206 Mr. A. Tylor on Tides and Waves. 



particles of water and move them is represented in a new manner. 

 The sun's effect can be calculated similarly to the moon's. 



The attraction of the moon when in a vertical line would not 

 produce any horizontal or vertical movement in a particle of 

 water below it ; and the attraction could not produce a heap of 

 water below it without the water being propelled from some 

 point of the ocean on which the rays of attraction fell at an angle 

 less than 90° ; and then I do not think the heap could exceed 

 2 inches in height*, for reasons which will be given hereafter. 



The mass of the moon is equal to a sphere of 118*75 miles 

 diameter of the same density as the earth, and situated at 3956 

 miles from the point to be attracted — that is, at the distance 

 of the radius of the earth. The circle F near C (fig. 4, PI. IV.) 

 should be only one sixth of an inch if drawn to scale. It 

 is shown in the position in which it would represent the action 

 of the moon on the ocean if it revolved round C in a lunar 

 month. Thus any point on the circumference of the earth must 

 be attracted to the centre of the earth by an attraction greater 

 than that of the moon to the same point in the ratio of 295520 

 to 1. For 60-263 2 = 3631, and 60-263 is the mean distance 

 of the moon from the earth ; then the density of the earth is to 

 that of the moon as 1*647 to 1, and the mass of the earth to 

 that of the moon as 49*5 to 1. Then 



3631 x 49*5 x 1-647 = 295520; 



that is, the effect of the attraction of the moon in a particle on 

 the surface of the earth (at the moon's mean distance) is only 

 . ] 520 of that arising from the attraction of the earth itself f. 

 The weight of any body on the earth would therefore be 

 lightened in that ratio, or in the proportion of 1 grain to 4-J 

 gallons of water (70,000 grains to the gallon), the moon being 



* This is a different case altogether from that of the estimate of collec- 

 tion of water at the equator • and the practical test given above is better 

 thafftheory. 



t This is calculated differently in a note to page 528, Herschel's ' Out- 

 lines of Astronomy/ 1873 : the cube of the sun's distance is erroneously in- 

 troduced into the calculation for finding the moon's maximum power to 

 disturb the water in the surface of the earth ; this brings the relative effect 

 of the moon's attraction to la Woooo °f gravity, according to Herschel. 

 This, however, is only -^j of the real quantity. My calculation is ac- 

 cording to the following law: — "Two such globes would (by the same 

 proposition) attract one another with a force decreasing in the duplicate 

 proportion of the distance between their centres " (Newton, page 24, edit. 

 1819). If Herschel's figures were correct, we should have tides of 3 inches 

 on our coast instead of 12 feet in height. Also the fictitious moon F placed 

 near C (fig. 4, PI. IV.), to represent the effect of the real moon, would 

 have only a diameter of 34'03 miles, and contain 20,629 cubic miles instead 

 of the larger quantity mentioned by me in the text. , 



