Haines. — A New A uxanometer. 
1 86 
and W may be anything from about 1-5 grm. down to 0*5 grm. or less, 
according to the nature of the plant on which the experiment is conducted. 
All stretching of the fibres is now compensated for except that of the 
fibre U, which connects the trolley and differential pulley. Stretching here 
is far less serious than elsewhere as it is not magnified by the instrument. 
It will be seen that, supposing the instrument be magnifying the growth 
a hundred times, even if the fibre stretch as much as the plant grows (which 
it is very unlikely to do) the error will only be one per cent., and is 
therefore scarcely worth correcting for. With lower magnifications and any 
very accurate work, however, the error may be completely eliminated by 
using a control fibre. A fibre 10 cm. long attached to a trolley of its own 
running on a rail by the side of the first may be fixed to a special hook on 
the stand carrying the differential pulley and be subjected by similar means 
to the same tension as the first fibre. The expansions and contractions of 
the control fibre are recorded at one end of the drum, and if they amount 
to anything appreciable, the correction for the particular length of the fibre 
U which has run out from E at any moment may be calculated and added 
or subtracted from the recorded reading as the case may be. In order to 
facilitate the determination of the length of U a scale of centimetres is 
provided beside the rail K, the zero-mark being perpendicularly below the 
bearings of E. When only a twelve hours’ observation is taken and the 
travel of the trolley is large, the paper on the drum, when unfolded, will 
reveal two graphs which may be added together algebraically to give the 
correct curve. 
Before an experiment, when no plant is connected with Y and the 
scale-pan W is empty, small weights are gradually added to a light scale- 
pan hanging at N, until the weight is found which will just set the experi- 
mental trolley and differential pulley, &c., in motion. Let the weight 
found = w v Next the weight is found which sets the trolley in motion 
when disconnected from the differential pulley. Let this weight = w 2 . 
Then, when the whole apparatus is fitted up for an experiment, and the 
weight in the scale-pan at N is w v the tension in the fibre U is given by 
the equation t — (w w + w 1 )-(w Jl + ^ 2 ), where W n is the weight of the scale- 
pan at N. 
i. e. t = w 1 — w r 
This is the value of t which should be substituted in the expression 
, 4 ^ R 
<$v — w = — +C, 
T l~~ r 2 
when finding the correct value of w which ensures compensation in the 
fibres Q, R, X 2 X 2 , Y, and Z (Fig. a). With a given value for the weights 
V and v', therefore, the complete working equation for W is as follows : 
'4R (Wj-W 2 ) 
r, — r 0 
W 
= 3V'-{- 
+ c 
}• 
