29 



II,— On Mnemonic Aids in the Study of Analym. By 

 Rev. Thojias P. Ktrkman, M.A., Rector of Croft-with- 

 Southworthf Lancashire. 



Read February 8, 1848, 



(I.) That mnemonical a,\dla in the study of the mathemadcs are 

 considered valuable, a«d to be worth the notice even of adepts 

 in analysis, appears from the following article, at page 291, 

 vol. iii., of the Cambridge Mathematical Journal, O. S. : — 



'^ Mnemonic JRule. — The following mnemonic rule fw the 

 * Cotangent* formula in spherical farigonometry may be found 

 uaeful. 



" If in any spherical triangle four parts be taken in succession, 

 as for example A, b, C, a, consisting of two means b, C, and 

 two extremes A) a ; then, ' iha product of cosines of the two 

 means is equal to the sine of the mean side X cotangent of the 

 extreme side - — sine of the mean anffle X cotangent of extreme 

 angled That is, 



Cos b. cos C rr sin b. cot a — sin C. cot A." 



Granting fully the usefulness of this consideration, particularly 

 to a mind familiar with mathematical analogies and symmetries, 

 I may be allowed to entertain a doubt as to how far ordinary 

 students of spherical trigonometry will find their memory's bur- 

 den hereby lightened. But I speak the result of some experi- 

 ence when I say, that few youths who have capacity to compre- 

 hend the proof of this formula, will fail to retain it firmly in 

 their memory, if it is at first presented to them thus : — 

 Cot 'Ang. si Gang and c6 b. co Caug are cot a. si b; 

 with the explanation and directions following. 



