300 Mr MOSELEY, ON THE 



To simplify the question, let the planes AC, BD which bound the 

 mass laterally be supposed to be parallel, the figure ABCD assuming 

 the form of a rectangle. Fig. 6. 



This hypothesis will introduce the following conditions : 



« = *' ^ = J - 7- 



Hence, by substitution the equation to the line of pressure becomes 



% — . sec 7 . sec . a;^ 



+ tan ^ .X 



cos (7 - 0) 

 cos 

 Avhich may be put under the form 



, p . ^ 1 , P , ( cos (y — (j)) P sin^ cos 7 -, 



^x — -~ sm cos^r = - cos 7 .cos . \k ' + -7 ^-— ; — - — *|. 



* 2a ^ "a ' ^ ^ COS0 4« cos ' 



It is manifest therefore, that the line of pressure is in this case 



a parabola — having its axis vertical and at a distance = —- sin cos 7 



^ a 



from the origin — having its concavity downwards — its vertex at a height 



_ cos (7 — 0) p sin' cos 7 

 ~ cos 4 « cos ' 



above the axis of x — and having for its parameter the quantity 

 • (^j . cos cos 7. 



Let us now seek to determine what relation must exist between 

 the forces impressed upon the mass which we have hitherto considered 

 of invariable form, that the equilibrium, may continue under the same 

 circumstances when its form and dimensions are made to admit of 

 variation. And let us suppose 



