596 
Proceedings of the Royal Society 
therefore 
& v ( Pi _ + .& + ^ =3. sin K-coSfc(cotr 1 4-cotr 2 4- cotr 3 ) . 
\sin r x sin r. 2 sin r 3 J 
But 
Pi + P«_ + _Pi_ = , r P_ ; 
sin r x sin r 2 sin r 3 sin r 
therefore 
= 3 sin k - cos k (cot r x + cot r 2 + cot r 3 ) . 
sin r 
But 
S rjp = - cos (k - r) , 
therefore 
- CQS ( K — 3 sin k — cos k (cot + cot r 2 + cot r.J , 
sin r 
therefore 
4 sin k = cos k (cot r x + cot r 2 +- cot r 3 - cot r ) , 
therefore 
cot r, + cot r 9 + cot r 3 - cot r _4an R 
tan k ■ ■ . ' " s~\ • 
4 2 
3. On some Remarkable Changes, Additions, and Omissions 
of Letters in Certain Cognate European Words. By the 
Hon. Lord Neaves. 
The subject of comparative philology has always interested 
scholars, but latterly the study has been carried on in a more 
scientific manner, and I may also say with more success, than at 
any former period. One great object in prosecuting the study is 
to detect the various disguises which words radically the same are 
apt to assume in different languages or dialects. The great 
scholars of two centuries ago were fully alive to the importance of 
this inquiry, and although they sometimes indulged in too great 
a latitude of conjecture, there is scarcely an etymological affinity 
now generally admitted of which traces and indications are not 
plainly to be found in the works of those learned men, and more 
particularly in the writings of Salmasius, the greatest of them all. 
