885 



further: 



p,, = - 15. 10-5. (16) 



Supposing the coeftieients />„ for large values of n to be of this 

 order of magnitude also if [1]7^0°, we see that we are allowed 

 to use the formula 



Oa n ,— o 



d a' 

 da A 



(17) 



without, on this account, having to fear an error in the resulting 

 d/([l]) 



values of a '"' V" "" larger than half a unit of the fifth decimal, if 

 Oa 



n>90. 



cl/([l]) 



In the next table I have collected the values of a —^ , computed 



oa 



according to this formula; for [1] = 0° I took n = 270, for the remaining 



a' 

 values of flj /2 = 135; the values of the constants « and — are those 



■' a 



of the table on page 3 of the "Investigations". 



The function a — r — is an even function of [1]; putting [1] = 

 oa 



= qsimv, q being a constant, the development becomes: 



da 



:=: X (»') = JS" ^27» COS 2n 



(18) 



I take qz=-\-^6°, thus putting [1] = -\- 36° sin ?v ; if from this 

 last equation we compute a value of lu in the first quadrant for 

 each value of [IJ from the preceding table, we have the value of 

 X{w) for six values of to and thus six linear equations, from which, 

 putting /,,, /,^, . . , etc. zero, /,, /,,.., /,o can be solved. The coeffi- 

 cients /,, /g and /i, appear to be zero and the following develop- 

 ment of X(w) results: .-£3-;ir^ ,- 



