3S6 Mr. J. L. Hogg on Friction in 



pressure, and reading off from the curve the corresponding 

 value of the decrement. In no case has this procedure 

 involved an extrapolation. 



After failing to obtain an analytical expression for the 

 relation between the logarithmic decrement and the pressure 

 which would be applicable over the whole range extending 

 from very small pressures right up to atmospheric pressure, 

 it was decided to rind, if possible, an expression which would 

 be applicable up to a certain pressure within the range for 

 which it is known that the McLeod gauge measurements are 

 quite reliable c Rayleigh * has shown that Boyle's law holds 

 down to 0*01 mm. of mercury, and Baly and Ramsay f found 

 the McLeod gauge measurements reliable for hydrogen. 

 Recently Scheel and Heuse t have applied a membrane mano- 

 meter, devised by them, to test Boyle's law, and McLeod 

 gauge measurements for air, and they state that they find 

 both valid down to about O'OOOl mm., provided proper care 

 is taken in drying the gas. 



An examination of the results at pressures less than 0*1 mm. 

 showed that the equation given abo^ 



»ve, viz.: 



G^- 1 )^' 



served the purpose exceedingly well, if the experimentally 

 determined value of //, given above was used, and if the 

 constants c and h were determined by means of values of p 

 between 0*1 mm. and 0*01 mm. of mercury, and the corre- 

 sponding values of I. 



The pressures chosen for the determination of these 

 constants were 0"0239 mm. and O0150 mm., the former of 

 these being a pressure actually measured by the gauge, while 

 the latter was chosen arbitrarily. The measurement of I 

 corresponding to the former was 0*00936, while the value 

 of I corresponding to the latter was 0*00620, and was obtained 

 from the curve as described above. The values of the 

 constants calculated from the above data are 



c = 0-1491 

 & = 0-0676. 

 The equation now takes the form 



r q -° 676 -ii.-Q.i49i 



[j-0'000020 l jP- {)l ^ i ' 



* Phil. Trans, vol. 196 (1901). 



t Phil. Mag. vol. xxviii. (1894). 



X Verkandl. d. Deutsch. Physikal. Gesellsch. xi. p. 1 (1909). 



