u 



REV. T. P. KIRKMAN ON MNEMONIC AIDS 



(k.) taf, vid (b). SorD is sum or diff. Cotk is coisxxg of 

 Aalf. CorSha is cos or sin of ha\S. Dab is difference of a an^ b. 

 3Vl stands here, and in many other mnemonics, conveniently for 

 BuM ; and refers to the quantities a and h in Dab. In CorS in 

 the second, and SorD in the first line, the cos goes with sum, and 

 sine with difference : no ambiguity can arise from the two mean- 

 ings of S in CorS and SorD, "We have here the two formulae : 



cos , ,s 



t^n i (A ± B) sin ^ <>^ ~ ^> 



cot^C cos^^^_^j^ 



or, read at 

 sm 



length, {k) is the tan, of half sum (or diff.) of angles AB, divided 

 by the cotan. of half C, is the cosine (or sine) of half the difference 

 of the sides aJ, divided by the cosine (or sine) of half their sum, 

 il.) The cfenominator on the left of (k) has taf instead of 

 cothf in the supplemental po/ar formula; or, 



tan ^ (g + 6) __ sin i (-^ — ^) " ' ^ 



im.) cos (p. cos c zr cos a. cos (f — h), where tan <p zz tan a. 

 cos C : and, in the supplemental polar formula, 



sin (p cosCzz. cos A, sin (^) — B), where cot f zz tan A cos c; 

 i e,, the first and last (prim* uli) are sines instead of cosines, 

 and tan <p becomes cot f . 



From (b)(k')yfe find A and B in terms of a 6 C; from (c) (ec) 

 we obtain A in terms of a be ; /gives a in terms of A B C ; (/) 

 gives a and b in terms of A B c ; (ff) and (m) give c in terms of 

 a b C, and (m) gives also C in terms of A B c. 



(6.) If space permitted me, it would be easy to give dozens 

 of such mnemonics in trigonometry. The following will be 

 intelligible, with the remark that chask is cos ^alf «in /ialf, re- 

 ferring to SUD and to two : ■ 



CorS is SuD or two chash. (o^ . (r, ,3, b") 



SiM mol SiD's two SorC. CbrS. (p) (vV 6, ^) 

 CoD mol CoM'g two CorS. CorS. (q) 



The antecedents of the two ora in any line are taken together, as are 

 the consequents. 



