THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 
39 
. . ° e é = 
As we may write h in place of 7, we have, thus, also given the value of c’2(¥—Y") 
Now put 
chy 
sy—-y) 
(yy) = ae J_in oO" 
(<2) (—m) 
nz 
+00 (m) 
—— ae Dane Wc 
Then, from the preceding developments, we see that 
(—m) m (m) 
Sinn = ( ees 1) : Tin ) 
(m) m (m) 
Jin = ( eae 1) Sin p) 
(—m) (m) 
—hr = ha 
Again 
(—my 
+o 
(0) (= 
ae Sin - = Jin =F J_, 
1) (=2) (=3) a 
np OOF spin oO) “ae dino? “se ies 
(1) (2) (3) + 
qe wine y She J 1+ ye + Sn. y + ete. 
Sea (Ne (0) eb) O. ©). 
aes) ls 0 7] = Jinan =F Sin 9 Yy =F Jin 0 OF + Jin 0 y° ain ete. 
Cas eo). oS) . 
ap Cin 00) = shiny a0h Sachin e0h a Ke 
O +a _(—m) ne 5 
Comparing the values of =_, J_, .y~™ and c-"2—y") 
we have 
(-1) (1) h378 Aes hi ts 
In =In =lA— aay 1 eg erga cE ete, fory”, 
(1) (1) hz hope hin ; 
cat Tin = Tin = hrA— 72.2 ate 923. «12.92.37.4 == etc., for Y> 
ae ©) We nis neas ‘ 
Fin =In = ig E23 + pose + ete, fory”, 
(2) (2) A222 hye AEE A 
Jon =In = iz vost poe t ete, fory, 
ete. = ete. = 
etc. 
(10) 
(11) 
(12) 
(13) 
