HARMONIC ANALYSIS!) AND PREDICTION OF TIDES 137 
receiving roller to wind up all the paper delivered by the feed roller, 
the tension on the paper being kept uniform by the friction device. 
To remove a completed roll of record the smaller sprocket is lifted 
from the receiving roller and a pin (89, fig. 25) at the back of the dial 
case is drawn out, releasing the upper bearing bracket. The bracket 
can then be raised and the receiving roller with its record removed. 
A similar bracket secured by a pin is provided for the removal of the: 
mandrel on which the blank roll of paper is placed. 
395. Marigram gears.—The pen that traces the tide curveismounted. 
in a carriage which is arranged to slide vertically on a pair of guiding’ 
rods and is controlled from a horizontal shaft at the back of the dial! 
case. On this shaft there is mounted a set of three sliding change 
gears (18, fig. 26), which are designed to mesh, respectively, with 
three fixed gears mounted on a shaft just above. By sliding the 
change gears in different positions any one of them may be brought 
into mesh with its corresponding fixed gear. These gears provide 
for ratios of 1:1, 2:1, and 3:2, according to whether the innermost, 
the middle, or the outer gears are in mesh. At the outer end of the 
shaft containing the fixed gears is a thread-grooved wheel 4 inches: 
in circumference (19, fig. 26), to which is attached one end of the 
pen-carriage chain (20, fig. 26). The chain is partly wound upon the 
wheel and from it passes through the dial case to the front of the 
machine, then upward over a pulley near the top to a counterpoise: 
weight within the dial case. The pen carriage is secured to this chain 
by means of a clamp and can be adjusted to any desired position. 
396. Scale of tide curve—With a working scale of unity, the rotation 
of the height summation wheel, as transmitted through marigram 
gear ratio of 1:1 to the curve-line pen, will move the latter vertically 
0.1 inch for each unit change in the sum of the harmonic terms and 
this may be taken as the basic or natural scale of the graphic record. 
This scale may be enlarged by the factor 3/2 or 2 through the use of 
one of the other gear ratios and may be further modified to any 
desired extent by the introduction of an arbitrary working scale 
factor. Letting G equal the marigram gear ratio (1, 3/2, or 2) and 
S equal the working scale factor applied to the amplitude settings,. 
the vertical scale of the graphic record may be expressed as follows: 
1 inch of graph represents 10/GS units of summation (461) 
1 summation unit is represented by GS/10 inches in graph (462) 
The scale ratio of the graph will differ with different units used in. 
the predictions. Thus 
Graph scale (amplitude settings in feet) = GS/120 (463) 
Graph scale (amplitude settings in meters) = GS/393.7 (464) 
Graph scale (amplitude settings in decimeters) = GS/39.37 (465): 
397. In selecting the marigram gear ratio and scale factor for the 
predictions at any station, it is the general aim to secure as large a 
scale as possible while keeping the graph within the limits of the paper. 
Some consideration must be given also to the limits of the height. 
dial scale and in some instances to the mechanical limits of the indi- 
vidual amplitude settings. The marigram gear ratio affects the 
graph only but the scale factor affects also the amplitude settings and 
the height dial readings. The extreme amplitude of the graphi¢ 
