X-3 



142 REV. T. r. KIJRKMAN ON THE 



because *2je-i=*2c-i ; whence, by addition of F, 

 *2,.iC'+F=g^|o-6,+ 10895-*6^_,+40-*6,_2-8145-*6 



— 5980-»6^_4-8465-*6^.5|, 

 which is the constant in (6Pj)+(6P3'y« 



We have next to sum the periodic constants in the {e+l) 

 terms 



■which are all of the form 6?,„**60^_„. If we write 



c+l=10A+^, x=60h+6{k—\) + c=60h+p-\- 1, 

 it is evident that no circulator but *60^_p_i can have value. 

 This will be affected in sP^r-i with dp, in sP^-? with dp_Q, &c., 

 the subindex retreating always by six on the circle 



do di d2 c?58 di,9 do di , . . 



The co-efficient of *60^_p_i will have the terms 



of which the eleventh term dp^Qo is identical with dp, the same 

 ten terms continually recurring-. 



Ifthene+l = 10^+A, 

 our sought sum is 

 h 



2880 



(^dp+dp.6-\- . . . +fi?p_54Y for ^-0; 



and if A 70, we shall simply have, besides this, as part of the 

 sum, 



2gg^(c?p+c?p-^+^;,-i2 + • • • to ^ terms) 



The quantity Dp is the sum of that column of ten numbers 

 do, d\, &c., above given in sP^j which contains dp. That is, 



