HARMONIC ANALYSIS) AND PREDICTION OF TIDES 135 
machine is operated the height pointer will indicate the predicted 
height of the tide corresponding to the time shown on the time dials. 
387. In order to increase the working scale of the machine when pre- 
dicting tides with smaller ranges, two additional circular height scales 
are provided, one with the circle divided into 20 units and the other 
into 10 units, with the units subdivided into tenths. These scales 
may be easily removed or replaced on the machine, the scale in use 
being secured in place by a small button at the top (9, fig. 23). The 
20-unit scale may be conveniently used when the extreme range of 
the predicted tide at any place is between 10 and 20 feet, and the 
10-unit scale when the extreme range is less than 10 feet. If the 20- 
unit scale is to be used, the value of each coefficient of both the cosine 
and the sine terms must be doubled before setting the component 
cranks, and if the 10-unit scale is used these original coefficients must 
first be multiplied by 4 before setting the values in the machine. If 
the extreme tide is less than 4 feet, the 40-unit dial may be readily 
used as a 4-unit scale by considering the original unit graduations as 
tenths of units in the larger scale. In this case the coefficients of the 
cosine and sine terms of the formula must be multiplied by 10 before 
entering in the machine. The factor used for multiplying the coeffi- 
cients to adapt them to the different height scales is called the work- 
ing scale of the machine. Working scales of 1, 2, 4, and 10 are now 
in general use to take account of the different ranges of tide at the 
places for which predictions are made. 
388. Predicted times of the tide.—Simultaneously with the summation 
of the cosine terms of formula (458) on the height side of the machine, 
the summation of the sine terms of formula (460), which was derived 
from formula (459), is being effected on the time side. Being con- 
cerned only with the time at which the sum of the sine terms is zero, 
no provision is made for registering the sum except at this time, 
which is indicated on the machine by the conjunction of the index 
point on the time chain and the fixed platinum index in the dial case. 
Near the time of a high water the index on the chain moves from right 
to left and near the time of a low water from left to right. The con- 
junction of the movable and fixed index is visible to the operator of 
the machine and he may note the corresponding dial readings for the 
time and height of the high or low water. 
389. Automatic stopping device——This device provides for auto- 
matically stopping the machine at each high and low water. Secured 
to the hand-crank shaft is a ratchet wheel and just above the ratchet 
wheel is a steel pawl (25, fig. 24) operated by an electromagnet (26) 
mounted under the desk top. The electric circuit for the electromag- 
net is closed by a contact spring that rests upon a hard-rubber cylinder 
(31, fig. 25) on the rear end of the shaft on which the time summation 
wheel is mounted. A small platinum plug in this rubber cylinder 
comes in contact with the spring, which is fitted with a fine motion 
adjustment, when the time summation chain registers zero. This 
closes the circuit and draws the pawl against the ratchet wheel, 
thereby automatically stopping the machine. The lateral screw 
motion of the shaft on which the rubber cylinder is mounted prevents 
the platinum plug from coming in contact with the spring on any 
revolution other than the one which brings the time chain to its zero 
position. The circuit is led through an insulated ring on the hub 
of the hand crank where a contact is kept closed by a spring. After 
