Mr Sharpe, On the Reflection of Sound at a Paraboloid. 133 



On the Reflection of Sound at a Paraboloid. Part II. By 

 The Rev. H. J. Sharpe, late Fellow of St John's College, 

 Cambridge. 



[JReceived April 1905.] 



38. The present Paper is a continuation of one with the 

 same title that appeared in 1899 in Vol. x. Part in. of the Pro- 

 ceedings of the Society. In it the Articles, Figures, and Equations 

 will be numbered on continuously from the 1st Paper. But 

 before going any further perhaps it will be well to correct some 

 Errata in the previous Paper. In Art. 3, No. 19 should be 

 No. 119. In Art. 11 after " u = " add " v being finite." In Art. 

 12 for the sentence "Also for a given reflector, &c." read "Also for 

 a given reflector, and a given distance from 0, high sounds are 

 more magnified than low ones." In Art. 13 for A = B = tt^ read 

 A = B = 7r~K In Art. 17, after the words "will be proportional 

 to," instead of what follows, read 



1_ V + £#-*■• 



The sentence after this can be readily corrected. 



In Art. 19 after (40) in the next line dele "or negative." In 

 the next line after the words " large values of A are " insert 

 " positive and." Towards the end of Art. after the words " when 

 u = " insert " and v is finite." In the last two lines of Art. 24 

 some correction is required. In Art. 21, Equations (47) to (48) 

 require correction. In Art. 20 in 3rd line for " large value " read 

 " large values." Art. 30 requires some correction. In Art. 36 

 and so in the results (92) and (93) I am doubtful about the results 

 obtained, but I hope to exhibit a better way of evaluating the 

 definite integrals involved. In Art. 37 a correction must be made, 

 for which my thanks are due to Prof. Larmor. 



Dele the sentence beginning " Here if v is increased, &c." The 

 true explanation is that as the progressive wave gets further and 

 further along the axis, its velocity which was at first rather > a. 

 gradually slows down till it ultimately = a. 



39. I propose in this Paper to consider more fully the case of 

 A = 0, but before doing so I should like to consider one or two 

 simple problems, which are analogous to the whole Problem before 

 us, whatever be the value of A, and which, it seems to me, throw 

 some light upon it. Suppose (Fig. 8) xx an infinite cylindrical 

 tube filled with air, stopped at and open towards x and x. 



