TIDAL OBSERVATIONS. ' 357 



of the semidiurnal lunar declinational tides agrees with that of one of the 

 semidiurnal solar declinational tides, being twelve sidereal hours ; also that 

 the angular velocities y — tr + ra- and y — c — w arc so ncarlj' equal, that obser- 

 vations through several consecutive years must be combined to distinguish 

 the two corresponding elliptic diurnal tides. Again, one of the lunar varhi- 

 iion tides has the same period as the chief solar semidiiirnal tide. Tliis 

 would be of great importance for tidal theory, were it not that its magnitude 

 must be so small as to be scarcely sensible. Each lunar declinational tide 

 varies from a minimum to a maximum, and back to a minimum, every nine- 

 teen years or thereabouts (the period of revolution of the line of nodes of the 

 moon's orbit). Observations conlinucd for nineteen years will give the 

 amount of this variation with considerable accuracy, and from it the propor- 

 tion of the effect due to the moon will be distinguished from that due to the 

 sun. It is probable that thus a somewhat accurate evaluation of the moon's 

 mass may be arrived at. 



6. There are also shallow-water tides Vvhich depend on the rise and fall of 

 the tide, amounting to some sensible part of the whole depth of the water, or, 

 which comes to the same, the horizontal velocity of the water being sensible 

 in comparison with the velocity of propagation of a long wave through some 

 considerable portion of the sea which sensibly influences the tides at the point 

 of observation. Helmholtz's explanation of compound sounds, according to 

 which two sovuids, each a simple harmonic, having mt, nt for their argumejits, 

 give rise, if loud enough, to sounds having for their arguments (m-|-?i)^, 

 {m — n)t, suggests that the compound action of the solar and lunar semidiurnal 

 tides must give rise to shallow-water tides, whose speeds are 2{a — ij) and 

 2(2y — a — T]). The action of the solar or lunar semidiurnal tide alone must 

 also (by the case m=^n) give rise to shallow-water tides. The following are 

 the speeds of these compound shallow-water tides which have (with one 

 exception not yet tried) been found to be sensible at some of the places dis- 

 cussed hereafter : — 



Speeds. 

 '2{rt — ri) fortnightly. 



2(2y — tT—rj) quarter -diurnal. 

 Helmholtz compound shallow- J 2v— 4(r4-2n 1 .,. ■, 

 water tides. i 2y + 2^-4, | ''"'"^'"'°'^- 



2(2y + ^^-3S}'i''^'^''"^^"™^^- 



One of the semidiurnal components contained in the above list has the same 

 period as one of the variation semidiurnal tides, and is therefore to be held 

 accountable for any deviation, whether of magnitude or of epoch, which the 

 tide of this period, calculated from observation, may show from the values 

 which might be expected merely from the lunar perturbation alone. 



7. The methods of reduction hitherto adopted*, after the example set by 

 Laplace and Lubbock, have consisted chieflj'^, or altogether, in averaging the 

 heights and times of high water and low water in certain selected sets of 

 groups. Laplace commenced in this way, as the only one for which observa- 

 tions made before his time were available. How strong the tendency is to 

 pay attention chiefly or exclusively to the times and heights of high and 

 low water is indicated by the title printed at the top of the sheets used 



* See ' Directions for reducing Tidal Observations,' by Staff-Commander Burdwood 

 (London, 1865, published by the Adniiralty) ; also Professor Haughton on fhe " Solar and 

 Lunar Diurnal Tides on the Coast of Ireland," Transactions of the Koyal Irish Academy 

 ibr April 185i. 



