On the Liquid and Gaseous States of Matter. 665 



As a matter oE fact Milne's numbers are better represented 

 by Bateman's formula if 0, 5'69, '45 are substituted for his 

 constants '4, 6*1, "5; and these give 9 ' 7 7 km. per sec. for the 

 speed at the surface. 



But, as Bateman's Table indicates, there is a depth at which 

 v has a maximum value: this occurs when J] 2 ^ 2 /v 2 =l — E~t, 

 in which ciselog (v/U) = E(tanh _1 E~3 -E~£), corresponding 

 to sine = E~3 with = (A/B) sin 2 ^e, i. e. with the above 

 constants to e=79^°, 0=154°; and for higher values of e the 

 solution will not apply, as there will be no total reflexion 

 of the wave. 



For the solution to be applicable throughout the earth and 

 with perfect symmetry we must have for the maximum speed 

 6 = -i-7r, or E = l (i. e. B = A/27r) with a formula of the type 

 T=A0-B0 2 . The value 11-12 for A with 6 expressed in 

 radians gives Milne's results with very fair exactness, and 

 thus 9*55 km. per sec. for the speed at the surface, the limiting 

 speed at the centre being \e times greater*, where e is the 

 base of Naperian logarithms. 



Christ Church. Oxford. 

 26 July, 1910. 



LXXIII. On the Equation of Continuity of the Liquid and 

 Gaseovs States of Matter. By B. 1). Kleeman, JD.Sc, 

 JB.A.j Machinnon Student of the Royal Society f. 



HPHE writer J has shown that the attraction between 

 JL two molecules besides that due to gravitation sepa- 

 rated by a distance z is 



J*(Jj^)(*/^>*, 



where ,r c is the distance of separation of the molecules in 

 the critical state, T is the temperature and T c the critical 



T . 



temperature, and ^ = r ^-. and Xx/m^ is the sum of the square 



roots of the atomic weights of the atoms of a molecule ; 



* In a problem suggested by Benndorf s and Herglotz's important papers 

 (' Science Abstracts ' for 1907, Xos. 883 and 98o), and .<-et in Jan. H 08 

 for the Senior Mathematical Scholarship Examination of the University, 

 I asked for the deduction of the relation = 2e--sin 26 from the fancv law 

 T = 4(R/TJ) sin 3 e, and also, Abel's transformation being cited, for the 

 proof that the ratio of the speeds at the centre and surface is \le. 



f Communicated by the Author. 



X Phil. Mag. May 1910, p. 783 : in subsequent references to this paper 

 it will be called (a). 



