308 Pneumatic Transmission, [July, 



before the British Association at Liverpool last year by 

 Mr. Robert Sabine, that gentleman has worked out a 

 number of formulae for calculating the work performed in 

 pneumatic tubes, and the result of his investigations on this 

 subject, cannot fail to be of great value, as it is one upon 

 which very little of scientific value has hitherto been pub- 

 lished. " The problem of a successful pneumatic system," 

 says Sabine, "is simply this: To make a given quantity of air 

 expand from one pressure to another in such a way as to return 

 a fair equivalent of the work expended in compressing it. It is 

 obviously impossible to regain the full equivalent of the work, 

 because the compression is attended with the liberation of heat, 

 which is dissipated and practically lost to us. Therefore, in 

 designing a pneumatic system, that which we have to do is 

 first to contrive means of compressing the air as economi- 

 cally as possible ; secondly, to get back as much as we can 

 of the mechanical effect stored up in our already compressed 

 air, irrespectively of the work which was employed in com- 

 pressing it. The utmost theoretical work which a given 

 quantity of air can be made to perform is evidently that of 

 expanding from the higher to lower pressure; and the 

 mechanical effect employed in propelling a carrier and air 

 through a given tube is therefore equivalent to that due to 

 the expansion of a tubeful of air from the higher to the lower 

 pressure." The speed at which a carrier travels in a hori- 

 zontal tube has been worked out by Sabine, and is expressed 

 by the following equation : — 



x/ 



2p- — t K feet per second. 



But when going up or down an incline — 



_ . / vf— W/ (sin a-\-pcos a) 

 S ~V 2g ^ ^ +w ^ j(i-\-t 1 )~ feet per secon(i ' 



In these equations the volume of the tube in cubic feet is 

 represented by v ; I represents the length of the tube in feet, 

 and d its diameter, also in feet ; W is the weight of the 

 carrier in pounds, and g the accelerated motion due to 

 gravity; / represents the mechanical effect performed by 

 one cubic foot of air ; jjl, the coefficient of friction of motion 

 of the carrier in the tube ; w z the weight in pounds of one cubic 

 foot of air at the higher pressure ; w 2 the weight of a cubic 

 foot at the lower pressure, and a the angle made by the tube 

 with the horizon, and which is -f when the carrier ascends, 

 but — when it descends. f is an empirical constant; 



