Runs mathematically straight and points almost absolutely true for the Polar star.
He also made important contributions to the mathematical theory of electrodynamics, and in papers published in 1845 and 1847 established mathematically the laws of the induction of electric currents.
Oliver Heaviside showed mathematically that uniformly-distributed inductance in a telephone line would diminish both attenuation and distortion, and that if the inductance were great enough and the insulation resistance not too high the circuit would be distortionless, while currents of all frequencies would be equally attenuated.
Amongst the earliest mechanical contrivances of Fraunhofer was a machine for polishing mathematically uniform spherical surfaces.
This equation, which is mathematically deducible from the kinetic theory of gases, expresses the behaviour of gases, the phenomena of the critical state, and the behaviour of liquids; solids are not accounted for.
When the interval is very small the discrepancy, though mathematically existent, produces no practical effect, and the illumination at B due to P is as important as that due to A, the intensities of the two luminous sources being supposed equal.
The choice between various methods of resolution, all mathematically admissible, would be guided by physical considerations respecting the mode of action of obstacles.
His not wholly satisfactory explanation was mathematically examined in 1835 by Richard Potter (Camb.
Mathematically we have thus in all cases to compute present value on the basis of a deferred as well as a limited annuity.
Most of the writers already noticed worked out the problems connected with the projection of images in the camera obscura more by actual practice than by calculation, but William Molyneux, of Dublin, seems to have been the first to treat them mathematically in his Dioptrica Nova (1692), which was also the first work in English on the subject, and is otherwise an interesting book.
This capacity is then a function of the geometrical dimensions of the conductor, and can be mathematically determined in certain cases.
This is mathematically expressed by the statement that dE is an exact differential of a function of the co-ordinates defining the state of the body, which can be integrated between limits without reference to the relation representing the path along which the variations are taken.
It was mathematically treated by Louis Carre in 1705 and Koersma in 1741.
It can be shown mathematically that the velocity of propagation will be greatly increased if the frequency of the light-wave is slightly greater, and greatly diminished if it is slightly less than the natural frequency of the molecules; also that these effects become less and less marked as the difference in the two frequencies increases.
The combination of ductility, which lessens the tendency to break when overstrained or distorted, with a very high limit of elasticity, gives it great value for shafting, the merit of which is measured by its endurance of the repeated stresses to which its rotation exposes it whenever its alignment is not mathematically straight.
In treating mathematically the propagation of other kinds of waves, it is necessary to analyse them into their simple-harmonic components, which may be treated as being propagated independently.
In astronomy he depreciates the merits of Newton and elevates Kepler, accusing Newton particularly, a propos of the distinction of centrifugal and centripetal forces, of leading to a confusion between what is mathematically to be distinguished and what is physically separate.
For long periods he was mathematically unproductive, but then sudden inspiration would come upon him and his ideas and theories poured forth far more quickly than he could record them.
It has now been firmly established, both experimentally and mathematically, that coronae are due to diffraction by the minute particles of moisture and dust suspended in the atmosphere, and the radii of the rings depend on the size of the diffracting particles.
Any scheme of abstract dynamics constructed in this way, provided it be self-consistent, is mathematically legitimate; but from the physical point of view we require that it should help us to picture the sequence of phenomena as they aCtually occur.
We may briefly notice the case of resistance varying as the square of the velocity, which is mathematically simple.
Unfortunately, the return of age is amongst the less satisfactory results of a general enumeration, though its inaccuracy, when spread over millions of persons, is susceptible of correction mathematically, to an extent to make it serve its purpose in the directions above indicated.
Weber at the same time deduced the mathematical laws of induction from his elementary law of electrical action, and with his improved instruments arrived at accurate verifications of the law of induction which by this time had been developed mathematically by Neumann and himself.
In this assertion we think he was mathematically wrong, though in his own hypothesis that the density does actually vary, he was probably right.
Z, (39) K o = 4 7 (- 4, To = 3715 (40) The range of the attractive force is mathematically infinite, but practically of the order (31, and we see that T is of higher order in this small quantity than K.
These figures of revolution have been studied mathematically by C. W.
The limiting conditions of the stability of these figures have been studied both mathematically and experimentally.
Stefan's law of radiation according to the fourth power of the temperature is too difficult to pursue, but if we are content with cognate results we can follow them out mathematically in a hypothetical law of the first power.
With this conception of the infinite as absolutely unconditioned should be compared what may be described roughly as lesser infinities which can be philosophically conceived and mathematically demonstrated.
Such are the evangelical principle of " doing as you would be done by the principle of justice, or " giving every man his own, and letting him enjoy it without interference "; and especially what More states as the abstract formula of benevolence, that " if it be good that one man should be supplied with the means of living well and happily, it is mathematically certain that it is doubly good that two should be so supplied, and so on."
This subject is mathematically discussed in the article Geometry: Projective.