4 PROCEEDINGS OF THE AMERICAN ACADEMY. 



apparatus. Again, the logarithmic decrement due to the friction in 

 the suspending fibre was not determined directly by experiment, and 

 in the discussion of the results obtained its value was calculated. 



The details of the method since used to exclude the mercury vapor 

 and to determine the decrement due to friction in the fibre will ap- 

 pear later. Meanwhile a summary of what has been accomplished is 

 given here. 



First, the decrement due to the friction in the suspending fibre of 

 the viscosity apparatus has been determined experimentally. 



Second, mercury vapor has been excluded to such a degree that, even 

 when the whole apparatus, in which the presence of the vapor would 

 be objectionable, was kept at a temperature of 150° C, the mercury 

 lines were absent from tbe spectrum of the gas enclosed. 



Third, the value of the decrement has been obtained for hydrogen 

 over a range of pressures extending from atmospheric pressure to 

 0.000016 mm. as indicated by the McLeod gauge. 



Fourth, an equation relating pressure to decrement has been ob- 

 tained which applies well at all pressures below 0.1 mm. as far as pres- 

 sures have been measured. The equation, above mentioned, is of the 

 form of Sutherland's equation given tentatively in the former paper. 

 It is 



fe-0 



p = c. 



In this equation k and c are constants to be determined from the ob- 

 servations ; / is the decrement due to whatever friction there is in the 

 gas under examination and to the friction in the fibre ; p is pressure ; 

 fi is the decrement due to the friction in the fibre. Its value has been 

 measured directly. The significance of the two slightly differing values 

 of /j., namely, /u. = 0.000020 and /x — 0.000022, which are found in the 

 following table, will appear later when the measurement is discussed in 

 detail. The first column of the table contains a series of values of 

 the decrement for hydrogen, each of which corresponds to a definite 

 pressure in the gas. The various values of the pressure are given 

 in the second column. The first three of them were obtained from 

 a manometer. Those which are marked thus,*, were obtained from 

 measurements made with the McLeod gauge, while the others were 

 obtained from a curve plotted from the directly observed values of the 

 decrement and pressure. From two values of p, the corresponding 

 values of /, and the value of /x, there are obtained two equations for 

 the determination of the constants k and c in the above equation. 

 These determined, it is clear that from any value of /, within the range 



