and the bottom B. If the stop-cock C be opened, the air contained in the 

 vessel R, will, by its elastic force, rush through the open stop-cock C, and 

 expand so as to fill the barrel. Thus the air which previously occupied the 

 dimensions of the vessel R, has now expanded through the dimensions of R 

 and A, B. Let the stop-cock C, be now closed, and the stop-cock D opened, 

 and let the piston P be pressed to the bottom of the barrel. The air contained 

 in the barrel will thus be forced out at the open stop-cock D, and driven into 

 external atmosphere. Let the stop-cock D be next closed, and the piston 

 again elevated, as in fig. 2. A vacuum will once more be produced in the 

 barrel, and on opening the stop-cock C, the air in R will again expand into 

 the barrel, occupying the extended dimensions as before. Let the stop-cock 

 C be again closed, and the stop-cock D opened. If the piston be pressed 

 I to the bottom of the barrel as before, the air contained in the cylinder will 

 ' again be expelled through the stop-cock D. By continuing this process, 

 alternately opening and closing the two stop-cocks, and elevating and de- 

 pressing the piston, a quantity or air will rush from the vessel R, on each 

 ascent of the piston, and the same quantity will be expelled through the tube 

 D, on each descent of the piston. 



It is evident that this process may be continued so long as the air which re- 

 mains in R, is capable of expanding, by its elasticity, through the open tube, 

 C, into the barrel above. 



A slight degree of attention only is necessary to perceive that the quantity 

 of air expelled from R, at each ascent of the piston, is continually diminished ; 

 and it will not be difficult even to explain the exact rate at which this diminu- 

 tion proceeds. Let us suppose the magnitude of the barrel A, B, to have any 

 given proportion to the dimensions of the vessel R ; suppose, for example, that 

 the dimensions of the barrel are the ninth part of those of the vessel. When the 

 piston is first raised from the bottom to the top, the air which previously occu- 

 pied the vessel expands so as to occupy the dimensions of the vessel and bar- 

 rel together. The barrel, therefore, will contain a tenth part of the whole of 

 the enclosed air ; for, since the vessel R contains nine times as much as the 

 barrel, the vessel and barrel together contain ten times as much as the barrel. 

 Consequently, the air enclosed in the barrel will necessarily be a tenth of the 



