Notes to the Meditation on Poncelet's Theorem. 525 



into two divisions, one of which is to use the A right pitch, the 

 other the A left" &c. I content myself with simply asserting 

 the fact as I have found it. 



The reason for this difference of hearing is probably that the 

 external passage of the ear is set in vibration, like a speaking- 

 trumpet, by the sounds that enter it, and that this vibration 

 modifies the pitch of the entering sound more or less according 

 to the form of the individual ear. 



The supposition that the waves of sound, before impinging on 

 the tympanum, have to pass through a thin film which covers it, 

 is less probable, since such a film would of course be subject to 

 change from time to time, and thus the whole phenomenon 

 might be altered. 



As may be supposed, I have not as yet been able to collect 

 any information on this subject. 



If, in measuring the number of vibrations of musical notes, 

 the above circumstance has not been taken into account, some 

 modest doubt of the accuracy of the results may not be altogether 

 unreasonable. 



Cologne, September 1860. 



LXXII. Notes to the Meditation on Poncelet's Theorem, including 

 a Valuation of the two new Definite Integrals 



*»£ log cos <£ rl log (l+V^— b 2 (cos <f>) % ) 



By J. J. Sylvester, M.A.,F.R.S., Professor of Mathematics 

 in the Royal Military Academy, Woolwich*. 



Note A. 



THE method given in the October Number of the Magazine 

 for approximately representing a quadratic surd by a 

 rational fraction is equally applicable to a surd of any degree. 

 To fix the ideas, suppose we wish to approximate in this manner 



to-v/ll 



If we assume N as the first approximation, and make 



i^p+v 7 !^ m=p+ j0 v / e; n=p+/9 2 ^/r; 



where p 3 = l, and write 



Communicated by the Author. 



