128 U. S. COAST AND GEODETIC SURVEY 
rear section contains the mechanism for the harmonic motions for 
the remaining 31 constituents for which the machine provides. 
359. The angular motions of the individual constituents, as indicated 
by the quantity at in formulas (458) and (459), are represented in the 
machine by the rotation of short horizontal shafts having their bear- 
ings in the parallel plates. All of these constituent shafts are con- 
nected by a system of gearing with the hand crank at the left of the 
dial case and also with the time-registering dials, so that when the 
machine is in operation the motion of each of these shafts will be 
proportional to the speed a of the corresponding constituent, and for 
any interval of time or increment in ¢ as indicated by the time dials 
the amount of angular motion in any constituent shaft will equal 
the increment in the product at corresponding to that constituent. 
360. Since the corresponding angles in formulas (458) and (459) are 
identical for all values of t, the motion provided by the gearing will be 
applicable alike to the solution of both formulas. The mechanism 
for the summation of the terms of formula (458) is situated on the side 
of the machine at the left of the operator, and for convenience this 
side of the machine is called the “height side” (fig. 21), and the mech- 
anism for the summation of the terms of formula (459) is on the right- 
ee side of the machine, which is designated as the “time side” 
(fig. 22). 
361. In table 37 are given the details of the general gearing from the 
hand-operating crank to the main vertical shafts, together with the 
details of ai! the gearing in the front section or dial case. It will be 
noted that S—6 (fig. 25) is the main vertical shaft of the dial case and 
is connected through the releasable gears to the hour hand, the 
minute hand, and the day dial, respectively. The releasable gears 
permit the adjustment of these indicators to any time desired. After 
‘an original adjustment is made so that the hour and mmute hand will 
each read 0 at the same instant that the day dial indicates the begin- 
ning of a day, further adjustment will, in general, be unnecessary, as 
the gearing itself will cause the indicators to maintain a consistent 
relation throughout the year, and by use of the hand-operating crank 
the entire system may be made to indicate any time desired. The 
period of the hour-hand shaft is 24 dial hours, and the hand moves 
over a dial graduated accordingly (3, fig. 23). The minute-hand 
shaft, with a period of 1 dial hour, moves over a dial graduated into 
60 minutes (2, fig. 23). 
362. The day dial, which is about 10 inches in diameter, is graduated 
into 366 parts to represent the 366 days in a leap year. The names of 
the months and numerals to indicate every fifth day of each month are 
inseribed on the face of the dial. This dial is located just back of the 
front plate or face of the machine, in which there is an are-shaped open- 
ing through which the graduations representing nearly two months 
are visible at any one time (J, fig. 23). The progress of the days as the 
machine is operated is indicated by the rotation of this dial past an 
index or pointer just below the opening (6, fig. 23). This pointer is 
secured to a short shaft which carries at its inner end a lever arm with 
a pin reaching under the lower edge of the day dial, against which it is 
pressed by a light spring. A portion of the edge of the dial equal to 
the angular distance from January 1 to February 28 is of a slightly 
larger radius, so that the pin pressing against it rises and throws the 
day pointer to the right one day when this portion has passed by. On 
