OF THE HYDROSTATIC PRESS. 129 



or by transposing and expunging the common terms, it is 



and this equation being converted into an analogy, gives 

 2^4-e' : 2d-\-e : : e : e'. 



Now, the quantity of extension that the material will allow before 

 rupture being very small, especially as compared with the quantities 

 2d' and 2d ; it therefore follows, that the quantities e' and e, in the 

 first and second terms, may be conceived to vanish, and the above 

 analogy becomes 



d' : d : : e : e'. 



From this it appears, that the extensions of the respective circum- 

 ferences, are inversely as the corresponding diameters ; but we have 

 stated above, that the resistance is as the extension divided by the 

 length; therefore, we have 



d d' 



d'''d' 



or which amounts to the same thing, 



d 2 : d' 1 ; 



hence this law, that the magnitude of the resistance offered by each 

 successive circular lamina : 



Is inversely as the square of its diameter, or, which is the 

 same thing, inversely as the square of its distance from the 

 common centre to which they are referred. 



From the general law thus established, the actual resistance due to 

 any point in the annulus, or to any thickness of metal, can very easily 

 be ascertained. 



Put r iz: C, the interior radius of the cylinder, of which the annexed 



diagram is a section, 

 rA, the entire thickness of the 



metal, 

 #:zi an, any variable thickness esti- A 



mated from a, the interior 



surface, 

 n the pressure on a square inch of 



the inner surface in pounds avoirdupois, 

 /m the measure of the straining force, or the resistance sustained 



by the first or interior lamina, and 

 c =i the cohesive force of the material. 

 VOL. i. K 



