ANY RATIO TO ONE ANOTHER. 



53 



Hence then, the equations (27,) (28,) and (29,) express generally 

 the relation between the parts of division, which in the several pro- 

 blems is restricted to a ratio of equality ; and it is presumed, that by 

 paying a due attention to the examples that have been proposed and 

 illustrated, the diligent reader will find no difficulty in resolving any 

 example that may present itself under one or other of the general 

 forms above investigated. 



In all the above cases, we have supposed the breadth, or that side 

 of the parallelogram which is denoted by b to be horizontal, and 

 coincident with the surface of the fluid ; but it is manifest, that 

 equations of the same form would be obtained from the other side, 

 having b in place of I, and / in place of b. 



10. OF RECTANGULAR PARALLELOGRAMS DIVIDED INTO SECTIONS 

 SUSTAINING EQUAL PRESSURES; WITH THE METHOD OF DETER- 

 MINING A LIMIT TO THE NECESSARY THICKNESS OF FLOOD-GATES, 

 AND OTHER CONSTRUCTIONS OF A SIMILAR NATURE. 



PROBLEM IX. 



70. A given rectangular parallelogram, is immersed in an 

 incompressible and non-elastic fluid, in such a manner, that one 

 of its sides is coincident with the surface, and its plane inclined 

 at a given angle to the horizon : 



It is required to divide the rectangle by lines drawn 

 parallel to the horizon, into any number of parts, such, 

 that the pressures on the several parts of division shall be 

 equal to one another. 



Let A ED represent a rectangular cistern filled with water, or some 

 other transparent and incompressible fluid 

 in a state of rest ; one side of the vessel 

 being removed, for the purpose of exhibit- 

 ing the fluid and the immersed parallelo- 

 gram, together with the several subordinate 

 lines on which the investigation depends. 



Suppose e, I, g and i to be the several 

 points of division, and through these points 

 draw the lines em, If, gk and ih, respec- 

 tively parallel to a b or dc, the horizontal sides of the figure. Bisect 

 the sides a b and dc in the points G and H; join GH, and draw the 

 zigzag diagonals am, ml, Ik, ki and ic, cutting the bisecting line 



