HARMONIC ANALYSIS AND PREDICTION OF TIDES 131 
against the small spring at the back, forces the crank-pin block 
outward against the flanges of the groove with sufficient pressure 
to prevent any slipping. A milled head wrench B is used for tighten- 
ing the clamp screw. A small rectangular block e of hardened steel 
is fitted to turn freely upon the finely polished axle of the crank pin. 
‘This block is designed to fit into and slide along the slot of the con- 
stituent frame. 
370. Positive and negative direction.—All the constituent crank shafts 
and cranks may be grouped into two ranges—those above the medial 
horizontal plane of the framework being in the upper range and those 
below this plane in the lower range. In the following discussion 
direction toward this medial plane is to be considered as negative 
and direction away from the plane as positive; that is to say, for all 
constituents in the upper range the positive direction will be upward 
and the negative direction downward, while for the constituents in the 
lower range the positive direction will be downward and the negative 
direction upward. 
371. Constituent dials —To indicate the angular positions of the 
constituent crank shafts, the pointer (a, fig. 31) moves around a dial 
(41, fig. 25) which is graduated in degrees. These dials are fastened 
to the frame of the machine back of the constituent cranks on both 
sides of the machine, those on the time side being graduated clockwise 
and those on the height side counterclockwise. These dials and 
pointers are so arranged that the angular position of a constituent 
crank shaft at any time will be the same whether read from the dial 
on the height side or from the dial on the time side of the machine, 
and at the zero reading for any constituent the height crank will be 
in a positive vertical position and the corresponding time crank in a 
horizontal position. At a reading of 90° the height crank will be 
horizontal and the time crank in a negative vertical position. 
372. With the face of the machine registering the initial epoch, such 
as January 1, 0 hour, of any year, the value of ¢ then being taken as 
zero, each constituent crank shaft may be set, by means of its releas- 
able gear, so that the dial readings will be equal to the a of the corre- 
sponding constituent as represented in formulas (458) and (459). If 
the machine is then put in operation, the dial readings will, for succes- 
sive values of ¢, continuously correspond to the angle (at+a) of the 
formulas, as the gearing already described will provide for the 
increment at. 
373. Constituent sliding frames.—For each constituent crank there 
is a hight steel frame (42, fig. 25) fitted to slide vertically in grooves in 
a pair of angle pieces attached to the side plates of the machine. At 
the top of the frame there is a horizontal slot in which the crank pin 
slides. As the machine is operated the rotation of the crank shafts 
with their cranks cause each crank pin to move in the circumference 
of a circle, the radius of which depends upon the setting of the pin on 
the crank. This motion of the pin, acting in the horizontal slot of 
the sliding frame, imparts a vertical harmonic motion to that frame. 
The frame is in its zero position when the center horizontal line of the 
slot intersects the axis of the crank shaft. Positive motion is the 
direction away from the medial horizontal plane of the machine and 
negative motion is toward the medial plane. The displacement of 
each constituent height frame from its zero position will always ‘equal 
the product of the amplitude setting of the crank pin by the cosine 
