128 U. S. COAST AND GEODETIC SUEVEY. 



from its zero position will always equal the product of the amplitude 

 setting of the crank pin by the cosine of the component dial reading, 

 and the displacement of each component time frame will always 

 equal the product of the amplitude setting by minus the sine of the 

 component dial reading. 



Component pulleys. — Each component frame is connected with a 

 small movable pulley (4^, fig. 16). For all components except 

 M2, S2, N2, Kj, Oj, and Sa on the height side and components Mj, 

 So, N2, and M4 on the time side this connection is by a single steel 

 strip, so that the pulley has the same vertical motion as the cor- 

 responding component frame. 



Doubling gears. — Because of the very large amplitudes of some of 

 the components two methods were used in order to keep the lengths 

 ■of the cranks within practical limits. For the components Mo, So, and 

 Ki two sets of shafts and cranks were provided, so tiiat the amplitudes 

 of these components may be divided when necessary and a portion 

 set on each. A further reduction in the length of the cranks for 

 these and the other components named in the paragraph above is 

 accomplished by the use of doubling gears between the component 

 frame and movable pulley. Two spur gears with the ratio of 1 : 2 

 (4-8, fig. 16) are arranged to turn together on the same axis. The 

 smaller gear engages a rack (4^) attached to the component frame 

 and the larger gear engages a rack (4?) attached to the component 

 pulley. Each rack is held against its gear by a flange roller (49), 

 and counterpoise weights are provided to take up the backlash in 

 the gears. Through the action of these doubling gears any motion 

 in the component frame causes a motion twice as great in the com- 

 ponent pulley. Doubling gears are provided on the height side of 

 the machine for components Mo, S^, Nj, Kj, 0^, and Sa and on the 

 time side for components M2, §2, Nj, and M^. 



Scales for amplitude settings. — The scales for setting the component 

 amplitudes are attached to the frame of the machine and are, in 

 general, graduated into units and tenths (44, fig- 16). The scales 

 are arranged to read in a negative direction; that is, downward for 

 the components of the upper range and upward for the components 

 in the lower range. On a small adjustable plate (4o) attached to 

 each component pulley there is an index line which is set to read zero 

 on the scale when the component frame is in its zero position. For 

 setting the crank pins for the component amplitudes the cranks to 

 be set are first turned to a negative vertical position. For the cranks 

 on the height side of the machine this position corresponds to a dial 

 ■reading of 180° and for the cranks on the time side to a reading of 90°. 



The scales on the height side of the machine, which are used in 

 setting the coefficients of formula (472) , are graduated uniformly one- 

 half inch to the unit. On the time side of the machine the scales are 

 modified in order to automatically take account of the additional 

 factor involving the speed of the component which appears in each of 

 the coefiicients of formula (473). Dividing the members of this for- 

 mula by m, the speed of component Mj, it becomes 



-^-fH sin (at + a) = (474) 



The modified scales are graduated 0.5 ajm inch to the unit. The use 

 of the modified scales on the time side of the machine permits both 



