180 



APPENDIX. 



< ==()+ (i A + h K), 



" = (,) + *L ( m + A + h + k), 



M. (<a) 



> = () + T^T ( ~ A - h + k), 



,' = () + ^ ( m + A - A - k). 



2 o 



But the values of h k m in (20) will now become h = sin. 2 /3, A = cos. 2 $ and * = 



-2 



jE_. We have finally, therefore, 



- V 



cos 



. 2 /3 - A ) 



(23). 



M \ r 

 ' = () + _L_ (A) 



The expression (21) gives to A the following values in parts of p for every fifth degree ofthe 

 arc /3 : 



ft A. A 



0-0000 30 + -0327 



5 + -0201 35 -0234 



10 -0334 40 + -0121 



15 -0404 45 -0000 



20 -0421 50 - -0121 



25 -0393 55 -0234 



30 + -032? 60 - -0327 



On examining the values (23) we observe that the greatest velocity takes place in the 



quadrant of D", and at the point where A attains its greatest positive value, viz., at 19 from 



H ; we also perceive that the least velocity occurs in the quadrant of D' and at the point 



where A attains its greatest negative value, viz., at 71 from E; and that the mean angular 



velocity is (o>) + 



M 



o 



. - . We have therefore, 

 2r 



Position when the velocity is greatest. 



Maximum 1 



Vvalue of <a = ' 

 Minimum I 



Greatest deviations "l 

 from mean value J 



"(.) + 1 r r r ( ^ +0-042) 

 M V r 



._ 

 M () \ 2 r 



Position when the velocity is least. 



