HARMONIC ANALYSIS AND PREDICTION OF TIDES 133 
side of the machine unmodified scales graduated uniformly to read in 
a positive direction. 
378. Summation chains.—The summations of the several cosine 
terms in formula (458) and of the several sine terms in formula (459) 
are carried on simultaneously by two chains, one (27, fig. 25) on the 
height side and the other (28, fig. 26) on the time side of the machine. 
The chains are of the chronometer fuse type, of tempered steel, and 
have 125 links per foot. The total length of the height chain is 27.6 
feet and of the time chain 30.6 feet. A platinum point is attached 
to one of the links of the time chain 3.5 feet from its free end for an 
index. 
379. Each of these chains is fastened at one end near the back part 
of the machine by a pair of adjusting screws (89, fig. 29, and 54, fig. 22). 
From these adjusting screws each chain passes alternately downward. 
under a constituent pulley of the lower range and upward over a con- 
stituent pulley of the upper range, spanning the space between the 
rear and middle section of the machine by two idler pulleys and con- 
tinuing until every constituent pulley on each side of the machine is 
included in the system. The movable pulleys are so arranged that 
the direction of the chain in passing from one to another is always 
vertical and parallel to the direction of the motion of the sliding frames. 
380. Summation wheels —The free or movable end of each of the 
chains is attached to a threaded grooved wheel (29, 30, fig. 25), 12 
inches in circumference and threaded to hold more than seven turns 
of the chain, or about 90 inches in all. These are called the height and 
time summation wheels. Each is mounted on a shaft that admits a 
small lateral motion, and by means of a fixed tooth attached to the 
framework of the machine and reaching into the threads of a screw 
fastened to the shaft the latter when rotating is forced into a screw 
motion with a pitch equal to that of the thread groove of the summa- 
tion wheel; so that the path of the chain as it is wound or unwound 
from the summation wheel remains unchanged. 
381. The height summation wheel (29, fig. 25) is located near the 
front edge of the middle section of the machine, where it receives the 
height summation chain directly from the nearest constituent pul- 
ley. The time summation pulley (30) is located inside the dial case 
near the lower left side, and three fixed pulleys are used to carry the 
time chain from the end constituent pulley to the summation wheel. 
Counterpoise weights are connected with the shafts containing the 
summation wheels in order to keep the summation chains taut. 
382. When all of the sliding frames on either side of the machine 
are in their zero positions, the corresponding summation wheel is 
approximately half filled by turns of the summation chain. Any 
motion of a sliding frame in a positive direction will tend to unwind 
the chain from the wheel, and any motion in the negative direction 
will tend to slacken the chain so that it will be wound up by the 
counterpoise weight. With several of the sliding frames on either 
side of the machine moving simultaneously, the resultant motion, 
which is the algebraic sum of all, will be communicated to the sum- 
mation wheel. The motion of the sliding frame being transmitted 
to the chain through a movable pulley, the motion of the free end of 
the chain must be twice as great as that in the pulley. The scale of 
the pulley motion is one-half inch to the unit of amplitude, and there- 
