520 Appendix to Mr. Drach's Paper on Epicyclic Curves. 



any contradiction. I infer that the supposition of plane-waves 

 is not allowable. 



I have been induced to make the last remark from having 

 seen it asserted by the Astronomer Royal in the Number of 

 the Philosophical Magazine for June, that I have pointed out 

 a difficulty in the interpretation of an equation applying to the 

 caseof plane- waves. Mr. Stokes asserted the same thing before; 

 and I then disclaimed, as I now disclaim, having pointed out 

 any difficulty. The equation is a very simple one, and easily in- 

 terpreted. A few steps of plain deduction conducts to a result 

 incompatible with fluid motion. It follows in due course that 

 the supposition of plane-waves cannot be made. This infer- 

 ence is in perfect accordance with the argument contained in 

 this communication, which I think Mr. Airy may find to be 

 worthy of some consideration. Any other inference would 

 have presented a real difficulty. 



Cambridge Observatory, 

 June 22, 1849. 



LXXV. Appejidix to Mr. Drach's Paper on Epicyclic 

 Curves in the last Jime Number. 



A NOTHER example, with series expanded. 



5 



n^-^-.-.p + q^^l, g=2. 



Let Q = Q'.a6. The equation is 



1^7 _ 7^2^ (2a?)5H- 14r4(2^)3-7r6(2^) = a7(Q/2_2) + 7«^^Q' 

 + A<2a^b^-\-S5a'^t^Q!-^S5aH\Q^-2)-^2la^b\Q!^-S(^) 



+ 7«i6(Q'4_4Q^2 _^ 2) + 67(Q/5__5Q^3 ^. 5Q^). 



When a = 6, the second member 



= a7{(Q' + 2)5^3(Q' + 2)4=rio«-J0-3r8a-8} 

 = r'^[r^a~^ — 3ra~^"^f 

 agreeably to Case 2. 



The following errors have to be corrected in the last 

 Number. 



Ex. o ^ Q ^ Q«^ 



n^^Sfor ^ read -^; 



