely to transmit this peculiarity to some at least of his offspring; on the other hand, there is not the slightest ground for supposing that a man who has had one finger chopped off, or has even lost his arm at any period of his life, will produce offspring who are defective in the slightest degree in regard to fingers, hand or arm.
The occurrence of the factor (Xr)- 1, and the necessity of supposing the phase of the secondary wave accelerated by a quarter of an undulation, were first established by Archibald Smith, as the result of a comparison between the primary wave, supposed to pass on without resolution, and the integrated effect of all the secondary waves (§ 2).
These statements do not warrant us in supposing that they rejected i and 2 Peter, though other Greek sources allege it.
The grounds for supposing this appear, however, to be wholly insufficient (see article on Acts by Bishop Lightfoot in 2nd ed.
But it has been laid down that a nuisance by noise, supposing malice to be out of the question, is emphatically a question of degree (Gaunt v.
There is nothing in the matter or the style of the Historia to preclude us from supposing that Geoffrey drew partly upon confused traditions, partly on his own powers of invention, and to a very slight degree upon the accepted authorities for early British history.
But the former device is too obviously a dens ex machina, the purpose of which would be equally well served by supposing with Fichte the individual self to be endowed with the power of subconsciously extraditing a world which returns to it in consciousness under the form of a foreign creation.
amount of left deflection given - the amount can easily be determined thus: The height of tangent scale for any degree of elevation is given with sufficient accuracy by the rough rule for circular measure It= X 1200 where a is the angle of elevation in minutes, h the height 3 of the tangent scale, and R the sighting radius; thus for 10 h _ 60 X R _ 2.0 Now supposing the sight is inclined IÃ‚° to the left, 3600 - which will move the notch from H to H' (see fig.
Resolving normally in the trajectory, and supposing the resistance of the air to act tangentially, (18) v(di/dt) =g cos i, where di denotes the infinitesimal decrement of i in the infinitesimal increment of time dt.
Supposing that the scale under this wire is divided into 2000 parts and that we are in possession of a standard Clark cell, the electromotive force being known at various temperatures, and equal, say, to 1.434 volts at 15Ã‚° C. The first process is to set the potentiometer.
must remain matter of conjecture; but there are reasons for supposing that, together with the prophecy of Malachi, they came to the compiler of the " book " of the Twelve Prophets anonymously, and he simply attached them at the point which his collection had reached (i.e.
=E.E.Z) is by Eudemus, and supposing without proof that he was also author of the first three books of the Eudemian Ethics, have further asserted that these are a better introduction than the first four books of the Nicomachean Ethics to the books common to both treatises (E.N.
Supposing that the Porte would yield to diplomatic pressure and menace so far as to make some reasonable concessions, he delivered his famous Moscow speech, in which he declared that if Europe would not secure a better position for the oppressed Sla y s he would act alone.
But the phenomenal idealists have not, any more than Kant, noticed the ambiguity of the term " phenomenon "; they fancy that, in saying that all we know is phenomena in the Kantian sense of mental appearances, they are describing all the positive facts that science knows; and they follow Kant in supposing that there is no logical inference of actual things beyond experience.
He supposed that this intuition of causality arises when will is resisted, and, further supposing that causality requires decision between alternatives, concluded that the intuition of will resisted is an intuition of will against will, mine against other (i.
2 Besides these gods, and others whose fame may be inferred (Dagon, 1 Much confusion can be and has been caused by disregarding"(b) and by supposing that the appearance of similar elements of thought or custom implied the presence of similar more complete organisms (e.g.
Clay made the mistake of supposing that he could arouse popular enthusiasm for a moneyed corporation in its contest with the great military "hero of New Orleans."
The amount is such that, supposing the average specific heat of the sun's body as high as that of water, there would result a general fall of temperature of 2.0Ã‚° to 2.5Ã‚° C. in the lapse of each year.
"But I have nothing here," replied Pierre, supposing that he was asked to give up all he possessed.
Balashev rode on, supposing from Murat's words that he would very soon be brought before Napoleon himself.
"Well, but supposing Mary Hendrikhovna is 'King'?" asked Ilyin.
Just what are we supposing we would see if we opened sawdust man 's skull?
This tree, more than most other Pines, illustrates the mistake of supposing that conifers should be clothed to the ground with branches, as the natural habit of such trees is often to shed their branches as other trees shed their leaves.
The Dutch, supposing it to be a native of our shores, called it the English Iris.
Aquarius people with their love of supposing, debating and "what-if-ing" also holds serious appeal to Gemini.
Guillaume 6 explains the ferromagnetism of Heusler's alloy by supposing that the naturally low critical temperature of the manganese contained in it is greatly raised by the admixture of another appropriate metal, such as aluminium or tin; thus the alloy as a whole becomes magnetizable at the ordinary temperature.
Supposing Ewing's hypothesis to be correct, it is clear that if the magnetization of a piece of iron were reversed by a strong rotating field instead of by a field alternating through zero, the loss of energy by hysteresis should be little or nothing, for the molecules would rotate with the field and no unstable movements would be possible.'
At the same time we are not justified in supposing that the scorpions stand in any way as an intermediate grade between any of the existing Epectinata and the Delobranchia.
Thus in many cases the difficulty of supposing that selection has acted on minute and imperceptible initial variations, so small as to have no selective value, may be got rid of.
"Well, supposing I do love him?" thought Princess Mary.
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.
But there is no difficulty in supposing that each division of the Levitical musicians had its own traditional music, certain instruments being peculiar to the one and certain to the other, in which case the assignment of a psalm to the Asaphites or Korahites will merely denote the sort of music to which it is set.
There is, however, no difficulty in supposing that such a thing was done in some sections of the Jewish Church, and it is probable that we must look for an explanation of the peculiarity not to the time but to the place where the second collection was formed.
This authority, it was advised, should consist of 40 members, of whom II should be nominated by the London County Council and 3 by the Corporation of the City (supposing these bodies to accept certain financial responsibilities proposed in the direction of river improvements), 5 by the governors of the Bank of England from the mercantile community, 2 by the London Chamber of Commerce, and I each by the Admiralty, Board of Trade and Trinity House.
By supposing the retardation to vary uniformly and continuously we, fall upon the case of an ordinary prism: but there;, is then no diffraction spectrum in the usual sense.
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