Solution of a Problem in physical Astronomy. 89 



0-04,08309 c\ and we shall have the two new terms — 

 0-1323498 cc and — 0-1076091 c\ Let the coefficients of these 

 two new terms be denoted by the Roman letters — i and — k 

 respectively, and the second theorem in Art. 12 of the first 

 Appendix becomes 



f-t-4- — -Lk — icc — kc* 



l_ * 4 ■ 4. 12 1 4.12-32 



4. The product of « (2 -f t< : £ + t 9 6 6 ' 4 )> which is found in, 

 the third theorem of the Art. before referred to, is = 



a cc V c* 



4 4.8 



2 a 4- ±acc + -A a^ 4 1 r it 10 



1 1-4 [ = / 2a + T a ^ + T6 a ^ 



I -i^-~ 



I 6 



— 1> J 



I 6 C J 



Here likewise, the terms — 4yC<; and — T 3 F c 4 may be added 

 to 0-3465736 cc and o*i 793226c 4 , which are == Ice and mc* 

 respectively ; the coefficients of which being denoted by the 

 Roman letters 1 and m, the third theorem in the Art. before 

 referred to becomes 



B =■-££- A 



|P — lec 



X 



5. These new forms to which the theorems are now brought, 

 it is evident, are no less convenient, and on examination they 

 will be found no less accurate, than the original ones ; and, that 



the common logarithm of—, (and consequently the hyperbolic 



logarithm of it,) is much more easily and expeditiously obtained 



MDCCC. N 



