CAYLEY ON NEWTON'S LAWS 235 



I have said in my article that no one who has ever rolled a pea on the table under 

 the tips of his index and middle fingers, crossed, will afterwards believe anything 

 whatever on the testimony of his "muscular sense" alone. Yet what other ground 

 have we, for believing in the objectivity of force, than the impression on our muscular 

 sense ? 



On January 20, 1883, Cayley replied : 



" Dear Tait, 



I ought to have written ever so long ago in answer to your question as to 

 the construction of a system of mechanics from general principles without Force, 

 Momentum, or Impulse but it could only have been to say that I did not know of any 

 attempt at such a construction the idea was quite new to me, and I have not taken it 

 in enough to see anything about it myself so that you will have lost nothing by the 

 delay. I hope your proposed communication to the R.S.E. will be published " 



On February 26, 1883, Cayley acknowledged receipt of the Paper in 

 these words : 



" Dear Tait, 



The whole discussion is beyond me I understand force I do not under- 

 stand energy. I am willing to believe that Newton's Action = Reaction potentially 

 includes d'Alembert's principle but I never saw my way with the former, and do see 

 my way with the latter and I accept Virtual Velocities + d'Alembert's principle as the 

 foundation of Mechanics. In this position of outer darkness, it would be quite useless 

 to attempt any remark on your paper. 



" I send herewith a paper from the A.M.J.; please look at the statement pp. 2-4 of 

 Abel's theorem in its most simple form " 



Tait replied as follows : 



38 GEORGE SQUARE, 

 EDINBURGH. 



28/2/83. 

 My dear Cayley, 



Many thanks for your paper, which I have already looked at and will read. 

 It seems to me that this work may, with a little trouble, be brought to bear on the very 

 important and difficult question of Kinetic Stability. If so, I hope you will develop it 

 largely. I suppose you know Boole's paper in Phil. Trans. It was from it that I first 

 got a notion of what Abel's Theorem really means. 



Your disclaimer in reference to my Abstract is really a vote in my favour. For 

 Virtual Velocities is merely the principle of Energy in a mathematical guise ; and 

 d'Alembert's principle is either the first or second interpretation of Newton's Lex III ; 

 and you say that you adhere to them. 



I say advisedly, either the first or second, for there are two quite distinct things 

 which go by the name of d'Alembert's principle : 



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