74 ; REPORT—1 883. 
§ 4. Meteorological Tides, Over-tides, and Compound Tides. 
Meteorological Tides. 
A rise and fall of water due to regular day and night breezes, 
prevalent winds, rainfall and evaporation, is called a meteorological tide. 
All tides whose period is an exact multiple or sub-multiple of a mean 
solar day, or of a tropical year, are affected by meteorological conditions. 
Thus all the tides of the principal solar astronomical series S, with speeds 
y—n, 2 (y—n), 3 (y—n), &e., are subject to more or less meteorological 
perturbation. Although the diurnal elliptic tide, S, or y—n, the semi- 
annual and annual tides of speeds 2y and 7», are all probably quite insens- 
ible as arising from astronomical causes, yet they have been found of 
sufficient importance to be included on the tide-predicter. 
The annual and semi-annual tides are of enormous importance in 
some rivers; in such cases the ter-annual tide (3y) is probably also 
important, although no harmonic analysis has been as yet made for it. 
In the reduction of these tides the arguments of the S series are ¢, 
2t, 3t, &c., and of the annual, semi-annual, ter-annual tides are h, 2h, 3h. 
As far as can be foreseen, the magnitudes of these tides will be constant 
from year to year. 
Over-tides. 
When a wave runs into shallow water its form undergoes a progres- 
sive change as it advances; the front slope generally becomes steeper 
and the back slope less steep. The most striking example of sucha 
change is when the tide runs up a river in the form of a ‘ bore.’ 
A wave which in deep water presented an approximately simple 
harmonic contour departs largely from that form when it has run into 
shallow water. Thus in rivers the rise and fall of the water is not even 
approximately a simple harmonic motion. From the nature of harmonic . 
analysis we are, however, able to represent the motion by simple 
harmonic oscillations, and thus to give the non-harmonic rise and fall of 
tide in shallow water it is necessary to introduce a series of over-tides 
whose speeds are double, triple, quadruple the speed of the fundamental 
astronomical tide. 
The only tides, in which it has hitherto been thought necessary to 
represent this change of form in shallow water, belong to the principal 
lunar and principal solar series. Thus, besides the fundamental astro- 
nomical tides M, and S,, the over-tides M,, Mg, Ms, and 8,, 8, have 
been deduced by harmonic analysis. 
The height of the fundamental tide M, varies from year to year, 
according to the variation in the obliquity of the lunar orbit, and this 
variability is represented by the coefficient cos‘ 5 J. It is probable that 
the variability of M,, M,, Mg, will be represented by the square, cube 
and fourth power of that coefficient. 
The law connecting the phase of an over-tide with the height of the 
fundamental tide is unknown, and under these circumstances it is only 
possible to make the argument of the over-tide a multiple of the argu- 
ment of the fundamental, with a constant subtracted. If that constant 
is found to be the same from year to year, then it will be known that the 
phase of an over-tide is independent of the height of the fundamental tide. 
The following schedule gives the over-tides which must be taken into 
consideration, the notation being the same as before :— 
