144 THEORY OF CONSTRUCTION AND SCIENTIFIC DESCRIPTION 



That any quantity however small, may be made to balance 

 any other quantity however great. 



151. If the diameter of the tube, the diameter of the cylinder or 

 bellows, and the weight upon the moveable board AB be given, the 

 weight of the fluid in the tube, or its perpendicular altitude to main- 

 tain the equilibrium, can easily be determined by means of the equa- 

 tion (114), which affords the following practical rule. 



RULE. Multiply the square of the diameter of the tube by 

 the load upon the moveable board, and divide the product by 

 the square of the diameter of the bellows or cylinder ; then, 

 the quotient will give the weight of the fluid by which the 

 equilibrium is maintained. 



EXAMPLE. The diameter of the bellows or cylindrical vessel is 18 

 inches, that of the tube or pipe, through which the fluid is conveyed 

 into the vessel, is one fourth of an inch, and the weight upon the 

 moveable board is 5760 Ibs. ; what weight of water must be poured 

 into the vertical tube, so that the whole may remain at rest ? 



In this example there are given, Dm 18 inches; c?=:| of an inch, 

 and w = 5760 Ibs. ; therefore, by performing as directed in the rule, 

 we shall have 



.25* X 5760 360 





Here it appears, that a quantity of water weighing llbs., disposed 

 in a tube of of an inch in diameter, is capable of balancing another 

 quantity of 5760 Ibs., disposed in a cylinder of 18 inches diameter; 

 it is therefore manifest, that the height of the one column must far 

 exceed the height of the other, and the excess of altitude may be 

 determined in the following manner. 



152. It has been abundantly proved by experiment, that a cubic 

 foot of distilled water, at the temperature of about 39 of Fahrenheit's 

 Thermometer, weighs very nearly 1000 avoirdupois ounces, or 62 Jibs. ; 

 consequently, the number of cubic inches in the column whose weight 

 is l^lbs., is found by the following analogy, viz. 



62 : 1728 :: l : 30f inches; 



hence, the solidity of a column which maintains the equilibrium is 

 30f- inches, and according to the conditions of the question, the 

 diameter of its base or section, is one fourth of an inch, and con- 

 sequently, the area of the base or section, is 



.25* X. 7854 = . 0490875 square inches. 



