360 REPORT— 1872. 



lated on the hypotliesis that the obliquity of the mean lunitidal spheroid is 

 oiilj^ equal to the hour-angle corresponding to that interval of time. 



11. We know, however, but little at present regarding the actual time of 

 the spring-tides in different parts of the ocean ; and it is not even quite 

 certain, although, as Airy remarks, it is extremely probable, that in the 

 southern seas they take place at an interval after the full and change, 

 although it may be at a less interval than on the Atlantic coast of Europe. 

 There must be observations on record (such as those of Sir Thomas Maclear 

 at the Cape of Good Hope, vrhich Staff-Commander Burdwood showed to 

 Sir W. Thomson in the Hydrographical OfRce of the Admiralty) valuable for 

 determining this very important element for ports on all seas -where any 

 approach to a knowledge of the laws of the tides has been made. 



To collect information on this point from all parts of the world wiU be 

 one of the most interesting parts of the work of the Committee. 



12. Another very interesting subject for inquiry is the lunar fortnightly, 

 or solar semiannual, tide, the determination of which will form part of the 

 complete harmonic reduction of proper observations made for a sufficient 

 time. The amounts of these tides must be very sensible in all places remote 

 from the zero line* of either northern or southern hemisphere, unless the 

 solid earth yields very sensibly in its figure to the tide-generating force f. 

 Thus it has been calculated that if the earth were perfectly rigid, the sura of 

 the rise from lowest to highest at Teneriffe, and simultaneous fall from 

 highest to lowest at Iceland, in the lunar fortnightly tides, would amount to 

 4-5 inches. The preliminary trials of plans for harmonic reduction referred 

 to below, make it almost certain tliat hourly observations, continued for a 

 sufficiently long time at two such stations as these, would determine the 

 amount of the fortnightly tide to a fraction of an inch, and so would give 

 immediate data for answering, to some degree of accuracy, the question how 

 much does the solid earth really yield to the tide-generating force ? 



13. A beautiful synthesis of the complex dynamical action to which the 

 semidiurnal tides are due, imagined by Laplace, will be used in this Report 

 to enable us to avoid circumlocution. A number of ideal stars ("astres 

 fictifs ") are assumed to move, each uniformly in the plane of the earth's 

 equator, with angular velocities small in comparison with that of the earth's 

 rotation, so that the period of each relatively to the earth is something not 

 very different from the lunar or solar twenty-four hours. Each one of the 

 approximately semidiurnal tides (§ 3) is produced by one alone of these 

 ideal stars. 



14. One of the ideal stars is what is commonly called in England the 

 '*' mean sun," bemg that point of the celestial sphere in the plane of the earth's 

 equator whose hour- angle is equal to mean solar time : for brevity we shall 

 call it S. Another of them might be the " mean moon " similarly defined 

 (called M) ; but, to allow the same Tables (§ Ki) to be used for the reduction 

 of tidal observations of different years, we shall take it as a point moving in 

 the plane of the earth's equator, with an angular velocity equal to the mean 

 angular velocity of the moon, and set at 0°-0 for its hour-angle at the com- 

 mencement of any series of observations J. 



Similarly K might be the first point of Aries, but, for the same reason, will 



* Thomson and Tail's ' Natural Philosophy,' § 810. 



t " On the Rigidity of the Earth," W. Thomson, Trans. R. S., May 1862 ; or Thomson 

 and Tait's ' Natural Philosophy,' §§ 832-849. 



X Other hour-angles to those here given were first used, but not proving of any practical 

 utility, the above were substituted for them, simplifying to some extent the ultimate cor- 

 rections depending on these assumptions. 



