294- Professor Barlow on the Hydrostatic Pressure 



presented to the Society of Civil Engineers, who now rank 

 amongst their numbers many of the most distinguished names 

 of the United Kingdoms connected with scientific and practi- 

 cal mechanics. 



The following is the particular part of the investigation to 

 which we have alluded. 

 To investigate the nature of the resistance opposed to any given 



thickness of metal in a cylinder or ring from internal pres- 

 sure. 



" It would appear at first sight, that having found the 

 strain on any points, D and C, it would only be necessary to 

 ascertain the thickness of metal to resist this strain, when 

 applied directly to its transverse area. This, however, is by 

 no means the case ; for if we imagine, as we must do, that the 

 iron, in consequence of the internal pressure, suffers a certain 

 degree of extension, it will be found that the external circumfe- 

 rence participates less in this extension than the interior, and 

 as the resistance is proportional to the extension divided by 

 the length, it follows that the interior circumference, and 

 every successive circular lamina from the interior to the exte- 

 rior surface, offers a less and less resistance to the interior 

 strain. The laws of which decrease of resistance it is at pre- 

 sent our object to investigate." 



" In the first place, it is obvious that whatever extension 

 the cylinder or ring may undergo, there will still be the same 

 quantity of surface in the section of the ring, which area is al- 

 ways proportional to the difference of the squares of the two 

 diameters. 



Let D be the interior diameter before pressure, and D + d 

 its diameter when extended by the pressure. 



Let also D ; be the exterior diameter before, and D' -\-d' the 

 same after the pressure. 



Then, from what is stated above, we shall have 

 D' 2 — D-^iB'+d'y— (D+dy 

 or, 2D / <f+<F=2Dd+d 2 . 

 "Whence {%&+#) :(2B+d)::d: d', 

 or, since d! and d are both very small, this becomes 



D' : D : : d : d f . 



That is, the extension of the exterior surface is to that of the 

 interior, as the interior diameter is to the exterior. 



