-1 
Or 
HARMONIC ANALYSIS OF TIDAL OBSERVATIONS, 
LF.] 
Schedule of Over-tides. 
Speed in degrees 
5 F < 
Tide | Coefficient Argument Speed per m. s. hour 
M, | (cost } 1)?| 4t+4(h—v)—4(s—2) | 4y—4e | 57°-9682082 
M, | (cos } 1)3| 6¢+6(h—v)—6(s—)| 6y—6s | 86°-9523126 
M, | (cost } 1*|8t+8(h—+)—8 (s—5)| 8y—8e | 115°-9364164 
S, 1 At 4y—4n 60°-0000000 
S¢ 1 6E 6y—6n 90°-0000000 
It will be understood that here, as elsewhere, the column of argu- 
ments only gives that part of the argument which is derived from theory, 
and the constant to be subtracted from the argument is derivable from 
observation. It is necessary to have recourse also to observation to 
determine whether the suggested law of variability in the magnitude of 
the M over-tides holds good. 
Compound Tides. 
When two waves of different speeds are propagated in the same 
water the vertical displacement at the surface is generally determined 
with sufficient accuracy by summing the displacements due to each wave 
“separately. If, however, the height of the waves is not a small fraction 
of the depth of the water, the principle of superposition leads to inaccuracy, 
and it becomes necessary to take into consideration the squares and pro- 
ducts of the displacements. 
It may be shown that the result of the interaction of two waves is 
represented by introducing two simple harmonic waves, whose speeds are 
the sum and the difference of those of the interacting waves. When 
the interacting waves are tidal these two resultant waves may be called 
compound tides. They are found to be of considerable importance in 
estuaries. : 
A compound tide being derived from the consideration of the product 
of displacements, we may form an index number, indicative of the 
probable importance of each compound tide by multiplying together the 
semi-ranges of the component tides. 
Probably the best way of searching at any station for the compound 
tides, which are likely to be important, would be to take the semi-ranges 
of the five or six largest tides at that station and to form index numbers 
of importance by multiplying the semi-ranges together two and two. 
Since these index numbers have no absolute magnitudes, we may omit 
the decimal point in forming them, Having selected as many of these 
combinations, in order of importance as may be thought expedient, the 
arguments of the compound tides are to be found by adding and sub- 
tracting the arguments of the components taken in pairs. 
