CONTENTS. IX 



49, page 33. The same determined when the point of division is estimated upwards, 

 art. 50, page 33. Practical rule for calculating ditto, art. 51, page 34. The solution 

 independent of the breadth of the parallelogram, art. .51, page 34, corol. Rectangu- 

 lar parallelogram divided into two parts sustaining equal pressures, by a line drawn 

 parallel to the diagonal, art. 52, pages 34, 35, and 36. Example for illustrating 

 ditto, art. 53, pages 36 and 37. Centre of gravity of the upper portion determined, 

 art. 54, pages 38, 39, and 40. Rules for the co-ordinates, art. 55, pages 40 and 41. 

 Example for illustrating ditto, art. 56, pages 41 and 42. Construction of the 

 figure, art. 57, page 42. The problem simplified when the line of division is 

 parallel to the diagonal, art. 57, page 42. Example for illustrating ditto, art. 57, 

 pages 42 and 43. Remarks on ditto, art. 57, page 43. The pressure not a neces- 

 sary datum, compare the concluding remark, art. 57, page 43, with equations (20 

 and 21), art. 54, page 40. Rectangular parallelogram divided into two parts sustain- 

 ing equal pressures, by a line drawn from one of the upper angles to a point in the 

 lower side, art. 58, pages 43 and 44. Practical rule for ditto, art. 59, page 45. 

 Example for illustrating ditto, art. 60, page 45. The same determined when the 

 line of division is drawn from one of the lower angles to a point in the immersed 

 length, art. 61, page 46. Practical rule for ditto, art. 62, page 47. Example for 

 illustrating ditto, art. 63, page 47. Centre of gravity determined, art. 64, pages 

 48,49, and 50. Remark on ditto, art. 66, page 51. Rectangular parallelogram 

 so divided, that the pressures 011 the parts shall be in any ratio, art. 67, 68, and 69, 

 pages 51 and 52. Remarks on ditto, art. 69, page 53. Rectangular parallelogram 

 divided by lines drawn parallel to the horizon, into any number of parts sustaining 

 equal pressures, art. 70, pages 53, 54, 55, 56, and 57. Practical rule for ditto, 

 art. 71, pages 57 and 58. Example for illustrating ditto, art. 72, page 58. Con- 

 struction of the figure, art. 72, page 59. Requisite thickness of floodgates deter- 

 mined, art. 73, page 59. Example for illustrating ditto, art. 73, pages 59 and 60. 

 Construction of the figure, art. 74, page 60. Remarks on ditto, art. 74, page 61. 

 Pressure on the sides and bottom of a rectangular vessel compared, art. 75, pages 

 61, 62, and 63. Examples for illustrating ditto, art. 76 and 77, page 64. 



CHAPTER III. 



ON THE PRESSURE EXERTED BY NON-ELASTIC FLUIDS UPON 

 PARABOLIC PLANES IMMERSED TN THOSE FLUIDS, WITH 

 THE METHOD OF FINDING THE CENTRE OF GRAVITY OF 

 THE SPACE INCLUDED BETWEEN ANY RECTANGULAR PARAL- 

 LELOGRAM AND ITS INSCRIBED PARABOLIC PLANE. 



Pressure on a parabolic plane, compared with that on its circumscribing rectan- 

 gular parallelogram, art. 77, pages 65 and 66. Practical rules for ditto, art. 78, 

 page 67. Example for illustrating ditto, art. 79, page 67. Centre of gravity of 

 the included space determined, art. 80, pages 67 and 68. Remarks on ditto, art. 80, 

 page 69. The same things determined when the base of the parabola is coincident 

 with the surface of the fluid, art. 81, pages 69 and 70, Practical rules for ditto, 

 art. 82, page 71. Example for illustrating ditto, art. 83, page 71. Remarks on 

 ditto, art. 83, page 72. The same things determined when the base of the parabola 

 is vertical, and just in contact with the surface of the fluid, art. 84, pages 72 and 

 VOL. I. b 



