TIDES. 45 



made free use of the learned astronomer's work, and will often 

 refer to it in the following pages. 



By the law of gravitation, which was discovered by Newton, 

 bodies attract one another in direct proportion to their respective 

 masses or weights, and inversely as the squares of the distances 

 between them. 1 In accordance with this law, it is evident that 

 our globe is being attracted in all directions by the various 

 celestial bodies. In dealing with the subject of tides, it will 

 however, only be necessary to consider the effect produced by 

 the sun and moon; the influence exerted by the other stars 

 and planets being insignificant and unworthy of notice by 

 reason of their great distance from the earth, notwithstanding 

 that in some instances their mass is very great. 



Theory of the Tides. The theory of the tides which is now 

 almost universally accepted, is that known as the Newtonian or 

 equilibrium theory. It is, however, based upon the hypothesis 

 that our globe is a perfect sphere, enveloped entirely by water 

 of uniform depth, and it can therefore only be received as 

 approximately correct. 



The sun and moon exert their attractive power with greatest 

 effect upon that part of the water of the ocean which is imme- 

 diately opposite to, and therefore nearest to them. 



Thus the sun, by overcoming or reducing terrestrial gravity, 

 raises the water into a heap on a line joining its centre with 

 that of the earth, and the moon raises a similar but larger 

 heap on a line joining its centre with that of the earth, the 

 elevation of these respective heaps being proportionate to the 

 relative effective powers of attraction of the sun and moon. 2 



1 The truth of this law has been placed beyond question by the vast number 

 of astronomical predictions based upon it, which have been fulfilled to the letter. 



2 Taking the mass of the moon and its distance from the earth as units of 

 weight and distance respectively, the mass of the sun will be represented by, say, 

 26,000,000, and its distance by 391. The attractive power which the sun exercises 



26 000 000 

 upon the earth as a whole, as compared with that of the moon, is thus as ' * 



to 1. In other words, the sun pulls at the earth with a force 170 times greater than 

 that exerted by the moon. 



The mean radius of the earth is 3956 miles, and the mean distance of the moon 

 from the earth 237,600 miles. If, therefore, we take the earth's radius as unity, the 

 distance of the moon from the centre of the earth will be represented by 60, from 

 its near side by 59, and from its far side by 61. 



The attractive forces exercised by the moon on the near and far sides of the 



earth are therefore as ^ to --, the difference being 6'7 per cent, (say ^). 



By the same process, assuming the mean distance of the suii from the earth 



