THE DECREMENT OF THE ARC OF VIBRATION OF A MICA PLATE. 443 
gas on the time of vibration turns mainly on the term A p. Now, though A is a function 
which we cannot calculate, yet we know that it is the same at corresponding pressures 
in two gases. The effect at such pressures varies therefore from one gas to another as 
the density, and therefore as the coefficient of viscosity. It is here supposed (as is 
practically true) that the term is so small compared with I, with which it is associated, 
that its square, &c., may be neglected. 
Taking the time of two oscillations (or of one complete oscillation) for air at an 
exhaustion at which the effect of the molar inertia has ceased to be sensible, but the 
slight decrease due to the removal of the viscosity has not yet come in, at 10 s '76, we 
get for the mean effect at pressures 760,660 . . . 160 about 0 S '20. The coefficient of 
viscosity for carbonic anhydride being 18 per cent, less than for air, we get 0 S '036 for 
the average difference of times in air and that gas, which is -g-jjoth °f the average time ; 
and since according to (8) pcc r we must deduct ‘003 from the ‘829 given above, leaving 
‘826, the mean of which and '820 gives '823, nearly the number adopted. Similarly 
the number IT21 for O in the first line should be raised about '002. 
There is still a small correction to make depending on the factor 7r 3 M 3 -f A Since 
by (8) ijl varies as this factor, and Z 3 is very small compared with 77 3 M 3 , and moreover 
p 
ixccl nearly, it will suffice to deduct — from Z, and use the Z’s so corrected. The cor- 
rection being, however, very small, it will suffice to take an average Z and make the 
deduction for it. The deductions for the six gases came to about '005, '009, '005. 
'003, ‘005, '001. Deducting these numbers from the relative viscosities given above, 
and reducing afresh to the scale air =1, we get the following final numbers : 
Air. O N CO, CO H 
l'OOO 1T17 0-970 0-823 0'970 0'500 
I have left kerosoline vapour to the last on account of the uncertainty as to its 
vapour density. It is a mixture of different substances, being the more volatile part 
of petroleum. I am informed by Mr. Greville Williams that it contains much 
pentane, the theoretical vapour density of which on the hydrogen scale would be 36. 
Taking at a venture D=36, and choosing suppose the pressure 54 millims., for which 
Z=:'0404, and further assuming the limiting logarithmic decrement for air before the 
breakdown to be O'lOOO, as it seems to be from Mr. Crookes’s table, we find 0'392 
for the relative viscosity of kerosoline vapour. This is pretty certainly too high. If 
we suppose the true number to be 0'380, we get for the air number corresponding to 
Z'='0425, Z= T129, which from the table of results for air belongs to p=7 40. This 
would give for the vapour density of kerosoline D'= X - — ■D = 3'408D = 49T6 if 
D=14'42. 
T000 x 82'5 
For the air pressure corresponding to 54 millims. in kerosoline we should have 
740 X 54T-82 , 5 = 484 , 3. For the corresponding logarithmic decrement we get from 
MDCCCLXXXI. 3 M 
