Obviously equimolecular surfaces are given by (Mv) 3, where M is the molecular weight of the substance, for equimolecular volumes are Mv, and corresponding surfaces the two-thirds power of this.
Hence S may be replaced by (Mv) 3.
Ramsay and Shields found from investigations of the temperature coefficient of the surface energy that Tin the equation y(Mv) 3 = KT must be counted downwards from the critical temperature T less about 6°.
Their surface energy equation therefore assumes the form y(Mv)i=K(T-6°).
N is the mean number of molecules which associate to form one molecule, then by the normal equation we have y (Mnv) 3 =2.121(r -6°); if the calculated constant be K 1, then we have also y(Mv)3=K,(r-6°).
Since the volume is constant, we have the condition mv'--l-(I-m)v"=constant.
If 2mu 2 denote the mean value of 2mu 2 averaged over the s molecules of the first kind, equations (3) may be written in the form Z mu g = 2 mv 2 = 2 mw 2 = 2x,0 2 1 =.
We accordingly put 1/2h = RT, where T denotes the temperature on the absolute scale, and then have equations (7) in the form mu 2 = mv '2 = ...
As, however, our terrestrial optical apparatus is now all in motion along with the matter, we must dealt .with the rays relative to the moving system, and to these also Fermat's principle clearly applies; thus V+ (lu'--mv'-Fnw') is here the velocity of radiation in the direction of the ray, but relative to the moving material system.
If m and m' are the masses, v and v' their initial velocities, and V the common velocity, then m(v - V) = m'(V - v'), therefore m + m')V, and hence (m y + m'v')f(m m') = V.
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We may also write ur 1 = I +zu 1+ &c., since z is very small compared with u, and expressing u in terms of w by (25), (we find l 21- mv i fi(z) i I +z(c R w + ' R 2 w) do) = 27rmoti(z) I -f-ZZ (Ki + R2/ This then expresses the work done by the attractive forces when a particle m is brought from an infinite distance to the point P at a distance z from a stratum whose surface-density is a, and whose principal radii of curvature are R 1 and R2.