Haines . — A New A uxanometer . 185 
of C are small compared with the length of this relation holds sensibly 
true throughout the experiment. 
If the only possible source of error were that introduced by stretching 
of the threads consequent upon changes in the relative humidity of the 
atmosphere, this condition would be sufficient in itself to ensure compensa- 
tion ; but as the fibres are also liable to stretch as a result of the tensions to 
which they are subjected, complete compensation will only be obtained if 
the average of the tensions in the fibres Z, Y, and (q + r) taken together be 
made equal to the tension in the fibre XjX 2 . This condition is secured by 
giving appropriate values to the weights V, v' and W (Fig. 2), and these 
values are determined. as follows: 
Suppose the tension maintained in the fibre u by the weight N = t. 
2 / R 
Then the tension in z will be equal to the w r eight of C + ■> and the 
t R 
l K. 
tension in Q = tension in R= 
/ i “^ 2 
As V = v', the tension in X is only due to the weights V, v', and we 
have 
t y 
T X 
T Z 
= w 
= v r 
= c + 
2 t R 
r, —r* 
T(Q + r) = 
2 tR 
where c represents the mass of the pulley c, and 
T x , t Yj &c., represent the respective tensions in the 
fibres X, Y, &c. For equilibrium a weight zv 3 is 
2 / R 
provided, equal to 
ri~r 2 
For compensation (see above), 
Ty + t z + t (Q+R ) 
3 
T X = 
, ( 2/R , 2/R 
1. e. V' = W + C+ + 
i r,-r 2 
m 
= jw + ~ t R +c| / 3, or collecting the constant quantities, 
( r \ ^2 ' ‘ 
R> r 2 , t, and C to one side of the equation, we get 
/ 4 £R 
3V'-w = — +C. 
r,—r 0 
With the exception of the value of t, which can be found by prelimi- 
nary experiment in a manner to be described later, all the quantities on the 
right-hand side of this equation can be easily found by direct measurement 
or weighing, so' that for perfect compensation a weight W is placed in the 
scale-pan, which satisfies the above equation using the given values of 
V and v'. If the tension produced in Y be found insufficient, or great 
enough to harm the growing point, the weights V and v' may be altered 
and the corresponding value for W again found from the equation and 
placed in the scale-pan. The value of V is of the order five to ten grammes, 
