PROFESSOR G. G. STOKES ON THE COEFFICIENT OF VISCOSITY OF AIR. 793 
vanishing at infinity. Hence the function f 0 (r) is the same in the two cases, save 
as to the value of the arbitrary constant, which is a factor of the whole, and which 
disappears from the expression (12) as well as from those of k and k'. 
The definition of k and k! is given by equation (99) of my former paper, viz. : — 
1 
m 2 a/o(«) 
— ik', 
(15) 
Now, by (13), (14), and (15), 
af 1 '(a) _ _ a/ 0 » _ m*af 0 (a) k + l- W P-1 +k'* + 2ik' > 
fi (a) /„'(«) ^ f 0 '(a ) ^k-l-iP (k-lf + k 1 * ’ 
whence we get, as before, for the part of the logarithmic decrement due to the 
external air, in consequence of the rotations of the two cylinders round their own 
axes, M' denoting the mass of air* which would be displaced by one if solid and of 
radius a, 
■\T 1 ! 4MVt P-l+k'Z , 1CX 
Nap. log. dec. = .0 «) 
In the Table given in Art. 37 of my paper, m denotes half the modulus of ma, or 
a / rr 
2 V uV 
This Table is not available for calculating the effect of the internal air, for which we 
must have recourse to the differential equation (9). The integral of this equation, 
expressed in ascending series, subject to the condition of not becoming infinite at the 
origin, is 
r i 
fii r ) = A|r + 
which gives 
of\(p) 
/i(«) 
1 = 
m 3 r 3 ( 
mV 5 ( 
m 6 i’ 7 
2.4 
2.4 2 .6 ' 
2.4 2 .6 2 .7~' 
m i a i 
m 6 « 6 
4 
+ 2.4.6 + 2.4 2 .6.8 + 
1 t m/cc* t m u cu 
1 + TT + 2A16 + 2,4 2 .6 2 .8 
6/76 
(17) 
+ ... 
Let the numerator of this fraction be denoted by E-J-7F, and the denominator by 
G + fH, where E, F, G, H, are real; then the real part will be EG+FH divided by 
G 2 +H 3 , and we shall have for the correction due to the internal air 
AT . . 2MV EG + FH 
Nap. log. dec. = 
5 1 
(18) 
MDOOCLXXXVI. 
