Vibrations of a Circular Membrane. 53 



2 ' f* 



critical temperature — and 1 -f ^ are constant. Therefore, 

 from (3) m 1 



T c 



— | = constant. 



»o 



That is, the critical temperature, and therefore C also, is 

 proportional to the fourth. power o£ the true atomic radius. 

 The truth of this law depends on the accuracy of the two 

 laws previously given, and the figures given in column 4 of 

 Table IV". are expected to be constant. The numbers in 

 column 2 are relative to helium. 



Table IV. 



Gas. 



»o- 



Tc. 



*0 



(To)*" 



He 



100 

 1:21 

 1-53 

 1-65 



1-83 

 1-93? 



5? 



62? 



1556 



2105 



288 

 377 



0-669 

 0433 

 0433 

 0-433 

 0-444 

 0-438 



Ne 



A 



Kr 



X 



Em 





The values to which doubt attaches or which are deduced 

 from previous considerations in this paper are marked with 

 a query. Helium, as one would expect, is an exception. 

 This and the constancy of the remaining ratios are direct 

 consequences of the relations previously given. 





VIII. Note on BesseVs Functions as applied to the Vibrations 

 of a Circular Membrane. By Lord Rayleioh, O.M., 

 F.R.S.* 



IT often happens that physical considerations point to 

 . analytical conclusions not yet formulated. The pure 

 mathematician will admit that arguments of this kind are 

 suggestive, while the physicist may regard them as con- 

 clusive - . 



The first question here to be touched upon relates to the 

 dependence of the roots of the function J n (z) upon the order 

 * Communicated by the Author. - 



