61G PROF. J. J. THOMSON AND MR. G. F. C. SEARLE ON THE RATIO OF THE 
Ex'plcmation of Table of Results and Methods of Reduction. 
Column 2 gives the approximate speed of the commutator. 
Column 3 gives the beats per minute between the standard fork and the auxiliarv 
fork driven by the electrically maintained fork. The auxiliary fork vibrated twice as 
fast as the driving fork, and was slightly slower than the standard. 
Column 4. The temperature of the fork given by a thermometer hung a short 
distance from the fork. 
Columns 5 and 6, The resistances of the arms AC and BD in legal ohms at 16° C. 
Column 7 gives the value of the resistance in CD required for the balance when 
both the condenser and the connecting wire were joined to the key of the commutator. 
We shall denote this by Each number is the mean of two observations made with 
the current from the battery flowing first in one direction and then in the opposite. 
The difference between the two readings very seldom amounted to more than 1 ohm. 
Column 8 gives the value of the resistance in CD required for the balance when the 
wire alone is joined to the key of the commutator. We shall denote this by Each 
is the mean of two readings corresponding to the two directions of the batterv 
current. 
Column 9 gives the difference between the last two columns. We must remark 
that, since the formula rtC = yj^b is not sufficiently accurate for our purpose, that 
this difference does not strictly represent the value of y, which would be required to 
balance the condenser alone. With the resistances employed we may write the 
formula (7) 
7_(7jt «)1 
D + D/3J ’ 
so that if, as in our case, we keep /3 and b constant, nO is not quite proportional to y. 
Strictly, we should find the capacity of the combination of the condenser and wire, 
and then subtract the capacity of the wire. What we have done is to calculate as if 
y^ — y 2 represented the capacity of the condenser. The difference amounts to writing 
in the small term y (y + “)/(y + b) /3, y^ — y^ instead of y^, since the correcting term 
inside the bracket, in the case of the wire, is too small to be appreciable. Since, how¬ 
ever, this term is already very small, and does not affect the result by much more than 
one part in 2000, and the change we have made only alters its value by 1 per cent, at 
most, it is evident that it will produce no appreciable effect on the value of the 
capacity. 
Cklumn 10 is headed “(reduced to 64).” Since the value of the capacity is given hy 
_ 7 f 1 _ 7(7_+y)l 
' D + i)ySr 
or witli sufficient accuracy for our purpose by 
