884 



putting ^j,, ^j^, ..., etc. zero, k^,k^, . . . ,ky^^ can be solved. The 

 coefficients k^ and ^,, appear to be zero and the following develop- 

 ment of i|> {w) results : 



10» . ±}:LJl — 10'. y^^{u^= - 108151 

 oe 



— 484 CO» 2 V' 



\ (10) 

 4-21 co« 4 «> 



-|- 1 CO* 6 u> . 



3. The derivative of the function /([I]) with respect to a is 

 determined by the formula 



^^([1])^ 1 fa^^o^LSJ. (11) 







a' 

 For a given value of [1] the quantity <i ^ '~ ^^'^' ^® developed 



thus: 



d a' 



a — — = p, -f p, CO» [3] -f ;?, cos 2 [3] + . . . + p„ cos n [3] -^ . . . ) 



da ZA \\}^) 



-f y. Bin [3] -}- ^, siVi 2 [3] -|- • . ■ -^ qn sin n [3] + • • • ' 



Thus: 



a/([l]) IV/" Ö a'\ 



da n 4=0 V "<* ^/« 



l"-i/ d a'\ 

 Again we derive the mean values - -2" a — -- ) for the values 



n s=o V "« ^/5 



n =z 270, 135, 90, 54 and the value [1 ] =:= 0°. The values of the constants 



e and - are those of the table on page 3 of the "Investigations". 

 a 



We get : 



1 "-1 / d a'\ 

 n=270 - S a— - . 10' = - 110691 



135 —110691 



90 — 110691 



54 —110706. 



Thus: 



Po + p,;, + . • • = Po + pi,5 + p„, 4- . . . = po + ;?»o -r Px.o + • • : (1^) 

 and : 



/>,7. = 0. Pi.. = 0, Pm = 0; (15) 



