28 CHAP. III. THE BALANCED CRESCOGKAPH 



to devise a universal apparatus based on a different method, 

 that of the incUned plane. 



Imagine the plant-holder so held that its lower pointed 

 end rests on an inchned plane which slopes down to the left ; 

 suppose further that the inclined plane is being pushed 

 forward to the right at a uniform rate. This will result in 

 the gradual subsidence of the plant-holder, the rate depend- 

 ing on the angle of inchnation (fig. ii). When the angle is 

 reduced to zero, the plane becomes horizontal, and there is 

 no subsidence, the balancing arrangement being thus put 

 out of operation. The rate of subsidence is, on the other 

 hand, gradually enhanced by a continuous increase in the 

 angle of inclination. 



The rate of forward movement of the inclined plane has 

 been assumed to be constant. It is obvious that greater 

 speed of movement of the plane will correspondingly increase 

 the rate of subsidence. The problem of balancing widely 

 different rates of growth w^as solved by appropriate modifica- 

 tions of the angle of inchnation of the plane and the rate 

 of its forward movement. In practice, instead of a solid 

 inclined plane, a board is employed the inchnation of which 

 can be varied. 



The rate of subsidence for balancing growth will thus 

 depend on the following 



1. On the constant of the particular apparatus ; 



2. On the angle of inclination ; and 



3. On the rate of forward movement of the plane as 

 determined by the period of rotation of the vertical 

 spindle. 



Taking these factors into consideration the formula for 



absolute measurement of 



J K tan i 

 the rate of growth [i per second = 7 



K is the constant of the apparatus ; 

 i is the angle of inclination ; and 



t is the period of a complete revolution of the vertical 

 spindle in seconds. 



