Gases at Low Pressures. 387 



How well the equation gives the relation existing between 

 p and / can be seen by a comparison of the numbers in the 

 second and third columns of the table. A number in the 

 third column is obtained by choosing a value of I from the 

 first column, inserting it in the equation and deducing the 

 value of p, which is then placed in the third column in 

 the same horizontal row as the chosen value of I. It will be 

 seen that the various numbers in this column agree very well 

 with the corresponding numbers in the second column, except 

 at the very lowest pressure used, 0*000016 mm., when the 

 difference is about 25 per cent. 



If instead of using the value 0*000020 for yit, we make use 

 of 0*000022, which was the smallest value of the decrement 

 actually measured, the values of c and k are 



c = 0*1194 



£=0*0677, 



and the fourth column gives the values of p calculated, in 

 the way described, from the equation with these values for 

 the constants instead of those used in the preceding case. 

 This calculation is carried out to call attention to the magni- 

 tude of the change produced by a slight change in the value 

 of the constant //,, which is subject to some uncertainty as 

 has been shown. It will be seen that it is only where the 

 decrement I is very small that the difference between the two 

 results is appreciable. The smallest value of p in the fourth 

 column is nearer to the corresponding value of j\ measured 

 by the McLeod gauge ; but the measured value is subject to 

 an inaccuracy about as great as the difference between the 

 measured and calculated values of j>. 



The results given above make it highly probable that the 

 measurements of pressure by the McLeod gauge are reliable 

 in the case of pure, dry, hydrogen for pressures as low as the 

 smallest pressure recorded in the table. 



It is to be observed that for pressures below, say, 0*01 mm. 

 of mercury the friction with which we have to do is largely 

 external friction, and this is proportional to the density of 

 the gas and the mean molecular speed. The friction and, 

 therefore, the decrement, corresponding to a given pressure, 

 will be smaller for hydrogen than for, say, oxygen or mercury 

 vapour. In the case of mercury vapour, the decrement at a 

 given low pressure ought to be about ten times as great as it 

 is for hydrogen at the same pressure, since the molecular 

 weight of mercury is about one hundred times that of 

 hydrogen, while the mean molecular speed is about one-tenth 

 as great as it is for hydrogen. 



2C 2 



