in BramalCs Presses, <$fc. 295 



But the resistance is as the extension divided by the length ; 

 therefore the resistance of the exterior surface is to that of the 



interior, as =- . =- or D 2 . D' ? . 



That is, the resistance offered by each successive lamina is 

 inversely as the square of its diameter, or inversely as the 

 square of its distance from the centre ; by means of which law 

 the actual resistance due to any thickness is readily ascertained. 



Let r be the interior radius of any cylinder, p the pressure 

 per square inch on the fluid, t the whole thickness of the me- 

 tal, and x any variable distance from the interior surface. 

 Let also s represent the strain exerted, or the resistance sus- 

 tained, by the interior lamina, then by the law last deduced, 



(r+xV '.rolls'. 7 tt,= the strain at the distance * from the 



v ■ y (>+ x )" 



interior surface, consequently 



*r~sd-/. 



rr.-f cor= sum of all the strains. 



fi 



(r+-,y 



This, when x=zt becomes 



Vr r + t/ r+t 



That it, the sum of all the variable strains or resistances on 



the whole thickness t, is equal to the resistance that would be 



rt 

 due to the thickness — — acting uniformly with a resistance s. 



Let us now suppose (the above law being established) the 

 radius r, and the pressure per square inch on the fluid p, to 

 be given, to find the thickness necessary to resist it, or such 

 that the strain and resistance may be in equilibrio, the cohe- 

 sive power of the metal being also given. Let % represent the 

 thickness required, and c — the cohesive power of the metal 



per square inch ; then the greatest strain the area can 



vxc 

 sustain is —— , and the strain it has to sustain is pr ; whence, 



when these are equal, we shall have 



r P=^+~x C > orpr+px=zxc, 

 pr 



whence nest 



c — p 



