Statistical meclianies 



19 



where 



(26) 



B, Ä 



dB dB 

 dÄ dÄ 



These four differentialcoefficients may be directly computed from the formulae 

 of § 9, through the computation is somewhat circumstautial. 

 According to (14) we have 



(27) 



sin B cos Ä= I = aj ^ -f -q + 7.3 C, 

 sin 5 sin J. = m = ^ + -q + ßg C, 

 cos B = n = 7, ^ + Y, T] -\- Y3 C, 



where = cos XH etc.. which direction cosines are expressed through ß and a in 

 the formulae (16). 



From (27) we get 



(28) 



tg^ = 



ßi ^ + ßs -1 + ßs c 



As 



COS 5 = Y, a + Y2 '1 + Ys ^ • 



i = sin i)- COS '|) 

 •r] == sin 0- sin (j) 

 C = COS r)- 



we find that the formulae (28) give us A and B directly as functions of d- and 

 We are hence able, it may be with some trouble, to form the differentialcoefficients 

 occurring in (26). 



We first obtain 



sin B 



dB 



or, because 



Ï1 



— sm — 

 8* 



Yi cos -Q- cos 4* + Ï2 ^"^^ ^^^^ 4* — T3 sin d-, 

 cosZS = 0, 



Y2 cos sin tjj — Y3 siu ■ö' • 



Further 



or 



sin B — = 

 dB 



Ï2 ^ = Ï2 Sin 9' cos <]; , 



sin 



= 72^. 



