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XXXIII. A Simple Theory of the Knudsen Vacuum Gauge. 

 By George W. Todd, fJ.Sc, B.A* 



PROBABLY the most reliable absolute instrument for the 

 measurement o£ extremely high vacua is the Knudsen 

 gauge. The following simple deduction for the pressure in 

 terms of the constants of the instrument may be interesting: — 



Consider two parallel strips A and B at a distance apart 

 less than the mean free path of the gas molecules. Let A be 

 at the same temperature T as the residual gas, while B is 

 maintained at a higher temperature IV The strip A will 

 be bombarded from the side away from B by molecules 

 having a velocity of thermal agitation V corresponding to 

 the gas temperature T. These molecules will rebound with 

 the same velocity. The strip A will also be bombarded from 

 B, but with molecules having a velocity of thermal agitation 

 Y 1 corresponding to the temperature T x of the strip B. 

 These molecules will rebound with a velocity corresponding 

 to the temperature of the strip from which they rebound, 

 i. e. with velocity V. Thus A will be repelled from B. 



We will use the Joule method of dividing the gas mole- 

 cules into six streams. The mass of the molecules striking- 

 each square cm. of A on the side away from B is pY/6 per 

 sec, where p is the gas density, so that the momentum re- 

 ceived per second is /jV 2 /3, since an impulse is given on the 

 rebound as well as on collision. On the side of A facing B 

 the momentum per sec. due to collision is pYi 2 /Q, and due to 

 the rebound, pY 2 /6. This, of course, assumes complete 

 interchange of energy. The difference between these is a 

 pressure 



P= £ (Yi 2 - V 2 ), repelling A from B. 

 Since the gas prsssureis p = pRT, P= ^j, (V\ 2 — V 2 ). 



But V 2 = 3p/p = 3RT, therefore F = ^ 2 p T ^-. . . (1) 



Now let each movable vane of the Knudsen gauge be a 

 vertical strip of area A at an average distance r from the 

 suspending torsion fibre. If the couple required to produce 

 a twist of one radian be X, and 6 radians be the actual 



* Communicated by the Author. 



Phil. Mag. S. G. Vol. 38. No. 225. Sept. 1919. 2 D 



