If there are no extraneous forces, the resultant linear momentum is constant in every respect.
Pierre now recognized in his friend a need with which he was only too familiar, to get excited and to have arguments about extraneous matters in order to stifle thoughts that were too oppressive and too intimate.
Partaking human food is now extraneous, yet can still be quite enjoyable.
In the Fragmente he aims at nationalizing German poetry and freeing it from all extraneous influence.
The new extraneous element introduced into Roman literature draws into greater prominence the characteristics of the last great representatives of the genuine Roman and Italian spirit - the historian Tacitus and the satirist Juvenal.
It is easily seen that the effect of extraneous, forces will.
It is evident that the normal blue is more or less diluted with extraneous white light, having its origin in reflections from the grosser particles of foreign matter with which the air is usually charged.
This extraneous influence may, however, be eliminated by surrounding the rod with a coil of wire carrying a current such as will produce in the interior a magnetic field equal and opposite to the vertical component of the earth's field.
The reason of this is apparently that the negative pressure of the pleural, and partly of the peritoneal, cavity tends to aspirate a liquid relatively thicker, so to speak, than that effused where no such extraneous mechanism is at work (James).
It is probable also that the " extraneous discourses " (Oi i wTEpLKoi Aoyoc) sometimes mentioned in them here mean dialectical discussions of a subject from opinions extraneous to its nature, as opposed to scientific deduction from its appropriate principles.
From the eight passages, which refer to the extraneous discourses, we find (1) that Platonic forms were made by them matters of common talk (reOptiXnrat, Met.
On the whole, the interpretation which best suits all the passages is that extraneous discourses mean any extra-scientific dialectical discussions, oral or written, occurring in dialogues by Plato, or by Aristotle, or by anybody else, or in ordinary conversation, on any subject under the sun.
Among all the eight passages mentioned above, the most valuable is that from the Eudemian Ethics (A 8), which discriminates extraneous discourses and philosophical (Kai ie rois i wTEpLKOLS XIyocs Kai iv roas Kara 4cXoac41av, 1217 b 22-23); and it is preceded (A 6, 1216 b 35-37 a 17), by a similar distinction between foreign discourses (h¦Xorpioc Aoyoc) and discourses appropriate to the thing (oiKEioc Aoyoc Tor, 7rpayp,aros), which marks even better the opposition intended between dialectic and philosophy.
Now, as in all eight passages Aristotle speaks, somewhat disparagingly, of " even (Kai) extraneous discourses," and as these include his own early dialogues, they must be taken to mean that though he might quote them, he no longer wished to be judged by his early views, and therefore drew a strong line of demarcation between his early dialogues and the mature treatises of his later philosophical system.
Meanwhile the difficulties in the way of contemporary nationmaking are fostered by many extraneous influences, as well as by dogged resistance of the races in question.
Organic acids such as vinegar, common salt, the natural ingredients of food, and the various extraneous substances used as food preservatives, alone or mixed together, dissolve traces of it if boiled for any length of time in a chemicallyclean vessel; but when aluminium utensils are submitted to the ordinary routine of the kitchen, being used to heat or cook milk, coffee, vegetables, meat and even fruit, and are also cleaned frequently in the usual fashion, no appreciable quantity of metal passes into the food.
" The occurrence of stones and boulders far removed from their parent source early attracted the attention of geologists, but for a long period the phenomena, now known as of glacial origin, were unexplained, and the drifts were looked upon as little more than ` extraneous rubbish,' the product of geological agents, quite distinct from those which helped to form the more ` solid ' rocks that underlie them."
In both cases no extraneous cause can be assigned; the period seems to be inherent in the star itself and not to be determined by the revolution of a satellite (no variability of the line-of-sight motion of Mira has been found, so that it is probably not accompanied by any large companion).
The musical growth is spoilt, the development of the themes is stopped, or prevented, by some reference to extraneous ideas.
In general the extraneous episodes have no great appropriateness to their context, and have the appearance of being abridged versions of stories that had been related at length in poetry.
The problem of determining the possible configurations of equilibrium of a system of particles subject to extraneous forces which are known functions of the positions of the particles, and to internal forces which are known functions of the distances of the pairs of particles between which they act, is in general determinate For if n be the number of particles, the 3n conditions of equilibrium (three for each particle) are equal in number to the 351 Cartesian (or other) co-ordinates of the particles, which are to be found.
A number of particles attached at various points of a string are acted on by given extraneous forces Pi, P, P3.
We shall suppose, in the first instance, that extraneous forces act on the frame at the joints only, i.e.
A state of stress independently of the action of extraneous forces.
When a plane frame which is just rigid is subject to a given system of equilibrating extraneous forces (in its own plane) acting on the joints, the stresses in the bars are in general uniquely determinate.
This system of equations must involve the three conditions of equilibrium of the extraneous forces which are already identically satisfied, by hypothesis; there remain therefore 2n ~ independent relations to determine the 2n3 unknown stresses.
A frame of n joints and vi 3 bars may of course fail to be rigid owing to some parts being over-stiff whilst others are deformable; in such a case it will be found that the statical equations, apart from the thre identical relations imposed by the equilibrium of the extraneous forces, are not all independent but are equivalent to less thar 2,13 relations.
The stresses produced by extraneous forces in a simple frame can be found by considering the equilibrium of the various joints in a proper succession; and if the graphical method be employed the various polygons of force can be combined into a single force-diagram.
It may be noticed that if we take an arbitrary pole in the force-diagram, and draw a corresponding funicular in the skeleton diagram which represents the frame together with the lines of action of the extraneous forces, we obtain two complete reciprocal figures, in Maxwells sense.
If an ideal section be drawn across the frame, the extraneous forces on either side must be in equilibrium with the forces in the bars cut across; and if the section can be drawn so \, as to cut only three bars, ~/\~ the forces in these can be found, since the problem.
When extraneous forces act on the bars themselves the stress in each bar no longer consists of a simple longitudinal tension or thrust.
Each extraneous force W acting on a bar may be replaced (in an infinite number of ways) by two components P, Q in lines through the centres of the pins at the extremities.
If the extraneous forces are n equilibrium the total work which they would perform in any such displacement would be zero, since they reduce to a zero force and a zero couple.
Conversely, we can show that if the, virtual work of the extraneous forces be zero for every infinitesimal displacement of the body as rigid, these forces must be in equilibrium.
In any infinitely small deformation of the frame as thus modified, the virtual work of the forces 5, together with that of the original extraneous forces, must ~ranish this determines S.
Consider, for example, a frame whose sides form the six sides of a hexagon ABCDEF and the three diagonals AD, BE, CF; and suppose that it is required to find the stress in CF due to a given system of extraneous forces in equilibrium, acting on the joints.
The equation of virtual work is then formed by taking moments about C, D, E, F of the extraneous forces FIC 2 which act at C, D, E, F, respectively.
We have seen that the stresses produced by an equilibrating system of extraneous forces in a frame which is just rigid, according to the criterion of 6, are in general uniquely determinate; in particular, when there are no extraneous forces the bars are in general free from stress.
When a frame has a critical form it may be in a state of stress independently of the action of extraneous forces; moreover, the stresses due to extraneous forces are F indeterminate, and may be infinite.
Jf there are no extraneous forces the equation of virtual work _________ reduces to S.
Again, when extraneous forces P act on the joints, the equation is Z(P.&P)+S.Os=-o, where op is the displacement of any joint in the direction of the corresponding force P. If ~(P. Op) =o, the stresses are merely indeterminate as before; but if ~ (P. op) does not vanish, the equation cannot be satisfied by any finite value of S, since Os =0.
This means that, if the material of the frame were absolutely unyielding, no finite stresses in the bars would enable it to withstand the extraneous forces.
We may note that a frame of n joints which is just rigid must have 3116 bars; and that the stresses produced in such a frame by a given system of extraneous forces in equilibrium are statically determinate, subject to the exception of critical forms.
In the case of a string stretched over a smooth surface, but in other respects free from extraneous force, the tensions at the ends of a small element s must be balanced by the normal reaction of the surface.
The work which would have to be supplied by other forces, extraneous to the field, in order to bring the particle from rest in some standard position P0 to rest in any assigned position P, will depend only on the position of P; it is called the statical or potential energy of the particle with respect to the field, in the position P. Denoting this by V, we have VX~x=o, whence X=--~.
It appears then that this sum is a measure of the total capacity for doing work against extraneous resistances which the particle possesses in virtue of its motion and its position; this is in fact the origin of the term energy.
These may be divided into two categories; we have first, the extraneous forces exerted on the various particles from without, and, secondly, the mutual or internal forces between the various pairs of particles.
Strato appears to reject Aristotle's idea of an original source of movement and life extraneous to the world in favour of an immanent principle.
Parallel with the senate, but extraneous to the main lines of the constitution, came the Council of Ten.
If the attraction of a central body is not the only force acting on the moving body, the orbit will deviate from the form of a conic section in a degree depending on the amount of the extraneous force; and the curve described may not be a re-entering curve at all, but one winding around so as to form an indefinite succession of spires.
In all the cases which have yet arisen in astronomy the extraneous forces are so small compared with the gravitation of the central body that the orbit is approximately an ellipse, and the preliminary computations, as well as all determinations in which a high degree of precision is not necessary, are made on the hypothesis of elliptic orbits.
Hence any apparatus, such as a galvanometer, may be partially shielded from extraneous magnetic action by enclosing it in an iron case.
In extraneous pigmentation we have coloured substances either in a solid or fluid state, gaining entrance into the organism and accumulating in certain tissues.
The idea that some extraneous substance is essential to the process is of ancient date; Clement of Alexandria (c. 3rd century A.D.) held that some "air" was necessary, and the same view was accepted during the middle ages, when it had been also found that the products of combustion weighed more than the original combustible, a fact which pointed to the conclusion that some substance had combined with the combustible during the process.
Though the animals have an oral siphon, they do not carry ovisacs like the siphonostomous copepods, but glue their eggs in rows to extraneous objects.
They are confined to the determination of what the truth of any matter of thought, taken for granted upon grounds psychological or other, which are extraneous to logic, includes or excludes.
Which asserts that when no extraneous forces act the sum of the kinetic and potential energies is constant.
Of a far more complicated nature than these offerings are the Soma-sacrifices, which, besides the simpler ceremonies of this class, such as the Agnishtoma or "Praise of Agni," also include great state functions, such as the Rajasuya or consecration of a king, and the Asvamedha or horse-sacrifice, which, in addition to the sacrificial rites, have a considerable amount of extraneous, often highly interesting, ceremonial connected with them, which makes them seem to partake largely of the nature of public festivals.
Nature according to him is purely physical; it has no purpose, no will, no laws imposed by extraneous authority, no supernatural ethical sanction.
Secondly, the application of extraneous matter to the body, as painting and tattooing, and the raising of ornamental scars often by the introduction of foreign matter into flesh-wounds (this practice belongs partly to the first category also).
If, therefore, the walls of the enclosure held the gas that is directly in contact with them, this equilibrium would be the actual state of affairs; and it would follow from the principle of Archimedes that, when extraneous forces such as gravity are not considered, the gas would exert no resultant force on any body immersed in it.
The relation between the three forces acting on any particle, viz, the extraneous force and the tensions in the two adjacent portions of the string can be exhibited by means of a triangle of forces; and if the successive triangles be drawn to the same scale they can be fitted together so as to constitute a single force-diagram, as shown in fig.
Regarded as a " correction " to be applied to the results of experiments on magnetic change of length, the magnetic stress being no less an extraneous effect than a stress applied mechanically.
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.'