No. 3.1 



MINOR PLANETS— LEUSCHNER, GLANCY, LEVY. 



15 



UO) Hygiea. 



1 +(/>(t?) = (1 -0.008064) {1 -0.0r)5937 sin 2i? + 0.017170 cos 2(? 



+ 0.01(i057 sin 4i? + 0.012244 cos 4t? 



+ 0.000905 sin (iiJ- 0.005081 cos Gt?+ 



+ ((>-:?„) ( + 0.000007 -0.000490 sin 2i? -0.001206 cos 2t> 



-0.000361 sin 4t? + 0.000409 cos 4t?+ )} 



where the coefBcients are in radians, and d„ is the value of i? at < = 0. 



Let 1 + <7 be the nontrigonometrical term in 1 + 0(d), take it out as a common factor, and 

 denote the numerical coefTicients by A^, B^, A^, Bt, A^, B^, 6„, a^, b^, a^, h^, respectively. 

 With these coefficients the following are computed: 



1 1 



K= 



1—w sin 1' 



S,= E 



C,= K 





- 1 {A,A, + B,B,) +Ia, (A,' + 5/) + |a,j 



-5,+|(^A-5^J -\bm2'+b,') +lbj^ 



\a, + ^^{A^,-B^,)-^^A,{ZB,>-A,')^ 

 -\b, -^^(A,B,+B,AJ - jr.B.iZA'' - 5,')] 



s^'- 



w 



C^ — — K ^a^ 



.w 



S/=Kj (b,+AA-B,a,) (15) 



.w 



C,'=-K^(a, + A,a, + B,b,) 

 C,"^K^ {b,-Ajb,-B,a,) 



There are check formulae for these quantities in Z 134, equation (153), (161')- In equa- 

 tion (153) there is a misprint; in equation (161') there are two misprints. The errors and their 

 corrections are noted in the list of errata which accompanies the second section of this paper. 



A part of the long period terms in iidz, denoted by [n8z\, is expressed by 



[ndz\ = S:, sin 2i;;+Cj cos 2!^ + S^ sin 4,^+C, cos 4c + 5e sin 6C+Ce cos 6^+ . . . . 



+ ^(C - Co) (5/ sin 2C + <7,' cos 2^ + S,' sin 4^ + C/ cos 4c + 



) + 



(I)"- 



Co)'^o'' + 



(16) 



{10) Hygiea. 



l+(P(t?) = (1-0.008064) {1-0.056384 sin 2«> + 0.017308 cos 2«? + 0.016186 sin 4ty 

 + 0.012342 cos 4i? + 0.000912 sin 6t>-0.005122 cos 6r?+ . . . 

 + (<? - t>o) ( + 0.000007 - 0.000494 sin 2^ - 0.001276 cos 2t> - 0.000364 sin U 



+ 0.000412 cos 4t> + 



) + 



. } 



