upon a Communication of Prof. Kelland. 343 



(2.) With respect to the equations at the foot of page 162, 

 we have 



8g 2 = £Za*+f**ip+g*# 



+ <2.{eflxly +fgly** + eglxlz). 



Hence expanding sin 2 — -£-, and omitting the parts multi- 



3S 



plied by F k 6 , &c., we have 



omitting all terms in which an odd power of either 8.r, ly or 

 82 occurs. 



Hence the term which Professor Kelland makes out to be 

 zero, equals 



ef~% /Ce2 § #2 $y\ + higher powers of h\ 



'which is clearly not zero. 



The error by means of which Professor Kelland shows 

 that this term is zero, is quite apparent in the middle of page 

 162. He reasons upon 8 p just as if it was r, i. e. the distance 

 of the particle whose coordinates are (x + $x) (y + $y) (2 + 8 s) 

 from that whose coordinates are w yz; whereas 8 p is quite 

 a different thing, namely, the perpendicular let fall from the 

 point x y z on the wave surface passing through the point 

 (x + tixj (y + $y) (2 + 82); which perpendicular is altered in 

 length when we put — hx for 8,r, leaving 83/ and 82 unal- 

 tered ; and this is fatal to Professor Kelland's reasoning. 



8 Park Terrace, Cambridge, 

 June 7, 1842. 



P.S. Oct. 7, 1842.— Professor Kelland evidently does not 

 suppose the axis of y to coincide with the direction of trans- 

 mission: for suppose that it does, then lp = 8^, and there- 

 fore equating the two expressions which Professor Kelland 

 assumes to be equal to w 2 at the foot of page 162, we have, 



v F(rK 2 • ohZy - F (r) s 9 . 2 #8y 

 2 — — 8 x* sin 2 — ■— = Z, — « 8 w 9 sin 2 -—■ ; 

 r 2 r . ■ 2 



or, retaining only the first power of k\ 



2^8tf 2 8v 2 = 2Z^-8y. 



A* <J 7* 



Now it is well known that one of these expressions is three 

 times the other. Hence Professor Kelland does not suppose 

 the axis of y to coincide with the direction of transmission. 

 The same may be said of the axes of x and *. 



