HARMONIC ANALYSIS AND PREDICTION OF TIDES. 129 



the height and time crank for any component to be set in accord with 

 the factor /jB" which is common to the coefficients of both formulas 

 (472) and (473) . There are also provided for special use on the time 

 side of the machine unmodified scales graduated uniformly to read in 

 a positive direction. 



Summation chains. — The summations of the several cosine terms in 

 formula (472) and of the several sine terms in formula (473) are car- 

 ried on simultaneously by two chains, one {27 , fig. 16) on the height 

 side and the other {28, fig. 17) 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 01 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. 



Each of these chains is fastened at one end near the back part of 

 the machine by a pair of adjusting screws {53, fig. 14, and 64, fig. 13). 

 From these adjusting screws each chain passes alternately downward 

 under a component pulley of the lower range and upward over a com- 

 ponent pulley of the upper range, spanning the space between the 

 rear and front component frames by two idler pulleys and continuing 

 until every component pulley on each side of the machine is included 

 in the system. The movable pulleys are so arranged that the direc- 

 tion of the chain in passing from one to another is always vertical 

 and parallel to the direction of the motion of the component sliding 

 frames. 



Summation wheels. — The free or movable end of each of the chains is 

 attached to a threaded grooved wheel {29, SO,^g. 16), 12 inches in cir- 

 cumference and threaded to hold more than seven turns of the chain, or 

 about 90 inches in all. These are called the height and time sum- 

 mation wheels. Each is mounted on a shaft that admits a small 

 lateral motion, and by means of a fixed tooth attached to the frame- 

 work 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 summation 

 wheel ; so that the path of the chain as it is wound or unwound from 

 the summation wheel remains unchanged. 



The height summation wheel {29, fig. 16) is located near the front 

 edge of the front component section, where it receives the height 

 summation chain directly from the nearest component pulley. 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 component pulley to the summation wheel. Counter- 

 poise weights are connected with the shafts containing the summa- 

 tion wheels in order to keep the summation chains taut. 



When all of the component 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 component frame in a positive direction will tend to un- 

 wind 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 component frames 

 on either side of the machine moving simultaneously, the resultant 

 motion, which is the algebraic sum of all, will be communicated to 

 the summation wheel. The motion of the component frame being 

 transmitted to the chain through a movable pulley, the motion of 



