THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FOURTH SERIES.] 



APRIL 1866. 



XXXVIII. On the Composition of Forces. By John Stevelly, 

 LL.D., Professor of Natural Philosophy, Queen's College, 

 Belfast*. 



IT is well known that the very beautiful demonstration of "the 

 parallelogram of forces " given by the immortal Laplace is 

 too intricate, and depends too much on advanced knowledge of 

 the differential and integral calculus and trigonometry, to be 

 used in the instruction of mere beginners in the study of me- 

 chanical philosophy. 



It has lately occurred to me that a most simple and almost 

 immediate deduction from " Laplace's principle M would prove 

 the parallelogram of forces in the case where the directions of 

 the components contain a right angle — from which case to the 

 general theorem, when the directions of the two components con- 

 tain any angle at the material particle on which they simulta- 

 neously act, is but one easy step, — and that nothing but the ex- 

 treme facility with which this master of analysis used the instru- 

 ments of his art could have caused him to overlook this almost 

 obvious and very simple method of proving what he takes about 

 two quarto pages to deduce. It also proves at once the first and 

 most important part of Poisson's proof of the parallelogram of 

 forces, which, however, is scarcely anything more than a transla- 

 tion of D'Alembert's very elaborate geometrical proof into the 

 language of algebraists and trigonometricians. 



I shall therefore, with the permission of the editors of the 

 Philosophical Magazine, give a simple geometrical proof of La- 

 place's principle, and the deduction from it which leads to the 

 general theorem, premising one or two preliminary points for 

 the sake of those readers who may be less familiarly acquainted 

 with the subject. 



* Communicated by the Author. 



Phil. May. S. 4. Vol. 31. No. 209. April 1866. S 



