218 Mr. Moon in Reply to Jesuiticus. 



were of that character, it would immediately cease to be so, 

 or in short, that a transversal undulation (if I may be per- 

 mitted the expression) would not be propagated according to 

 any law. With a full sense of the value of Mr. Airy's con- 

 tributions to other departments of science, I cannot shut my 

 eyes to the fact, that by allowing such investigations as the 

 one under consideration (which but for its adopted parentage 

 would not be worth a comment) to pass not merely Avithout 

 censure, but with apparent sanction, he has introduced an 

 absence of precision, — a laxity of principle (so to speak) into 

 mathematical inquiries, which has produced the most injurious 

 effects both in the mixed and the pure sciences. 



But to come to the error which Jesuiticus imagines he has 

 found in my reasoning. He says, " that in substituting for u, 



and for w', 



du 7 d*u W 



du 7 d? u h 2 n 

 dx d x z 1 . 2 



the substitutions stopping at 7i 2 , merely require that h should 

 be small in comparison with the length of a wave, not in re- 

 spect to u" 



It is true that if we suppose the initial disturbance to be 



2 TV 



represented by a sin — (v t — x), the substitutions stopping at 



/i 2 are defensible on the ground suggested by Jesuiticus ; but 

 does Jesuiticus conceive that when Mr. Airy wrote out this 

 demonstration, he ever thought about the length of the wave, 

 or any other circumstance connected with the initial vibration ? 

 If he does, I can only say that he is a very extraordinary per- 

 son. In my paper I took Mr. Airy's investigation for what 

 it purported to be, namely a proof that a certain hypothesis 

 as to the disposition of the particles and the nature of their 

 mutual action, without reference to the form of the initial dis- 

 turbance, leads to the conclusion that transversal undula- 

 tions may be propagated ; and in that point of view I have 

 no hesitation in saying it entirely fails ; and, independently 

 of all others, on the ground I have pointed out, i. c. of false 

 approximation. If Jesuiticus has any doubt as to whether 

 Mr. Airy did or did not consider himself to have proved the 

 proposition generally, I would recommend to his attention 

 Art. 127 of Mr. Airy's Tract, in which he takes the general 

 integral of the equation 



