Art. XIX. — The Production of the Tides, Mechanically 



Considered. 



By T. Wakelin, Esq., B.A. 



[Bead December 15, 1887.] 



Let US suppose the earth to be composed of grains of sand, 

 all separate, not one grain in actual contact with another. 

 Let us further suppose, for a moment only, that the force 

 which draws them, as is supposed, towards the moon, acts 

 equally on every particle — on every grain of sand. In this 

 case the earth will keep its form, whatever form it may 

 have. 



Now let us take, in part, the actual case. The grains of 

 sand composing the earth on the side nearest the moon are 

 drawn by a greater force than are the grains composing the 

 earth on the side farthest from the moon. This force — the 

 gravitative force of the moon on the earth — varies inversely as 

 the square of the distance from the moon's centre, supposing 

 the moon to be a perfect sphere, and knowing that the 

 attractive force of the moon may be considered as con- 

 centrated at the moon's centre. I only wish here to deal 

 with the principle of the moon's action in producing the 

 tides, or rather one of the principles. I have been unable to 

 iind any work in Wellington which treats of the Dynamical 

 Theory of the Tides, or of anything relating to it, except 

 what is contained in Newcomb's " Popular Astronomy," and 

 I wish here, therefore, to keep to the direct action of the 

 moon, as it is generally understood. 



Let us consider the action of the moon on three portions 

 of the earth : — (a) the portion nearest the moon ; (6) the 

 portion in the centre of the earth ; and (c) the portion of 

 the earth farthest from the moon. The first portion (a) is 

 drawn by a greater force than the second — the central 

 portion (6), and it therefore bulges towards the moon. The 

 second portion (h) is drawn by a greater force than is the 

 third portion (c), and this last portion, therefore, is left a 

 little behind, and bulges away from the moon. These two 

 bulgent portions are the two tides. The force producing these 

 two tides is measured by the difference of the accelerations 



