OF AIB AND OTHER GASES. 



19 



If I is the Napierian logarithmic decrement per second, and L the observed 

 decrement of the common logarithm (to base 10) of the arc in tune T, then 



L = lT\og 1<s e (20). 



If n is the coefficient of t in the periodic terms, and T the time of five 

 complete vibrations, 



w7 T =10 7 r (21). 



Let K=JcT\og w e (22), 



then K is the part of the observed logarithmic decrement due to the viscosity 

 of the wire, the yielding of the instrument, and the friction of the air on the 

 axis, and is the same for all experiments as long as the wire is unaltered. 



Let /i be the value of ft at temperature zero, p. that at any other 

 temperature 6, then if /i is proportional to the temperature from absolute zero, 



/ = (!+ ad) A*. (23), 



where a is the coefficient of expansion of air per degree. 



Equation (9) may now be written hi the form 



frQ(l+x)(l + a6)T+K=L (24), 



where l+x is the series in equation (9), x being in most cases small, and may 

 be calculated from an approximate value of /v 



The values of Q are to be taken from the Table according to the arrange- 

 ment of disks in the experiment. 



In this way I have combined the results of forty experiments on dry air 

 in order to determine the values of fi a and K. Seven of these had the first 

 arrangement, six had the second, six the third, nine the fourth, and twelve 



the fifth. 



32 



