HARMONIC ANALYSIS AND PREDICTION OF TIDES 127 
354. The first tide-predicting machine used in the United States was 
designed by William Ferrel, of the U. S. Coast and Geodetic Survey. 
This machine, which was completed in 1882, was based upon modified 
formulas and differed somewhat in design from any other machine 
that has ever been constructed. No curve was traced, but both the 
times and heights of the high and low waters were indicated directly 
by scales on the machine. The intermediate heights of the tide could 
be obtained only indirectly. A description of this machine is given 
in the report of the Coast and Geodetic Survey for the year 1883. 
355. The first machine made to compute simultaneously the height 
of the tide and the times of high and low waters as represented by 
formulas (458) and (459), respectively, was designed and constructed 
in the office of the Coast and Geodetic Survey. It was completed in 
1910 and is known as the United States Coast and Geodetic Survey 
tide-predicting machine No. 2. The machine sums simultaneously 
the terms of formulas (458) and (459) and registers successive heights 
of the tide by the movement of a pointer over a dial and also graphi- 
cally by a curve automatically traced on a moving strip of paper. 
The times of high and low waters determined by the values of ¢ which 
satisfy equation (459) are indicated both by an automatic stopping 
of the machine and also by check marks on the graphic record. 
356. The general appearance of the machine is illustrated by figure 
21. Itis about 11 feet long, 2 feet wide, and 6 feet high, and weighs 
approximately 2,500 pounds. The principal features are: First, the 
supporting framework; second, a system of gearing by means of which 
shafts representing the different constituents are made to rotate with 
angular speeds proportional to the actual speeds of the constituents; 
third, a system of cranks and sliding frames for obtaining harmonic 
‘motion; fourth, summation chains connecting the individual constitu- 
ent elements, by means of which the sums of the harmonic terms of 
formulas (458) and (459) are transmitted to the recording, devices; 
fifth, a system of dials and pointers for indicating in a convenient man- 
ner the height of the tide for successive instants of time and also the 
time of the high and low waters; sixth, a tide curve or graphic represen- 
tation of the tide automatically constructed by the machine. The 
machine is designed to take account of the 37 constituents listed in 
table 38, including 32 short-period and 5 long-period constituents. 
357. The heavy cast-iron base of the machine, which includes the 
operator’s desk, has an extreme length of 11 feet and is 2 feet wide. 
This forms a very substantial foundation for the superstructure, 
increasing its stability and thereby diminishing errors that might 
result from a lack of rigidity in the fixed parts. On the left side of 
the desk is located the hand crank for applying the power (J, fig. 24), 
and under the desk are the primary gears for setting in motion the 
various parts of the machine. The superstructure is in three sections, 
each consisting of parallel hard-rolled brass plates held from 6 to 7 
inches apart by brass bolts. Between these plates are located the 
shafts and gears that govern the motion of the different parts of the 
machine. 
358. The front section, or dial case, rests upon the desk facing the 
operator and contains the apparatus for indicating and registering 
the results obtained by the machine. The middle section rests upon @ 
depression in the base and contains the mechanism for the harmonic 
motions for the principal constituents Mo, S., Ki,O1, N2, and My. The 
