THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 119 
This shows that the arguments (g—3q’), and (2g — 69’), have coefficients in the 
final expressions for the perturbations greatly affected by the factors of integration. 
In case of the argument (gy — 3g’), we should compute the coefficients with more deci- 
mals; also those of (0 — 39’) and (2g — 3q’), since in the developments the coefficients 
of these affect those of (g —34q’). 
From 
sin 5 Z.sin § (¥ + ©) =sin$ (Q— Q’)sin} ¢@—7) 
sin I. cos 2 (¥ + ®) = cos $(Q—Q’) sin $ (¢— 7’) 
cos 5 J. sin 5 (¥ —®) = sin} (Q— 9’) cos 4 (7+ 7) 
cos 5 I.cos 4 (© — ®) = cos 4(Q — 2’) cosh (7 4 7) 
where, if §2’ > &, we take § (860° + 9 — 2’), instead of 4 (Q— 9’), we find 
vy 
B=116° 15’ 36.7 
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Shes 1 0 S583 
An independent determination of these quantities is found from the equations 
cos p sing = sin?’ cos (Q — 8’) 
COS p COS g = Cos 7 
cos psinr = cos?’ sin (Q — Q’) 
cos pcosr = cos (2 — 2’) 
sin p = sin?’ sin (Q — 9’) 
sin Jsin ® = sin p 
sin cos © = cos psin (¢— q) 
sin Zsin (¥ — r) = sini p cos (¢ — q) 
sin Icos (J —r) = sin (t—q) 
cos I = COs p COS (t— 4). 
