HARMONIC ANALYSIS AND PEEDICTION OF TIDES. , 125' 



On the same center with the day pomter there is a smaller index 

 (7, fig. 12) which may be turned either to the right toward a plate in- 

 scribed ''Common year," or to the left to a plate inscribed ''Leap 

 year." When this smaller index is turned toward the right, the day 

 pointer is free to move in accordance with the change in radius of the 

 edge of the dial. If the smaller index is turned toward the left, the 

 day pointer is locked and must hold a fixed position throughout the 

 year. For the prediction of the tides for two or more common years 

 in succession the day dial must be set forward one day at the close of 

 the year, in order that the days of the succeeding year may be cor- 

 rectly registered. The day dial can be released for setting by the nut 

 (5, fig. 12) immediately above the large dial ring. A slower move- 

 ment of the day dial is provided by a releasable gear on the vertical, 

 shaft 5-^ (fig. 16). 



There are three main vertical component shafts S-18 (fig. 18), S-14- 

 (fig. 19), and S-16 (fig. 14), to which are connected the gearing for the 

 individual components. The period of rotation of each is 12 dial 

 hours, and all move clockwise when viewed from above the machine. 

 The connections between these main component shafts and the indi- 

 vidual component crank shafts are, in general, made by two pair of 

 bevel gears and an intermediate horizontal shaft, except that for the 

 slow moving components Sa, Ssa, IVIm, Mf, and Msf , a worm screw and 

 wheel and a pair of spur gears are in each case substituted for a pair 

 of bevel gears. In each case the gear on the main vertical shaft is 

 releasable so that each component crank shaft can be set independ- 

 ently. 



Main component shaft S-13 in the front component section drives 9 

 individual component crank shafts representing 6 components, 3 of the 

 components being provided with two crank shafts each. These 6 

 components are M^, S,, K^, Nj, M4, and 0^, the first three having the 

 double crank shafts. Main component shaft S-I4 at the front 

 of the rear component section drives 16 component crank shafts repre- 

 senting one component each. These are Mg, MK, S4, MN, v^, Sg, n^f 

 and 2N in the upper range, and MS, Mg, K,, 2MK, L,, M3, 2SM, and 

 Pi in the lower range. Main component shaft S-16 at the back of 

 the rear component section drives 15 component crank shafts. The 

 components represented are 00, X2, S^, M^, J^, Mm, and Ssa, in the 

 upper range, and 2Q, Rj, T,, Qi, Pi, Mf , MSf , and Sa in the lower range. 



For each of the five long-period components motion is communi- 

 cated from the intermediate shaft by a worm screw and wheel to a 

 small shaft on which is mounted a sliding spur gear. The latter en- 

 gages a spur gear on the component crank shaft, but may be easily 

 disconnected by drawing out a pin on the time side of the machine^ 

 thus permitting the component crank shaft to be turned freely when 

 setting the machine. 



Gear speeds. — The relative angular motion of each individual com- 

 ponent shaft must correspond as near as possible to the theoretical 

 speed of the component represented. The period of rotation of each 

 of the three main vertical shafts being 12 dial hours, the angular 

 motion of each of these shafts is 30° per dial hour. Table 38 con- 

 tains the details of the gearing from the main vertical component 

 shafts to the individual component cranks, the number of teeth in 

 the different gears for each component being given in columns I, 11^ 

 III, and IV. In designing the predicting machine it was necessary 



