100 Mr. R. Moon on the Law of Gaseous Pressure. 



as we have stated, Mollweide gave a demonstration in 1808. 

 In his second way, Delambre makes use of a diagram from 

 which he obtains both his own Analogies and those of Napier. 

 This way of demonstration is substantially the same as that 

 which was independently discovered and printed in the ' Pro- 

 ceedings of the London Mathematical Society/ vol. hi. p. 13. 

 One step in the recent process, however, is simpler than the 

 corresponding step in Delambre's, namely the proof of the equa- 

 lity of the angles M VA and C V P. 



It may be remarked that if one of Napier's Analogies is given, 

 we may deduce another immediately by using one of the trian- 

 gles associated with the fundamental triangle ; and then Napier's 

 two other Analogies follow by the aid of the polar triangle. 

 Thus we may say that the other three may be deduced immedi- 

 ately from any one of them. But with respect to Delambre's 

 Analogies, the case is rather different. Take these in the order 

 in which they are given in my ' Spherical Trigonometry.' Then 



(1) and (4) are so related that either can be deduced from the 

 other by using an associated triangle ; but nothing new is ob- 

 tained from (1) or from (4) by using the polar triangle. And 



(2) and (3) are so related that either can be deduced from the 

 other by using an associated triangle, or by using the polar tri- 

 angle. Thus from one of Delambre's Analogies we cannot de- 

 duce immediately the other three. If one of Napier's Analo- 

 gies is given and one of Delambre's, we can deduce immediately 

 the other six. Also the other six may be deduced immediately 

 from (1) and (2) of Delambre's Analogies; and the other six 

 may be deduced immediately from (3) and (4) of Delambre's 

 Analogies. 



I. TODHPNTER. 



Bourne House, Cambridge. 



XIII. On the Law of Gaseous Pressure. By Robert Moon 

 M.A.j Honorary Fellow of Queen's College, Cambridge*. 



I DESIRE to offer some remarks upon Mr. Strutt's further 

 criticism t of my views as to gaseous pressure, for which I 

 have not had opportunity hitherto. 



I fail to find in Mr. Strutt's second paper any reply to my 

 inquiry why we are to reject the formulae 



a 2 



K v+c p)> (1) 



* Communicated by the Author. 



f See Phil. Mag. for September last. 



