PROGRESS OF OUR KNOWLEDGE OF THE TIDES. 121 
given port rendered it quite simple to mechanically combine 
the various components into the complex wave of nature. 
Given the harnmnic constants for any port, and a tide-pre¬ 
dicting machine, quite accurate predictions of the tides can 
now be made as easily as the roughest predictions could he 
made by the old methods. 
Considerable progress has been made in the study of tidal 
oscillations in the great oceanic basins by Dr. R. A. Harris, 
of the Coast and Geodetic Survey, and the following is taken 
from his notes on the subject, but with modifications to suit 
the present case. 
This study of the causes of the tides aims to actually pick 
out from the oceans and other bodies of water such systems 
as are capable of independent oscillation in approximately 
the period of the tidal forces. More than this, it supposes 
the tidal forces to be distributed over the waters of each sys¬ 
tem, and the time of elongation of the water particles—that 
is, the time of high or low water—to be thus determined with 
reference to the tidal body. This having been done, and the 
theoretical results compared with the observed values, it is 
asserted, I believe for the first time, that in most cases the 
dominant ocean tides have their origin in definite systems whose 
free periods of oscillation are very nearly those of the tidal forces, 
and that the time of high or low ivater in each is the time when 
the virtual work of the tidal forces upon the system becomes zero• 
For the semidiurnal tides there are 7 such systems pointed 
out. For the diurnal tides the systems are much fewer and 
less certain. A system may comprise several regions, com¬ 
paratively simple in form, styled “ oscillating areas.” If 
these areas could be partitioned off, each would have as its 
free period of oscillation approximately the period of the 
tidal body. From the tides thus produced are derived both 
stationary and progressive waves. The former will be noticed 
further on. 
If diagrams are constructed showing the intensity and 
direction of the tidal or disturbing forces for each 5 or 10 
degrees of latitude, making separate figures for the semi- 
