XIV 



THE THEORY OP THE LONG INEQUALITY 



13. Hence we shall find for the coefficients aM x , &sc, in (Art. 8,) 



log aM x = T-8975641, 

 log aM % = 1-2219740, 

 log aM b = 0-8763454 -, 

 log oM, = 0-1864584 -, 

 log aMg = T-6778939, 

 log aM n = 0-3878377, 



log fflJV, = 0-0641950 -, 

 log aN 3 = 0-5250656, 



log aK x = 0-3202750, 

 logaJT 3 = 0-9595044 -, 

 log aK b = 0-3560816, 



log aM 2 m T-4616115 - 

 log aM t = T-6894009 -, 

 log aM, = 1-9145597 -, 

 log aM s = 0-8459271, 

 log aM w = 0-0560459, 

 log aM u = 1-28667 -. 



log aN 2 = 0-3787041 -, 

 logaNi = T-7567708 -. 



log aK 2 = 0-8005295 -, 

 log aK 4 = 1-1198185, 

 log aK 6 = 0-5667868 -. 



A negative sign written after the log of a quantity signifies that the quantity is negative. 



14. 



tfbSlh 



da 2 \ da da? ) ' 



dM 2 

 da 





dJf, 



. log a 2 — -^ = 0-3456178, log a 2 -j-i = 0-0793316 - 



2 dM 2 



da 



da 



t dM 3 a ( Q db 2 (h) d%(h) «*»&,«> d<b./ih 



a ^ = -T6{ 33a -da-- 7a -d^~ 9a -d^- a -d^)^ 



dM t at dfc/i) , ePV 4) «b<* 5 dV J) \ 



a 2 -=-i = - - 70a -i 10a 2 — V - "«* -?r- ~ « 4 "tV > 



da 8 V rfa da 2 da 3 da 4 / 



,<Hf, 



rd6 3 «> d6,<l>\ 



=-- = {^.«»»**(3%^:)W(=g 



da 



+ 





dM 6 a / dftXD 



a 2 ~ = — 24a— j 24a 



da lo \ da 



-it 



22a" 



12a 3 



da 3 



4 dV- J) \ 



t dM 1 _a ( n db,W 



da 



dM, 



da 



..dM, 

 da 



,dM n 

 da 



-8a- W 



d%W 



da* 



{4 (6 (|) + 6,(i)) _ 8 + 6a ~ (5 <l> + 6/D) + a 2 £ (&„(!> + bSi))}, 



eta" 



124a 



- - f- 



16 V da 



db 3 M d*b a d) 



+ 5d 



5( 



da 2 



-— + 26a 2 —V 

 aa aer 



da 



- 10a 3 



d 4 6,^\ 



da 3 da 4 J ' 



d 3 6,XJ) . d 4 6 n <^\ 



+ lla 3 — -- + 

 da 3 



a "da^J' 



