and the instrument was found to perform as well as any that have 

 met my observation. 



But Mr. Prince went further ; he connected the discharging valve 

 with a second pump of similar construction ; and the elasticity of 

 the air remaining in this, plus the elasticity of the discharging valve, 

 must equal the elasticity of the air in the receiver, augmented by 

 being condensed from the bulk S into s ; therefore 



-j-=:v-i- g X {A + v) 



an expression identical with the performance of Haas's pump. It 

 is however laborious to work, and exhausts only at the end of the 

 stroke. 



That form is perfect in which the receiver communicates freely 

 with the space S, and when the air which expands into this is con- 

 densed into s, this latter communicates freely with S', In such an 

 instrument 



ss' 

 :r = ^ X (A + v) 



Such is described by Mr. Little in vol. VI. of our Transactions, 

 but it requires s and s' to be of considerable magnitude. Mr. 

 Cuthbertson's machine is similar in principle, but in it the spaces 

 above and below the piston are connected for an instant while the 

 receiver valve is open ; to say nothing of the complexity of its 

 construction, which is diJOficult either to execute or keep in order. 



The Air-pump which I have the honour of proposing to the 

 Academy, seems to possess peculiar advantages, while its parts can 

 be made by ordinary workmen, and it can be afforded at a much 

 less price than most of those which can pretend to equal it in power. 

 A section of it is exhibited in plate 1. 



