Chap. 7] 



GRAVITATIONAL METHODS 



221 



sion of the same formula. They involve the second and third powers of p, 

 while I2 involves the fourth power : 



= r 



p dp 



f 



Jo. 



ip _ r p 1'°^' 



(p2 + ^2)5/2 L3^2(p2 + f2)3/2j^^ 



p'dp ^ _r^i^Mii>- 



(p2 + f2)B/2 



{P' + ^') . 



''n+i 



[log. (p + Vp' 4- f2)]pS+^ 



> (7-756) 



The integrals expressing the azimuth variation are represented by Fourier 

 series of the form 



h = B. -\- h sin a -\- c cos a 4- d sin 2q! + e cos 2a 



so that the four coefficients are 



/.2T i.2r 



Trb = / /l sin a da ird = / /l sin 2q; do: 



Jo Jo 



ttC 



Jo 



/i cos a da 



ire 



Jo 



h cos 2a da. 



Like the coefficients in eq. (7-71), these are obtained from observations of 

 elevations hmm. azimuths on one circle : 



b = — 52 /i sin a d = — 52 /i sin 2a 



m m 



c = — 52 /i cos a e = — 52 ^ cos 2a, 



m "^ m 



so that in eight azimuths 



b = 0.25[0.707(/i2 + hi - he - h) ■{- h - h] 



c = 0.25[0.707(/i2 - hi- he + h) + /ii - h] 



(7-76) 

 d = 0.25[/i2 - hi + h - h] 



e = 0.25[/ii - hs -\- h - hr]. 



