Haines. — A New A uxanometer. 
183 
latter runs on two grooved wheels on the single rail K, and carries a glass 
pen L (see inset, Fig. 1), the point of which rests on the drum G. 
G revolves once in 12 hours and possesses clips, which are not shown in the 
figure, for affixing graph paper. As the plant grows the pulley C drops by 
the same amount as the plant apex rises. Suppose the plant apex rises 
and the pulley C falls a distance d, then if the thread R passes round 
a groove on E of radius r v Q round a groove of radius r 2 , and U round 
a groove of radius R, it can be easily shown that the trolley F and pen L 
2 d R 
move along the drum a distance -. For, if the pulley E turn through 
r i~ r 2 
one complete revolution, F moves a distance 2 n R (to the left, say), the 
thread R descends a distance 2 ir r v and the thread Q ascends a distance 2 n r 2 . 
C descends a distance equal to half the difference between the distances 
moved by the threads Q and R, = f {2 tt r x — 2 tt r 2 } = it {r 1 — r 2 ). The magnifi- 
distance moved by F 2 tt R 2 R 
cation or ratio 
distance moved by c T \ r i~ r ^ 
plant grow a distance d the pen moves a distance 
2 dR 
so that if the 
When the plant 
grows it allows the differential pulley to turn so that the trolley F carrying 
the pen may move over the drum. The movement is produced by a small 
hanging weight N, and communicated to the trolley by means of the fibre 
‘S which passes over the pulley M. In order that there may be no undue 
strain on the plant, the weight N is such that it only just exceeds the 
value of the limiting friction of the trolley and pulleys. With the same 
object the weight D is provided to counterbalance the weight of C. 
As the pen moves along and the drum G revolves, a spiral line is 
traced out, the pitch of the spiral representing the twelve hours’ growth 
2 R 
multiplied by . The pulley E is made with five separate grooves 
r i ~ r 2 
of radii 5 cm., 4-9 cm., 4*8 cm., 4 >6 cm., and 4-0 cm. (see inset to Fig. 1), so 
that any desired magnification may be obtained by using appropriate pairs 
or threes of the grooves. Any of the fibres may be affixed to any of the 
grooves on E, the end of each fibre being provided with a little hook which 
fits into a notch on the circumference and so facilitates the operation of 
altering the magnification. At T is a clock-work mechanism for rotating 
the drum. It is actuated by a heavy weight (not shown) hanging on the 
end of a flexible brass wire which passes round a drum at H. The weight 
is wound up by the handle P. The pulleys throughout are mounted on 
needle or ‘ frictionless ’ bearings. 
In the apparatus in its simplest form as described above, it will be 
noted that any stretching of the fibres due to changes in humidity in the 
atmosphere all acts in the same direction, namely to make the growth 
appear too much , and as the magnification is large, and there is great length 
