MECHANICAL PHILOSOPHY. PNEUMATIC* 



[TATE'S 



like manner, fresh air rushing in from the air i 

 receiver communicating with it. And these alternate 

 ascents and descent* of the piston render the air in the 

 receiver so rarefied, that at length its pressure is inade- 

 quate to open the valves and pass into the barrels. It 

 ,iu that each turn of the toothed wheel, driving one 

 n to thel-ottoni of the barrel and mi- >er to 



the top, withdraws one barrel full of air ; so that the 

 air in the -.revioimly to this turn of the whenl, 



now occupies both the receiver and one of the barrels. 



Let R be the capacity of the receiver, and B that of 

 each barrel : and the density of the atmospheric air 

 being D, lot D., D,, D s , &c., be the densities of the 

 n the receiver after 1, 2, 3, A-c., strokes or turns of 

 the wheul : then since, at every turn, tho volume of air R 

 is dilated into R + B, we have 



D, (R + B) - D . R /. D, - D ,, J 



R v* 



B)-P,.K 



D a - D 



-t-B' 



And generally D. = D 



R 



"> tne density after n 



turns. Hence tho density decreases in geometrical pro- 

 gression. As the mass, or quantity of air, is equal to 

 its volume multiplied by its density (page 742), there- 

 fore after n strokes, the quantity of air in the receiver is 



D " R ~ (JHTB^" R " D (R +B>" 



The quantity of air in the receiver decreases, therefore, 

 in geometrical progression ; but as a decreasing geo- 

 metrical progression may be continued indefinitely, it 

 follows that the quantity can never be actually exhausted 

 in any number of strokes of the air-pump. 



As the pressure of the atmosphere on the receiver 

 becomes very great after the pump has long worked, it 

 is necessary that it possess considerable strength ; and 

 the bell form, as exhibited in Fig. 202, is given to it to 

 secure this condition, the glass of which it is formed 

 being also very thick. The valves are usually of strong 

 oil-silk, in little brass frames, traversed by a grating. 



PROBLEM. To find the number of strokes necessary 

 to reduce the air in the receiver to a given density. 



Let d be the given density : then D being the original 

 density, 



R 



.'. log. d 



log. D + n (log. R log. (R + B) } 

 log. d log D 



log. R- log. (R + B) 



And if, as is usual, the original density, or that of the at- 

 mosphere in its ordinary state, be represented by 1, we shall 

 have _ log. d _ 



" log. R log.(R~+B) 



The density d U here, of course, a proper fraction, and 

 therefore log. d is negative, but the denominator being 

 evidently negative a!so, the expression is positive ; ana 

 In rr, as inferred above, if d = 0, that is, if the receiver 

 .ksolutely exhausted of air, log. d, and therefore n, is 

 infinite. 



Although two barrels are connected with the receiver 

 in ll.iwksbce's air-pump, but only one barrel is exhausted 

 at each stroke ; yet the working of the two pistons 

 simultaneously, at each turn of the wheel, considerably 

 diminishes the labour of the operation ; for the atmo- 

 spheric pressures on the upper surfaces of the two pistons 

 being the same, the force required to work the pump is 

 only that necessary to overcome the diilV-rrnce of the 

 pressures on the under surfaces of the pistons, snd the 

 friction of the pistons themselves. If only one barrel 

 were employed, the ascent of its piston would be opposed 

 by the difference, conntantly augmenting, between the 

 pressures on its upper and under surfaces, in addition 



PfefJi 



to the friction, [f, however, the asc > 



I from tlio pressure of tli ro, a 



exhausting barrel would atuwcr evory purpose, 



would be simp!' 



'.VS AlR-l'UMI'.' ^ i-h a simplification is 

 given to tlio pump r.msh-,. m. a i 1 



after his name. A B (Fig. 204) is the barrel or cylinder 

 communicating with the receiver by means of 

 the pipe B C. In tin lion the barrel 



is closed at top, but furnished with a valve A 

 opening upwards ; the piston also has a valve 

 1) opening upwards ; and a third valve B, like- 

 wise opening upwards, covers the pipe B C. 



As the piston ascends from the bottom of 

 the barrel, forcing up the air above it, and 

 leaving a vacuum below, D is the only valve 

 that closes ; the atmospheric air originally in 

 the barrel is forced out at A, and the exh.v 

 cylinder is instantly supplied with air from the 

 receiver through the pipe B C. Upon the 

 descent of the piston, the valve A closes, the 

 pressure from without exceeding that from 

 within the cylinder, so that in its next, anil in 

 every succeeding ascent, the piston is relieved 

 from the pressure of the atmosphere upon it. 



If, as before, R, B represent the capacities 

 of the receiver and barrel respectively. D the density of 

 the atmospheric air, and D, the density of the air in 

 the receiver after n strokes of the piston, we shall have, 

 as in the former case, 

 R 



DH = D (jT~Y;T5) "> the density after n strokes. 



In this pump the exhaustion may be carried on to a 

 much greater extent than in the common pump before 

 described, because the valve D, being relieved from the 

 downward pressure of the atmosphere, will open for a 

 very slight pressure upwards, and consequently will 

 allow of the passage of air in a more rarefied state. 



But as the foregoing expression for D. is the same as 

 that furnished by ilawksbee's machine, and consequently 

 the expression for n, the number of strokes producing a 

 given degree of exhaustion, must bo tho same in both 

 constructions, provided only that the barrels are all 

 equal, it may seem that there is no difference in the 

 exhaustive powers of the two. It must be remembered, 

 however, that in the former investigation the valves are 

 supposed to open at even the nth stroke, however high a 

 number n may be ; but as, in the former construction, 

 the valve of the descending piston sustains the pressure 

 of the atmosphere, which in the present contrivance is 

 removed, a greater elasticity in the air below the valve 

 is necessary to open it; so that, in Smeaton's pump, 

 a greater degree of rarefractiou will be ultimately 

 attained. 



TATK'S AIR- PUMP. This pump was first described 

 by tho inventor in the Philosophical Mug-izitte for 

 April, is:,;;. Us chief peculiarity is, that whde it has, 

 like Smoaton's pump, only a single cylinder or barrel, it 

 has a double piston. This double piston performs the 

 work of the two pistons in the ordinary double-barrelled 

 air-pump, and that with only half the motion. 



In the annexed diagram (Fig. 205), C 1) is the cylinder 

 or barrel ; A and B are solid pistons, rigidly connected 

 by a roil K, and moved by the piston-rod 

 A 1 1 , passing through a stuffing-box S. V 

 ire valves opening outwards ; an<l II 

 an open pipe, at the middle of thecylinder, 

 ,' to the receiver from which the air 

 is to be exhau-.; 



The distance between the extreme faces 

 about j}ths of an inch less 

 than one-half the length of tho cylinder; 

 this Jths of an incli being the space re- 

 quisite for clearing tho exhausting-pipe II 

 Til'- pistons are each about 1$ inch in 

 thickness, and the rod K connecting them 

 may be of any section consistent with 

 .,'th. The ell'ective len^li of the 

 stroke is equal to the space between one side of the pipe 



Tig Mi. 



