332 Lord Rayleigh on Stability of Simple Shearing 



arithmetic has been given already by Stokes*. Thus from 

 the ascending series 



Sl {2) = -13*330] 0, ^(2) = 11-62838; 

 s 2 {2) = - 2-25237, t 2 {2) = -11-44664. 



In calculating from the descending series the more important 

 part is Xi, since 



-%c z ' 2 -2i 3 'V /2 V 2.^3/2(1-0 



e = e ' = e 



For 77 = 2 Stokes finds 



2i= -14-98520 + 43-81046 i, 



of which the log. modulus is 1*6656036, and the phase 

 + 108° 52' 58"*99. When the multiplier C or C is intro- 

 duced, there will be an addition of +30° to this phase. 

 Towards the value of S : I find 



-13-32487 + 11-63096 i ; 



and towards that of S 2 



- 2-24892- 11-44495 L 



For the other part involving D or D' we get in like 

 manner 



- -00523- -00258 i, 



and - -00345- '00170 i. 



It appears that with the values of C, D, C, D' defined by 

 (16), (17) the calculations from the ascending and descending- 

 series lead to the same results when rj = 2. What is more, 

 and it is for this reason principally that I have detailed the 

 numbers, the second part involving 2 2 loses its importance 

 when 7] exceeds 2. Beyond this point the numbers given in 

 the table are calculated from 2i only,. Thus (?7>2) 



, 1 + a i = lV*, V2 -* 3 V*'< V2^ 2 +./8-,/6) 



s, f i 1-5 1.5.7.11 1 



I 1.144(^) 3 > 2+ 1.2.144 2 (^) 3 '"J 9 K J 



f 1.5 1.5.7.11 1 . 



\ 1.144(i'77) 3 / 2+ 1.2.144 2 (i77) 3 "'J' ^ } 



* Loc. cit. Appendix. It was to take advantage of this that the 

 4i 9 " was introduced in (5). 



