OF THE HYDROSTATIC PRESS. 127 



And from this, we obtain the following practical rule. 



RULE. Multiply the force with which the piston of the 

 forcing pump descends, by the square of the diameter of the 

 safety valve ; divide the product by the load on the safety 

 valve, and extract the square root of the quotient for the 

 diameter of the forcing pump. 



The foregoing twelve examples exhibit all the varieties of cases that 

 can arise, from the combination of the six data which we have em- 

 ployed in our theory, viz. the diameters of the cylinder, the forcing 

 pump and the safety valve ; together with the entire pressure on the 

 piston of the cylinder, the power applied to the plunger of the forcing 

 pump, and the weight upon the safety valve. 



We have determined each of the quantities, composing the several 

 fundamental equations, in terms of the others, and have drawn up 

 rules from the general expressions, merely for the assistance of those 

 who are not accustomed to algebraic reductions; those who are, 

 will prefer finding each quantity directly from the general equation 

 expressing its value. 



137. It is manifest from the principles of mensuration, that the area 

 of a transverse section of the cylinder, or the base of the piston, is 

 expressed by .7854 D 2 ; and we have shown, equations (89) and (96), 

 that the entire pressure upon the base of the piston in the case of 

 equilibrium, is 



consequently, if n denotes the pressure in pounds avoirdupois on one 

 square inch of the piston, then we have 



P p w 



n =7imtf' r ' ~-7JS54d* al -T7854F- (104). 



Now, from principles investigated by Professor Barlow, of the Royal 

 Military Academy at Woolwich, it appears, that if c denote the cohe- 

 sive force of the material employed in the construction of the cylinder, 

 t its thickness, and r the interior radius ; then, in order that the strain 

 produced by the pressure, shall not exceed the elastic power of the 

 material ; it is necessary that 



ct 



In order to demonstrate this, let ABD be a transverse section of the 

 cylinder, perpendicular to the axis passing through c ; then, sup- 



