' Mr. A. Tylor on Tides and Waves. 205 



This is the equation to equilibrium of the ocean-surface in the 

 case where no interfering currents, caused by difference of tem- 

 perature in the ocean, are present*. A complete oceanic tide 

 stretches from coast to coast, and is always divided into three 

 regions (central, anterior flowing, and posterior ebbing), re- 

 versing direction each six hours ; that is, in the part where there 

 was propulsion, aspiration succeeds, and vice versa. A perfect 

 tide would stretch over a space on parallel of latitude repre- 

 sented by the rotation of the earth in six hours. 



The mass of the central ocean is represented, in PL II. figs. 

 1 and 2, and PI. III. fig. 1, as moving 180 feet per hour on 

 the average of each tide of six hours, but in alternate and oppo- 

 site directions. A movement of 3 feet per minute in the cen- 

 tral ocean 20,000 feet deep would communicate a velocity of 

 three miles an hour where the water was 238 feet deep, by the 

 composition of forces. I suppose that this slow motion in a 

 vast mass of water of great and equal depth would be horizontal 

 alone, as it is not possible to suppose vertical motion without 

 creating a gap below or behind the tidal current. The hori- 

 zontal motion would be also limited ; for the sum of the motion 

 of all the particles of water in the Atlantic tidal stream could 

 not exceed the area of the gap emptied and filled on the oppo- 

 site coasts of the Atlantic each alternate tide. In this respect 

 the tide is like a wave, the relation of whose movements to 

 the size of the gap made when generated is clearly shown in 

 fig. 1 (p. 216). The force of the moon will be estimated; and 

 the relation of its attraction to a particle on the ocean is shown 

 in fig, 4, PL IV. The direction in which the moon can affect 



* From the equation Q = AV, using Q and g for discharge per second, 

 and A for cross section, and from observation, I have 



v 3 /q * m\ a v 3 / av i v la i /r ,\ 



v = Vq I- (2),and v=VAvT or v=VA-T ; -- (3) 



from which I obtain a new equation to the flow of water in uniform motion 

 — that is, only when \=v. This is 



i 2\A~ r Qr 



(4) 



which applies to water in canals in uniform motion, as in fig. 3, Plate III. 

 The tendency of every river is to approximate in all parts of its course to a 

 uniform mean velocity. The river carries sand and mud from the mountains 

 to the sea along its channel at a nearly uniform rate. Increase of quantity 

 of water flowing at any point balances decrease of slope throughout all 

 rivers. A steamer ascending the Rhine meets a current descending at one 

 velocity at different slopes. This is proved by the consumption of fuel 

 being equal per mile from the sea to Mayence, except where back-water 

 on one side increases velocity on the other, or where shallows retard the 

 ship. I do not find (R the mean hydraulic depth) of value in calculations. 



