882 



ƒ([!]) being the function defined in the first chapter of the "In- 

 vestigations". From this definition results (with the notation of this 

 chapter) : 



2n 



Oe 2n:J Oe A 







da c ■ 



For a given value of 111 the quantity r- — (which is a function 



oe Li 



of [1] and [3] only, as regards the angular variables) can be developed 

 thus : 



_^ = p, +p,co5[3] -f p, co«2[31 + ... -{-pnCosn[d] \- . . .) 

 -\- q, sin [3J -i- q, sin 2 [3J + . . . f qu sin 7i ['S] -\~ . . .) 

 Then we have: 



a/([i]) .3. 



oe 



and : 



1 —1 /d a'\ 



- iM — ~ = Po + />« -t- />2,. -h P3- + • • • , (4) 



n t=o \0e LsJ t 



/d a'\ d «' In 



( ^ — being the value of — -- for 31 = — .». 



(6) 



r = - 2 K- T I — P» — /'S,. — P3» — • • • 



We are able to judge of the magnitude of the coefficients p„ for 

 large values of n by considering the mean values 



1 "-1 /d a'\ 



n s=o We A/s' 

 for different values of n. Choosing n — 270, 135, 90, 54 and 



a 

 11 1 ^ 0° and taking for the constants e and - the values of the 



table on page 3 of the "Investigations", I get: 



1 "—1 /d a'\ 

 n = 270 -£_-). 10* = - 108614 



n s=o \oe Ay, 

 135 —108614 



90 —108614 



54 —108616. 



