XXVI INTRODUCTION. 



the general reader, the most important formulae of a practical and 

 general nature have been thrown into rules, in words at length, 

 whereby all the arithmetical operations required in the solution 

 of the examples, can be performed without any reference to the 

 algebraical investigation, which is the surest way of uniting 

 precept with example. 



After the same method, the third chapter treats of the pres- 

 sure exerted by non-elastic fluids upon parabolic planes immersed 

 in these fluids, with the method of finding the centre of gravity 

 of the space included between any rectangular parallelogram 

 and its inscribed parabolic plane. This is a valuable proposi- 

 tion in the practice of bridge-building, and it is very satisfactory 

 to find in prosecuting one branch of science, the means of ac- 

 complishing another ; to discover in a subject purely hydrostatic, 

 a method by which to find the position of the centre of gravity 

 of the arch, with all its balancing materials, and consequently 

 many important particulars respecting the weight and mechani- 

 cal thrust, with the thickness of the piers necessary to resist the 

 drift or shoot of a given arch, independently of the aid afforded 

 by the other arches. The method laid down in Problem 

 XII. for this purpose is presumed to be new; at any rate we 

 have not seen it noticed by any previous writer on Mechanics. 

 But its development belongs to Hydraulic Architecture ; the 

 principle here established being all that is required in Hy- 

 drostatics. 



Chapter IV. introduces the reader to the pressure of non- 

 elastic fluids on circular planes, and spheres immersed in those 

 fluids as independent bodies, the extremity of the diameter of 

 the figure being in each case coincident with the surface of the 

 fluid. These problems could easily have been extended to 

 examples of elliptical planes and solids, but the investigation 

 would not embrace any practical result : and where that is un- 

 attainable, this work presumes not to advance. 



The Fifth Chapter, in which are classed the tetrahedron, 

 cylinder, conical frustum, and indeed the frustum of any other 

 regular pyramid, completes this branch of fluid pressure ; but 

 the investigation is directed altogether to the pressure of the 

 fluid upon the internal surfaces of the vessels under considera- 

 tion. Indeed this was part of the inquiry when the sphere was 



