132 U. S.ZCOAST AND GEODETIC SURVEY 
of the constituent dial reading, and the displacement of each consti- 
tuent time frame will always equal the product of the amplitude 
setting by minus the sine of the constituent dial reading. 
374. Constituent pulleys —Each constituent frame is connected with 
a small movable pulley (43, fig. 25). For all constituents except 
M., S., No, Ki, O1, and Sa on the height side and Mz, S,, No, and M, 
on the time side this connection is by a single steel strip, so that the 
pulley has the same vertical motion as the corresponding frame. 
375. Doubling gears.—Because of the very large amplitudes of some 
of the constituents two methods were used in order to keep the lengths 
of the cranks within practical limits. For Mz, S:, and K, two sets of 
shafts and cranks were provided, so that the amplitudes of these 
constituents 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 large constituents is accomplished by the use of doubling 
gears between the sliding frame and movable pulley. Two spur 
gears with the ratio of 1:2 (48, fig. 25) are arranged to turn together 
on the same axis. Thesmaller gear engages a rack (46) attached to the 
sliding frame and the larger gear engages a rack (47) attached to the 
constituent 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 sliding frame causes a motion twice as great in the 
constituent pulley. Doubling gears are provided on the height side of 
the machine for constituents M:, S:, No, K,, O,, and Sa and on the 
time side for constituents Ms, S:, No, and Mg. 
376. Scales for amplitude settings ——The scales for setting the con- 
stituent amplitudes are attached to the frame of the machine and are, 
in general, graduated into units and tenths (44, fig. 25). The scales 
are arranged to read in a negative direction; that is, downward for 
the constituents of the upper range and upward for the constituents 
in the lower range. On a small adjustable plate (45) attached to 
each constituent pulley there is an index line which is set to read zero 
on the scale when the sliding frame is in its zero position. For 
setting the crank pins for the constituent 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°. 
377. The scales on the height side of the machine, which are used in 
setting the coefficients of formula (458), 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 constituent which appears in each of 
the coefficients of formula (459). Dividing the members of this for- 
mula by m, the speed of constituent M2, it becomes 
= = fH sin (at+a)=0 (460) 
The modified scales are graduated 0.5 a/m inch to the unit. The use 
of the modified scales on the time side of the machine permits both 
the height and time crank for any constituent to be set in accord with 
the factor fH which is common to the coefficients of both formulas 
(458) and (459). There are also provided for special use on the time 
