12 



PNEUMATICS. 



gress is stopped at a certain point a'b'. 

 The resistance which thus arrests the 

 motion of the piston, is the increased 

 elastic force of the air, owing to its hav- 

 ing been driven by the piston into a 

 diminished space. It is worthy of notice, 

 that an uniform law governs this increase 

 of elastic force, arising from the dimi- 

 nished bulk of the air, which is, that the 

 elastic force, or the pressure exerted by 

 the air against the sides of the vessel 

 which contains it, is increased in pre- 

 cisely the same proportion as the space 

 which it occupies is diminished. To 

 establish this remarkable law some fur- 

 ther explanation will be necessary. 



Let a syphon tube ABC (Jig. 1 1 .), 

 open at both ends, be filled to the 

 level x y with mercury. The air which 

 fills the tube will then have the same 

 density, and be in all other respects 



. 11. 



CA| 



similar to the external atmosphere. Let 

 the end C be now closed, so as to pre- 

 vent the escape of air, and let the level 

 y of the mercury in the closed leg be 

 marked on the exterior surface of the 

 tube. Let mercury be then poured in 

 at the open end A ; as this fills the leg 

 A B, it will press with its entire weight 

 upon the mercury x B //, and force it up 

 in the tube BC. The air in this tube 

 will then be reduced in bulk, or con- 

 densed. Let the mercury be poured in 

 at A, until the mercury in B C rises to 

 half the height y C, so that its surface 

 being at z, C z will be half of C ;/. The 

 air which originally filled the space C y 

 is now confined to half that space C z. 

 It exerts a pressure on the surface z, 

 which supports a column of mercury, 



whose height is equal to the difference 

 between the levels e and z, together 

 with the weight of the atmosphere 

 pressing on the surface e. Now, in its 

 original state, before any mercury had 

 been poured in at A, it supported only 

 the weight of the atmosphere on x. If 

 the difference of the levels z and e be 

 now measured, it will be found to be 

 exactly equal to the height of the baro- 

 meter, thereby indicating that the force 

 which presses on the surface z, is equal 

 to twice the weight of the atmosphere. 

 Thus it appears, that when air is con- 

 densed into half the bulk which it occu- 

 pies when free, it exerts double the 

 pressure. In like manner, if mercuiy 

 be poured in at A, until the air in C y 

 is reduced to one-third of its bulk, it 

 will be found to exert three times its 

 original pressure; and so on. Hence 

 we may in general infer, that the elastic 

 force with which confined air presses 

 against the sides of the vessel which 

 encloses it, is equal to the force which 

 was necessary to condense it ; and that 

 both of these increase in precisely the 

 same ratio as the space occupied by the 

 air is diminished. Since the density of 

 any fluid increases in the same propor- 

 tion as the space it occupies is dimi- 

 nished, it follows also that the elastic 

 force of air or other fluid is proportional 

 to its density. 



This law, though generally true, is 

 not found to be exact in extreme cases, 

 both of condensation and rarefaction. 

 When a high degree of condensation 

 is required, a greater degree of com- 

 pressing force is found to be necessary 

 than that which would result from the 

 above law. If an external pressure of 

 15 Ibs. on each square inch be sufficient 

 to confine atmospheric air in its ordi- 

 nary state, it would only require a pres- 

 sure of 150 Ibs. on the square inch to 

 confine it when reduced to one-tenth of 

 its bulk by compression, but it is found 

 to require a somewhat greater force. In 

 other words, when a great degree of 

 condensation is effected, the elasticity 

 of air increases in a somewhat higher 

 ratio than the density. 



In like manner we find, that in high 

 degrees of rarefaction the law is also 

 not precise, highly rarefied air having 

 a less degree of elasticity than that 

 which would be consistent with the law. 

 This, indeed, is a necessary consequence 

 of the former, or rather it may be con- 

 sidered as another way of expressing the 

 same fact. 



