310 Pneumatic Transmission. [July, 



the loads through to Holborn the air was exhausted to 14*44 

 lbs., and in sending back the empty carriers it was com- 

 pressed to 15*06 lbs. per square inch. From these data the 

 mechanical effect due to the expansion of one cubic foot of 

 air in the two experiments has been deduced to h.ave been 

 31*964 foot-pounds with exhaustion, and 31*945 foot-pounds 

 with compression. 



In employing the same amount of mechanical effect, and 

 the air remaining of the same mean specific gravity, Sabine 

 finds "that the mean speed of transmission varies inversely 

 with the length, and inversely also with the square root of 

 the diameter of the tube. Thus, with an equal mechanical 

 effect expended upon it in each case, a very light piston 

 would travel through a tube of one mile long with exactly 

 twice the speed with which it would travel through a similar 

 tube two miles long. And further, if we had two tubes, 

 each a mile long, one having a diameter of 4 feet and the 

 other a diameter of 1 foot, the air in the larger tube would 

 only travel half as fast as that in the smaller one, assuming, 

 of course, the total work performed during the transit to be 

 in each case equal. The cause of this is simply that the 

 greater portion of the mechanical effect which in the larger 

 tube is used for moving the greater mass of air, is, in the 

 smaller one, converted into speed. If the case arose, there- 

 fore, that a pneumatic transit had to be made with a stated 

 expenditure of work, we should proceed economically by 

 adopting a tube of small rather than one of large sectional 

 area. With an equal utilised engine power in each case, 

 the mean speeds of transit of air through two tubes are in- 

 versely as the cube roots of their diameters and lengths. 

 For instance, with a utilised effect of 10-horse power, the 

 velocity of transit in a tube eight miles long, being 20 feet 

 per second, that attainable with the same power in a one 

 mile length of the same tube would be 40 feet T and if we had 

 two tubes of equal length — one eight times the diameter of 

 the other — the speed attained in the larger tube would be 

 only half that attained in the former. To obtain the same 

 speed of transit of a very light piston in two tubes of equal 

 length and different diameters, other things being equal, the 

 utilised horse-power must be directly proportioned to the 

 diameter, whilst to produce the same mean speed of 

 transit of very light pistons in tubes of equal diameter but 

 different lengths, other things being equal, the utilised 

 horse-powers of engines may be taken as directly pro- 

 portional to the lengths. Similarly, when the lengths 

 and diameters are equal, but the mean specific gravity of air 



