Bremin-er — Errors Affecting LGgaritliniic Comvidations. 471 



Then we shall have 



fiin c sin A = sin a sin (7 



sin c cos ^ = 771 sin (6 — J/) 



cos c = m cos (6 — J/) 



Hence in order to nnd c there must be computed 



tan 31 = tan a cos C 



tan A = . \,^ ... tan C 



sin {b—M) 



tan (6— iJ/) 

 tan c = 



cos A 



Accordingly we have 



/(log tan 3/) =f't-{-f'2 



f{3f) = ^^^° ^/ cos i!/ (/',+/' 2+/ 'i) 



/(log sin ^/) = cos^ i'/(/'i+/'s+/i'')+r'3 



/(log siD[6-J/]) = —cot (b—M) sin 3i cos ATl/'i-f/'a-h/'J-f/'* 



,^ sin iJ/cos 3/ , -, , ,, I ^» \ I ^/ 



/(logtan [(6^3/]) = -31^,-,/, eos (6-3/; ^^+-^ ^+-^ ^^+-^ » 



/(log tan yl) = / (log «in M) —/(log sin [6—3/] )+•/'« 



( /(log sin 3/)-/(log sin (6-3/) ) 

 /(log cos ^) = — sm' A j h -hT 1 



^/i 4. V sin 3/ cos 3/ ^^, ^ ^, ^ y. ^_l_^> 



. /(log tan c) = - si^^5_^./-)cos(6-3/) ^-^ ^^-^ ^+*^ ^^^^^ "^ 



H-sin^^ cos*3/(/'i4-/'u+/'iH-sinM . /'« 



+sin« ^ cot (b—M) sin 3/ cos 3/ (/'i4-/'a4-/'i) 



-sin'^ ^ ./'i+sin-' ^ ./'o f sin'^ ^ • f'tS'i 



finally, 



/(c) = --- sin 2c {/(log tan c)+/% | 



