The Dynamics of Particles And of Rigid, Elastic, And Fluid Bodies: Being ...

Cover The Dynamics of Particles And of Rigid, Elastic, And Fluid Bodies: Being ...
The Dynamics of Particles And of Rigid, Elastic, And Fluid Bodies: Being ...
Webster, Arthur Gordon, 1863-1923
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der Phjs. n. Chem. S6, p. 177, 1898.
Digitized by VjOOQIC 12S, 1*4, 125] CHARACTERISTICS OF POTENTIAL, 363 2^. Its first partial derivatiTes are eYerrwhere holomorphic 3*^. Its second deriTatives are finite.
4*^. V yanishes at infinity to the first order, Urn (JRF) = 3f ; >j-> 0-' s~ vanish to second order.
Ox dy OS ' y b^. V satisfies everywhere Poisson's differential equation lim(i?|^) = -3fcos^.
d^^ + W^ '^' ^ " ^""^^ and outside of attracting matter, Laplace's equation c*V d*V d*V _ ^ Any f
...unction having all these properties is a Newtonian potential function.
The field of force X, Y, Z is a solenoidal vector at all points outside of the attracting bodies, and hence if we construct tubes of force, the flux of force is constant through any cross -section of a given tube. A tube for which the flux is unity will be called a unit tube. The conception of lines of force and of tiie solenoidal property is due to Faraday.
Since F is a harmonic function outside of the attracting bodies, it has neither maximum nor minimum in free space, but its maximum and minimum must lie within the attracting bodies or at infinity.


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