TIDAL OBSERVATIONS. 359 



night might not, all things considered (accuracy, economy, and sufficiency for 

 all scientiiic Avants), be preferable to a self-registering tide-gauge. 



10. One of the most interesting of the questions that can be proposed in 

 reference to the tides is, how much is the earth's angular velocity diminished 

 by them from century to century ? The direct determination of this amount, 

 however, or even a rough estimate of it, can scarcely be hoped for from tidal 

 observation, as the data for the quadrature required could not be had directly. 

 But accurate observation of amounts and times of the tide on the shores of 

 continents and islands of all seas might, with the assistance of improved 

 dynamical theory, be fully expected to supply the requisite data for at least 

 a rough estimate. In the mean time it may be remarked that one very 

 important point of the theory, discovered by Dr. Thomas Young and inde- 

 pendently by Airy*, affords a ready means of disentangling some of the 

 complicacy presented by the distribution of the times of high water in dif- 

 ferent places, and will form a sure foundation for the practical estimate of a 

 definite part of the whole amount of retardation, when the times of spring- 

 tides and neap-tides are better known for all parts of the sea than they are 

 at present. To understand this, imagine a tidal sjiheroid to be constructed 

 by drawing an infinite niimber of lines perpendicular to the actual mean sea- 

 level continued under the solid parts of the earth which lie above the sea- 

 level, and equal to the spherical harmonic term or Laplace's function, of the 

 second order, in the development of a discontinuous function equal to the 

 height of the sea at any point above the mean level where there is sea, and 

 equal to zero for all the rest of the earth's surface. This spheroid we shall 

 call, for brevity, the mean tidal spheroid (lunar or solar as the case may be, or 

 lunisolar when the heights due to moon and sun are added). The fact that 

 the lunar semidiurnal tide is, over nearly the whole surface of the sea, greater 

 than the solar, in a greater ratio than that of the generating force, renders it 

 almost certain that the longest axes of the mean lunitidal and solitidal 

 spheroids would each of them lie in the meridian 90° from the disturbing 

 body (moon or sun) if the motion of the water were unopposed by friction ; 

 or, which means the same thing, that there would be on the average of the 

 whole seas, loiv water when the disturbing body crosses the meridian, were 

 the hypothesis of no friction fulfilled. But, as Airy has shown, the tendency 

 of friction is to advance the times of low and high water when the depth and 

 shape of the ocean are such as to make the time of low water, on the hypo- 

 thesis of no friction, be that of the disturbing body's transit. Now the wcU- 

 known fact that the spring-tides on the Atlantic coast of Europe are about a 

 day or a day and a half after full and change (the times of greatest force), 

 and that through nearly the whole sea they are probably more or less behind 

 these times, which Young and Airy long ago maintained to be a consequence 

 of friction, would prove that the crowns of the lunitidal spheroid are in 

 advance of those of the solitidal spheroid, and therefore that those of the 

 latter are less advanced by friction than those of the forme-. It is easilj'' 

 conceived that a knowledge of the heights of the tides and of the intervals 

 between the spring-tides and the times of greatest force, somewhat more 

 extensive than we have at present, would afi"ord data for a rough estimate 

 of the proper mean amount of the average interval in question — that is, of the 

 interval between the times of high water of the mean lunitidal and mean 

 solitidal spheroids. The whole moment of the couple retarding the earth's 

 rotation, in virtue of the lunar tide, must be something more than that calcii- 



* See the coUeeted works of Dr. Thorocas Young, vol. ii. No. LIT. (London, 1855, John 

 Murray), and Airy's ' Tides and 'Waves,' g§ 450, 544. 



