REVIEWS — NOTES OK CENTBAL AMEBICA. 359 



different sign from R^-i , cos k <f> has changed its sign ; that is, k <£ 

 is between the nevr limits, s - + — and (?-fl) ~ -f-— ■ . Thus, the 



8 ■ v 



least multiple of — which exceeds s ■» + — , is toe yarne with the least 



multiple of </>, which exceeds stt + — ; and the law holds universally, 



if it can be shewn to hold in one instance. But reasoning exactly 

 similar to that which we have just employed, proves it to hold when 

 6=0. Therefore it is universally true. This leads at once to the 



conclusion that 4> — — For take 

 2 



k $ = s Tr + ^ + p, p being < «jb. 

 Then k— = s - + — + g. a being < — . 



But by taking s sufficiently large, k may be made as great as we 



please, while p — q retains a limited value. Therefore the equation, 



8 8 



k (</> — — ) =.p — q, cannot subsist, unless <f> = — . That is to say: 

 Ji 2 



the resultant of two forces, each equal to unity, and whose directions 



8 

 make an angle 6 less than a right angle, is 2 cos — 



The proof of the Parallelogram of Forces, in the most general 

 case, follows from the result now obtained, by a few easy and well 

 known steps, which it is not necessary to state. 



REVIEWS. 



Notes on Central America : particularly the States of Honduras and 

 San Salvador : their geography, topography, climate, population, 

 resources, productions, etc., etc., and the proposed Honduras Inter- 

 oceanic Railway ; with original maps and illustrations. By E. Gr. 

 Squier, formerly Charge d' Affaires of the United States to the 

 Republics of Central America. New York : Harper & Brothers. 

 1855. 

 The title page of this volume, of which the above gives only a 



partial conception, will remind some readers of rarely read dumpy 



