Mr. A. Cayley on a Bicyclic Chuck. 65 



it j for no account is taken of friction or viscosity. But apart 

 from all this, is it not obvious that the physical condition of a 

 small mass of air is independent of any velocity animating all its 

 parts ? If the pressure changes, why not the other properties 

 of air with it ? 



With regard to Mr. Moon^s analytical argument, I would 

 remark that the question at issue is a purely physical one. Apart 

 from their meanings, it would no doubt be difficult to establish 

 the proportionality of the symbols p and p. But Mr. Moon's 

 reasoning is fallacious. In any particular case of motion in one 

 dimension, p, v, and p are doubtless functions of x and t. Eli- 

 minate a: and t, says Mr. Moon, and you are left with p, a func- 

 tion of V as well as p. In this expression lurks an ambiguity. 

 Mathematicians often say that one quantity is a function of a 

 second, meaning that they inaj/ depend on one another, without 

 exclusion of the particular case of independence. If Mr, Moon 

 objects to this use of the word function, his inference that jo is a 

 function of v does not follow. His opponents, of course, main- 

 tain that when you eliminate A' and /, v wall disappear with 

 them; but they do not arrive at this conclusion, as Mr. Moon 

 seems to suppose (Phil. Mag. vol. xxxvi. p. 117), as the result 

 of a process similar to that adopted b}^ him. Whether an assump- 

 tion is gigantic or not depends on the grounds on which it is 

 made; and I have never heard that Boyle's law was regarded 

 otherwise than as a clear result of experiment. It is a part of 

 that result that the velocity of the containing vessel (which is 

 shared by the gas) is not an element in the matter. 



If you begin by throwing overboard the relations between 

 symbols which exist in virtue of their physical interpretation, 

 you need not be surprised if an analytical process fails to force 

 them back on you. 



I am, Gentlemen, 



Your obedient Servant, 



John W. Strutt. 



VI. On a Bicyclic Chuck. By A. Cayley, KKS."^ 



T RETAIN the former title ; but I wish chiefly to describe the 

 general plan of a curve-tracing apparatus. The arrange- 

 ment may be considered as consisting of two chucks, X, Y, ca- 

 pable of connexion in any manner, and of a pentagraph working 

 from the underside of a bridge, the pencil V on the upper sur- 

 face of chuck X, or, say, on the chuck-table X, and the pencil Q 

 on the chuck- table Y, each pencil being capable of attachment 

 to the corresponding chuck-table. 



* Communicateil by the Author. 

 Phil. Mag. S. 4. Vol. 41. No. 290. July 1872. F 



