Fig. 94.—Photographic reproduction of the Balanced Crescograph. L, L', magnifying compound lever. R, recording plate. P, plant. C, clock work for oscillation of the plate and lateral movement. G, governor. M, circular growth-scale. V, plant-chamber.
For purpose of simplicity of explanation, I assumed the growth rate to have a definite value of 1⁄50,000 inch per second. But the rate varies widely in different plants and even in the same plant at different days and seasons. In practice the rate of growth for which compensation has to be made varies from 1⁄150,000 to 1⁄25,000 inch, or from 0·17 µ to 1·0 µ per second. We have thus to secure some means of continuous adjustment for growth, the rate of which could be continuously varied from one to six times. This range of adjustment I have been able to secure by the compound method of frictional resistance and of centrifugal governor. As regards frictional resistance the two pointed ends of a hinged fork rub against a horizontal circular plate not shown in the figure. By means of the screw head S, the free ends of the fork spread out and the circumference of the frictional circle continuously increased. The centrifugal governor is also spread out by the action of the adjusting screw. By the joint actions of the frictional control and the centrifugal governor, the speed of rotation can be continuously adjusted from 1 to 6 times. When the adjusting screw is set in a particular position, the speed of rotation, and therefore the rate of subsidence of plant-holder, remains absolutely constant for several hours. The attainment of this constancy is a matter of fundamental importance, and it was only by the employment or the compound system of regulation that I was able to secure it.
The method of obtaining balance now becomes extremely simple. Before starting the balancing movement by clock regulation, the plant is made to record its magnified growth by the Crescograph. The compensation is effected as follows: the speed of the clockwork is at the beginning adjusted at its lowest value, and the pressure of a button starts the balancing movement of the plant downwards. On account of partial balance the record will be found to be less steep than before; the speed of the clock is gradually increased till the record becomes perfectly horizontal under exact balance. Overbalance makes the record slope downwards. In figure 95 is seen records of underbalance (a) and overbalance (b), to the extent of about 3 per cent.
Fig. 95.—Balanced Crescographic record: (a) showing effect of underbalance and (b) overbalance of about 3 per cent. (Magnification 2,000 times.)
It will thus be seen that the effect of an external agent may be detected by the upsetting of the balance; an up-movement indicates (unless stated to the contrary) an enhancement of the rate of growth above the normal; and a down-movement, on the other hand, a depression of the normal rate.
Calibration.—The calibration of the instrument is obtained in two different ways. The rate of subsidence of the plant-holder, by which the balance is obtained, is strictly proportional to the rate of rotation of the vertical spindle and the attached train of clock-wheels. A striker is attached to one of the wheels, and a bell is struck at each complete revolution. The clockwork is adjusted at a medium speed, the bell striking 35 times in a minute. A microscope micrometer is focussed on a mark made on the plant-holder, and the amount of subsidence of the mark determined after one minute; this was found to be 0·0525 mm. As this fall occurred after 35 strokes of the bell the subsidence per stroke was 0·0015 mm.
Determination of the absolute rate of growth.—If growth be found balanced at N strokes of bell per minute, the rate of subsidence per second
= N × ·0015⁄60 mm. per second
= N × ·000025 mm. per second
= N × ·025 µ per second
= N × 10-5 inch per second.
Example.—The growth of a specimen of Zea Mays was found balanced when the number of strokes of the bell was 20 times in a minute.