If there are no extraneous forces, the resultant linear momentum is constant in every respect.
In the Fragmente he aims at nationalizing German poetry and freeing it from all extraneous influence.
Partaking human food is now extraneous, yet can still be quite enjoyable.
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).
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.
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.
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.