HARMONIC ANALYSIS AND PREDICTION OF TIDES 129 
the last day of December this pointer will move back one day to its 
original position. 
363. On the same center with the day pointer there is a smaller index 
(7, fig. 23) 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. 23) immediately above the large dial rmg. <A slower move- 
ment of the day dial is provided by a releasable gear on the vertical 
shaft S-6 (fig. 25). 
364. There are three main vertical shafts S-13 (fig. 27), S-14 
(fig. 28), and S-16 (fig. 29), to which are connected the gearing for the 
individual constituents. 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 shafts and the individual con- 
stituent crankshafts are, in general, made by two pairs of bevel gears 
and an intermediate horizontal shaft, except that for the slow moving 
constituents Sa, Ssa, Mm, 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 cach case the gear on the main vertical shaft is releasable 
so that each crankshaft can be set independently. 
365. Main shaft S-13 in the middle section of the machine drives 9 
individual crankshafts representing 6 constituents, 3 of them being 
provided with two crankshafts each. These 6 constituents are Mo, 
Se, K,, No, M,, and O,, the first three having the double crankshafts. 
Main shaft S-14 at the front of the rear section of the machine drives 
16 crankshafts representing one constituent each. These are Mg, 
MK, S,, MN, v2, Ss, 2, and 2N in the upper range, and MS, Msg, K,, 
2MK, L., M3, 28M, and P, in the lower range. Main shaft S—16 at 
the back of the rear section drives 15 crankshafts. The constituents 
represented are OO, d2, S;, M,, J:, Mm, and Ssa, in the upper range, 
and 2Q, Ro, T2, Q:, p:, Mf, MSf, and Sa in the lower range. 
366. For each of the five long-period constituents motion is com- 
municated from the intermediate shaft by a worm screw and wheel 
to a small shaft on which is mounted a sliding spur gear. The latter 
engages a spur gear on the crankshaft, but may be easily discon- 
nected by drawing out a pin on the time side of the machine, thus 
permitting the crankshaft to be turned freely when setting the 
machine. 
367. Gear speeds —The relative angular motion of each constituent 
crankshaft must correspond as nearly as possible to the theoretical 
speed of the constituent 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 shafts to the 
individual crankshafts, the number of teeth in the different gears 
for each constituent being givenincolumnsI,II,III,andIV. In design- 
ing the predicting machine it was necessary to find such values for these 
