Displaced by the sphere, and assumes a statical state of conditions and that the conductor itself exerts no disturbing influence.
If V be the potential, p the density of free electricity at a point in the atmosphere, at a distance r from the earth's centre, then assuming statical conditions and neglecting variation of V in horizontal directions, we have r2 (d/dr) (r 2 dV/dr) - - 4.rp = o.
Gauss had shown how to reduce all the phenomena of statical electricity to mere attractions and repulsions exerted at a distance by particles of an imponderable on one another.
This paper of Thomson's, whose ideas Maxwell afterwards developed in an extraordinary manner, seems to have given the first hint that there are at least two perfectly distinct methods of arriving at the known formulae of statical electricity.
This was, of course, even more repugnant to Maxwell's mind than the statical distance-action developed by Poisson.
Although modern mercurial pumps have assumed a multiplicity of forms, their actions can be reduced to two principles, one statical, the other hydrodynamical - at the same time instruments have been devised utilizing both these principles.
Calling the sum of the pressure and potential head the statical head, surfaces of constant statical and dynamical head intersect in lines on H, and the three surfaces touch where the velocity is stationary.
Social physics will consist of the conditions and relations of the facts of society, and will have two departments, - one, statical, containing the laws of order; the other dynamical, containing the laws of progress.
It abounds with remarks of extraordinary fertility and comprehensiveness; but it is often arbitrary; and its views of the past are strained into in the coherence with the statical views of the preceding volume.
Hales is best known for his Statical Essays.
Hydro- statical principles can be applied to density determinations in four typical ways: (I) depending upon the fact that the heights of liquid columns supported by the same pressure vary inversely as the densities of the liquids; (2) depending upon the fact that a body which sinks in a liquid loses a weight equal to the weight of liquid which it displaces; (3) depending on the fact that a body remains suspended, neither floating nor sinking, in a liquid of exactly the same density; (4) depending on the fact that a floating body is immersed to such an extent that the weight of the fluid displaced equals the weight of the body.
The general theory of this kind of brake is as follows: - Let F be the whole frictional resistance, r the common radius of the rubbing surfaces, W the force which holds the brake from turning and whose line of action is at a perpendicular distance R from the axis of the shaft, N the revolutions of the shaft per minute, co its angular velocity in radians per second; then, assuming that the adjustments are made so that the engine runs steadily at a uniform speed, and that the brake is held still, clear of the stops and without oscillation, by W, the torque T exerted by the engine is equal to the frictional torque Fr acting at the brake surfaces, and this is measured by the statical moment of the weight W about the axis of revolution; that is T =Fr=WR...
The value thus obtained is generally appreciably greater than that obtained by a statical method in which the rod is pulled out by an applied tension.
This may be termed the statical breaking strength.
For a statical load, range of stress nil, A=0, kmax.
= K, the statical breaking stress.
Let t be the statical breaking strength of a bar, loaded once gradually up to fracture (t = breaking load divided by original area of section); u the breaking strength of a bar loaded and unloaded an indefinitely great number of times, the stress varying from u to o alternately (this is termed the primitive strength); and, lastly, let s be the breaking strength of a bar subjected to an indefinitely great number of repetitions of stresses equal and opposite in sign (tension and thrust), so that the stress ranges alternately from s to -s.
In his Statical Essays (1727) he gave an account of numerous experiments and observations which he had made on the nutrition of plants and the movement of sap in them.
The polarization itself is determined from the electric force (P,Q,R) by the usual statical formula of linear type which becomes tor an isotropic medium (.f',g',h') = c2(P,Q,R), because any change of the dielectric constant K arising from the convection of the material through the aether must be independent of the sign of v and therefore be of the second order.
Poinsot's earliest work was his Elemens de statique (1803; 9th edition, 1848), in which he introduces the idea of statical couples and investigates their properties.
And throughout, wherever the survival from 1843, the identity bug-bear, is for the moment got rid of in what is really a more liberal conception, the statical doctrine is developed in a brilliant and informing manner.
Lotze's logic then represents the statical aspect of the function of thought in knowledge, while, so far as we go in knowledge thought is always engaged in the unification of a manifold, which remains contradistinguished from it, though not, of course, completely alien to and unadapted to it.
As a simple example of the geometrical method of treating statical problems we may consider the equilibrium of a particle on a rough inclined plane.
This is essentially a theorem of projective geometry, but the following statical proof is interesting.
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.
Independent statical proofs are of course easily given.
If c be the statical increase of length which is produced by the gravity of the mass M, we have Kc=Mg, and the period is 2 ~r~t(c/g).
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=--~.
According to dAlemberts formulation, the extraneous forces together with the effective forces reversed fulfil the statical conditions of equilibrium.
The motion being assumed to be small, the tensions of the two strings may be taken to have their statical values Mgb/(a+b), Mga/(a+b), where a, b are the distances of G from the two threads.
This fruitful conception, however, Bacon does not work out; and though he uses the word cause, and identifies form with formal cause, yet it is perfectly apparent that the modern notions of cause as dynamical, and of nature as in a process of flow or development, are foreign to him, and that in his view of the ultimate problem of science, cause meant causa immanens, or underlying substance, effects were not consequents but manifestations, and nature was regarded in a purely statical aspect.
His general conception of the universe may therefore be called mechanical or statical; the cause of each phenomenon is supposed to be actually contained in the phenomenon itself, and by a sufficiently accurate process could be sifted out and brought to light.
But The Truth Is That A Complete Solution Of The Statical Problem For All Forms Up To That At Which Instability Sets In, Would Not Suffice For The Present Purpose.
The degree of instability, as measured by q, is not to be determined from statical considerations only; otherwise there would be no limit to the increasing efficiency of the longer wavelengths.
Since the only cause for these convection currents is the statical instability produced by radiation, and the rapid stifling of radiations within the body produces there a temperature gradient falling very slowly, they would be for the most part extremely slight.
Rapidly falling temperature must (and visibly does) produce furious motions which wholly outrun mere restoration of statical balance.
The statical experiments of C. H.