814 
MR, H. TOMLINSON ON THE INFLUENCE OF STRESS AND 
and spheres I have proved, in the paper just alluded to, that the coefficient of 
viscosity of ordinary air is given by the formula 
fi = •000l7l55(l + 0-002751^--00000034« 2 ),*.(6) 
where t is the temperature of the air in degrees Centigrade and the units C.G.S. 
units. From these four formulae we can readily determine the logarithmic decrement 
due to the resistance of the air on the horizontal bar Y Y and on the two vertically 
suspended cylinders. The mode of proceeding is as follows :—First, from equation (6) 
is found the value of p, which enables in to be obtained from equation (5). Then 
we obtain by interpolation, from the Table given on p. 46 of Prof. Stokes’s paper, the 
value of k', and, by substituting this last in equations (8) or (4), according as we are 
determining the effect of the resistance of the air on the bar V Y or on the two 
vertical cylinders, the logarithmic decrement required. The vertical cylinders are 
connected to the bar Y Y by the two suspenders x, x, the cylindrical portions of 
which are affected by the air to an extent which must be calculated independently of 
the long cylinders, which they connect with Y V.t The effect of the resistance of the 
air on the other portions of the suspenders was determined experimentally by using 
the bar B L for Y Y, and observing the logarithmic decrement, first when the bar was 
vibrating with the suspenders attached, and afterwards with the suspenders removed, 
but with brass cylinders introduced into the hollow bar Y Y, of equal mass with the 
suspenders, and so adjusted that the moment of inertia remained unaltered.| By this 
means it was ascertained that the portions of the suspenders which were not cylindrical 
were equivalent to a certain length of the long vertical cylinders. This equivalent 
length would vary so slightly with the vibration-period that we may without sensible 
error consider it a constant; accordingly, in order to allow for this portion of the 
suspenders, the length of each of the long vertical cylinders was estimated at so much 
more. 
* For the coefficients of t and t~ in this formula I have taken as my authority Holman (‘ Phil. Mag.,’ 
vol. 21, 1886, p. 199), as not only do Prof. Holman’s investigations seem to have been very carefully 
conducted, and to agree as regards the effect of change of temperature on the coefficient of viscosity with 
those of Meter, Puluj, and others, but also they are more in accordance with my own in this respect 
than are those of Maxwell, who found the coefficient to vary as the absolute temperature. 
Meyer and Puluj have obtained values for the absolute coefficient of viscosity of air which differ from 
my own, but I prefer to use my own results, as these were obtained by experimenting with cylinders and 
bars of somewhat similar dimensions to those used here, and also under similar conditions to those 
holding here. I believe the equations given above to be capable of expressing the logarithmic decrement 
due to the resistance of the air with certainly a less error than 1 per cent. 
f Because Jc’ varies for cylinders of different diameters. 
J For this purpose the caps were removed from the ends of B lf aud the brass cylinders, by means of 
companion-screws cut along their axes, were adjusted at the required distance on the screws attached to 
the caps ; the caps were then replaced. 
