On Boyle s Law at Very Low Pressures. 11 



Then if x = r sin 6 cos </>, y — r sin 6 sin $, z = r cos 0, it may 

 be proved that 



These equations hold both for positive and negative values of 

 w, which seems. a somewhat remarkable result*. Hence 



dx 



i=(n+2-<T)(,n-i-<T)WL-l i -y'LV-2, 



2 d^_, = _ {n + 2 _ (T) {n + l-^-qr'-l^yJ-^ 



From these equations the values of the magnetic forces are 

 obtained in their normal form, The first terms vanish for 

 the zonal harmonics for which a = ; and the second terms 

 vanish inside the sphere when ?i<cr-f-2. For the case of a 

 uniform charge we must put ra = 0, cr = 0, and obtain the 

 values previously found. The magnetic forces on any sphere 

 being of the nature of surface harmonics the expression for 

 the electromagnetic energy of the field is also calculated 

 without difficulty f. 



II. Boyle's Law at Very Low Pressures. 

 By William Sutherland %. 



f^\ REAT interest attaches to the question whether gases at 

 \~A lower and lower pressures show more and more rigorous 

 conformity with Boyle's law, or. as some experimenters have 

 maintained, after approximating to Boyle's law as a limit up 

 to a certain degree of rarefaction, at still lower pressures 

 depart from it. For the kinetic theory gives no hint that 

 departure from Boyle's law is to be looked for at low pressures; 

 so that if such a departure existed it would point to a new 

 property of matter uncontemplated in the kinetic theory. 

 Usually it is supposed that surface-condensation of gases on 



* The equations are easily generalized to give very simple expressions 

 for the pth. differential coefficient of a tesseral harmonic in terms of 

 tesseral harmonics. 



f Reference should have been made to a second paper by J. J. Thomson 

 (Phil. Mag. 1889, vol. xxviii. p. 1), in which possible effects are taken 

 into account, for which there is at present no experimental evidence. 

 The above investigation shows that the difference between the results of 

 Heaviside and J. J. Thomsons original paper are not due to the effects 

 discussed in his second paper. 



X Communicated by the Author. 



