XII. Elementary Demonstration of the Composition of Pres- 

 sures. By Thomas Jackson, LL. D. F. R. S. Edin. 

 and Professor of Natural Philosophy in the Universi- 

 ty of St. Andrew's. 



(Read June 3. 181 6 J 



IT is well-known as a fundamental principle in statics, that 

 " Two pressures, represented in direction and quantity by 

 **■ two adjoining sides of a parallelogram, are equivalent to one 

 " represented in direction and quantity by the diagonal 

 which passes through the point at which these sides meet." 

 A demonstration of this proposition, that shall be at once suf- 

 ficiently concise, and sufficiently elementary, to admit of its be- 

 ing with propriety introduced into a course of academical in- 

 struction, has been hitherto, so far as I know, a desideratum. 

 The following may perhaps be found to possess that advan- 

 tage. 



u 



Lemma. 

 " If the equivalent of two pressures, represented by the ad- 

 " joining sides of a rectangle, given in species, be always re- 

 " presented in direction by the corresponding diagonal, it shall 

 " be represented by the same in quantity." 



Let 



