Pearson — On Compufailon of TuIoh. 657 



the Tides." But the principle of the method is one wliich never 

 occurred to either of these philosophers, nor, if known at all, has it 

 heen published by anyone else. The principle inrolved is this : that 

 the configuration of land and water on the surface of the globe brings 

 it to pass that the direction of the moon's motion in respect to the 

 equator makes a very great difference in the magnitude of the tide- 

 wave which reaches our shores. For when the moon advances from 

 south to north declination, crossing the equator, as she sometimes does, 

 at an angle of 28 degrees, it is seen that her line of motion approxi- 

 mately coincides with the general trend of the Atlantic Ocean, at the 

 time when the earth's rotation brings that part of the globe directly 

 beneath her, and this causes a further development of the tide-wave 

 in the direction of Europe and IS'orth America ; whereas, when the 

 moon declines from north declination to south, her course is diagonal 

 to the former one, crossing the Atlantic, roughly speaking, in the 

 direction of its Ireadth, whilst in the other case she crossed in the 

 direction of its length. The like phenomena take place in connexion 

 with the obverse action of the moon on the opposite side of the globe, 

 when that is the agency considered. The same remarks also apply 

 in regard to the action of the sun, only this action is much more 

 gradual and constant. PoUowing out the principles thus briefly 

 enumerated, a patient attention to the actual phenomena for twelve 

 years has enabled me to di-aw up tables of computation which include 

 every possible cause which can effect or interfere with the working of 

 the tides. 



Other principles of computation, however, have found favour with 

 the Tidal Committee of the British Association, for the details of which 

 the Annual Reports must be consulted. In the "Harmonic Analysis 

 of the Tides," as it is called, the various changes of level to which the 

 sea is subject, moment by moment, in consequence of the tide-generat- 

 ing forces, are ascertained by the enumeration of a series of Harmonic 

 Functions, each of which involves the time for which the computation 

 is made, certain quantities depending on the angular velocity of the 

 earth's rotation, the rates of relative orbital motion of the moon and 

 sun, and certain constants. The relative merits of these rival theories 

 (for such they are, though to a certain extent based on common funda- 

 mental physical laws) can only be tested by comparison with observa- 

 tion, and for this purpose no place is more eligible than Liverpool, 

 where the equinoctial tides sometimes range as far as thirty-one feet 

 from low-water. I am not aware, however, that this has been done. 



Meantime, I desire to send to the Academy a sort of challenge-list 

 of comparisons, taken for a semi-lunation in the month of June, 1882. 

 The atmospheric conditions during this period were exceedingly con- 

 stant, and so they very slightly affect the results. I am now engaged 

 in forming a Table, the arguments of which are the direction and force 

 of the wind on the one hand, and the height of the barometer on the 

 other. By the aid of this, predictions may be made with much 

 accuracy in unsettled weather. 



