Analytical Proof of the Parallelogram ofFoites, 201 



and as no other apparatus is required than our eyes and the 

 objects of our inspection, it would seem that they were easily 

 made. But it requires rather an acquired power over the 

 organs of vision to be readily successful. Sir Ddvid Brewster 

 applied "binocular" convergence upon two figures, drawn 

 side by side to superimpose one upon the other, and compare 

 their exactness in point of size and form. I have extended 

 the same operation to figures of unequal size, though of the 

 same form. My son had just completed a half-size copy of a 

 drawing representing an Arab on horseback, the correctness 

 of which had been questioned. It was evident that, being 

 placed at distances proportionate to their size, the images 

 of the original and copy on the retina would be equal when a 

 consistent illusive image might be obtained by convergence. 

 The original was hung on the wall, and the half-size copy sus- 

 pended at about half the distance from the observer, at such 

 an angle that one could be fully seen beside the other. I 

 converged or superimposed the images, and found them so 

 nearly to coincide, that the common outline was merely ele- 

 gantly softened by the inequalities. In this experiment it ap- 

 peared as if the eye, when the figures did not exactly coincide, 

 had some power to complete the work or conceal the imper- 

 fections. "^''^ 

 I have just succeeded in substituting a blank tablet for one 

 of the pictures, and in tracing upon it with a pencil the illusive 

 image converged from the other tablet. But this is not a 

 very practicable method of copying pictures, requiring unusual 

 command and steadiness of the optical axes for even the most 

 moderate success in the operation. '•• <--^-^\y'^^ -^^'i' 



: ao!?gfobjdnor> 



XXVI. Analytical Proof of the Parallelogram of Forces^ oq 

 By T. H. Pratt. - Tifinii adi 



7b the Editors of the Philosophical Magazine and Journa^f . 



Gentlemen, 



IN my work on Mechanical Philosophy, I have given a proof, 

 of the Parallelogram of Forces which depends on the sonnj 

 hition of the following functional equation, _>, ,,,,, ,., ^^tm 



C fit \1 2 -B ioti aew fSiotJt 



T 1 111- . iOi' -[.'Ti "P'^i'^* em«K 



1 there solved this equation indirectly, ihe following ih^^^ 



rect solution may be acceptable to some of your readers, .jg}^ 



