PENDULUM METHODS 



167 



The movement of the point on its elhptical trajectory can be 

 represented by that of a point moving uniformly on a circle 

 of the same amplitude (sinusoidal law of the pendulum). 

 In particular the passages over the bars at a, b, c and d 

 will synchronize with the points of the same order a', &', 

 c' and d' on the circle (Fig. 103) and o'p measures on this 

 figure, y, one of the desired coordinates for finding zz\ 



Y" 9 



Fig. 103. 



This uniform circular synchronous motion is indicated 

 aboveground by a registering pen in the receiving appara- 

 tus; an electromagnet records the passages over the bars 

 by controlling the penholder in the circuit. 



Thus we may get the figure o", a", b", c", d" (Fig. 103a), 



the last four points being the passage points of the pendulum 



over the bars. The value of y deduced from the diagram 



will then be 



o"mk ,.^s 



y = -p^ (11) 



The same reasoning with another projection following 

 the other system of bars (reglets) would give from the same 

 diagram completed by the other four points of contact:^ 



o"nk , . 



X = -pr (11a) 



The ratio of the recording pen and the transmitting 

 pendulum is k" /k. k" and k'" depend on the values of the 

 lengths OX and OY, usually different. 



1 FoRAKY, loc. cit., p. 71. 



