92 Mr. Hellins's Second Appendix to the improved 



computing the values of a, b, and c, and of deriving the other 

 logarithmic terms from them, and having introduced a new 

 and more compendious notation of several of the ( terms in each 

 of the first three theorems, it will be proper next to exhibit those 

 theorems in this improved state, and, after that, to give an 

 example or two of computing by them. 



A = 



" r( ' + ' ) * l + a + iac(=b) + -|^a^(=c). 



A , i f-i-4- — -i-& — ice — kc 4 



o A — v <^ 3C+ i cc ' 



2 ' A — ».(«+*)* X , Q a b 



f p — \cc — mc* 

 3- B=-^-A— 7^7F x ( +S -fa + j + f. 



C p — kc — mc 4 

 Or, putting A to denote the product of ^-r~j^ x<j , g , a , b, ■ c 



this theorem will be more concisely and commodiously ex- 

 pressed thus; B = y(Atf — A). 

 4. B' = y (A'a — A). N. B. S = a + b + c. 



1 1 . We might now proceed to an example of computing by 

 these theorems ; but it will be very convenient first to set down 

 the constant numbers and constant logarithms which are to be 

 used ill these computations. 



The constant numbers, taken from Art. 12 of the first 

 Appendix, and Art. 2, 3, and 4 of this Appendix, are the fol- 

 lowing : 



e = 0-1931,472, h == 0-0823,604, p = 1-3862,944, 



f =0-1463,198, 1 = 0-1323,498, 1 = 0-1534,264, 



g = 0-1187,936, k = 0-1076,091, m = 01331,774. 



