798 



SCIENCE. 



[Vol.. 11., No. 46. 



ed for by the decliuatious of the sun and 

 moon, and their greater or less distance from 

 the earth. 



, The cause of the tide ma}- be roughl}- stated, 

 according to tlie equilibrium theor}', thus : the 

 sun or the moon attracts the water on the side 

 of the earth nearer to it more than it does the 

 earth itself, and attracts the earth itself more 

 than the water on the farther side ; the con- 

 sequence being that water is heaped up on the 

 sides of earth away from and toward the at- 

 tracting body. Or, more exactlj', we may im- 

 agine 



° " The rise and fall of the water at any point of the 

 earth's surface to be produced by making two disturb- 

 ing bodies (moon and anti-moon, as we may call them 

 for brevity) revolve around the earth's axis once in 

 the lunar twenty-four hours, with the line joining 

 them always inclined to tlie earth's equator at an 

 angle equal to the moon's declination. If we assume 

 that at each moment the condition of hydrostatic 

 equilibrium is fulfilled, — -that is, that the free liquid 

 surface is perpendicular to the resultant force, — we 

 have what is called ' the equilibrium theory of the 

 tides' " (art. 805). 



Newton made a modification of this theor}^ 

 which was intended to take into account the 

 rotation of the earth, bj' supposing that the 

 full effect of the attraction was not exerted 

 immediately under the attracting body, but 

 that the tide was of the nature of a wave, and 

 by its inertia lagged behind the place where 

 it should have been found in case the earth 

 was not rotating. This retardation he thought 

 might be more than a whole daj' in some cases. 

 He was not able to submit the whole theory 

 to rigorous computation for lack of sufficient 

 data as to the mass of the moon and the height 

 of the tides ; but, from the tidal observations 

 then available, he computed the mass of the 

 moon necessary to produce them according to 

 his theory, and obtained a result which we 

 know to-day to be about twice too large. 



In 1738 the French academy proposed the 

 problem of the tides as the subject of a prize- 

 essay, and elicited important essay's ou the sub- 

 ject from Bernouilli, Maclaurin, and Euler, to 

 each of which was awarded a prize, and in each 

 something of importance was added to New- 

 ton's theory ; but the foundations of an exact 

 and complete theory were first made in the 

 ' Mecanique c(51este ' by Laplace, in five vol- 

 umes, 1799-1825. 



The science of mathematical analysis had 

 not been greatly developed at the time New- 

 ton wrought upon this subject. His work is 

 expressed in geometrical forms in which his 

 genius is unapproachable. But the new meth- 

 ods of analysis founded upon the calculus, the 



principles of which were discovered equally b}' 

 Newton and bj- Leibnitz, received a rapid and 

 wonderful development during the seventeenth 

 centurj' at the hands of Lagrange and the con- 

 tinental mathematicians. It was to the then 

 existing state of advancement in this particu- 

 lar that the great success of Laplace was due, 

 which enabled him to unravel to so remarkable 

 a degree the intricate interactions of the bodies 

 of the solar system, and give for the first time 

 the fundamental equations of the tides on cor- 

 rect principles. But it must be admitted that 

 Laplace, in integrating his differential equa- 

 tions, seems to have become involved in intri- 

 cate formulae whose full significance he has 

 not correctl}' interpreted. 



At about the same time, Dr. Thomas Young 

 made an important investigation of the action 

 of the tides, which was published in the Encj-- 

 clopaedia Britannica, where it has been repub- 

 lished in succeeding editions to the present 

 daj'. The special point of importance in his 

 investigation was the discussion of the effect 

 of friction upon the tides, which he showed to 

 be such as to explain many difficulties, and that 

 its magnitude might be such as to completel}- 

 change the character of the tide at certain 

 places so as to make low water take the place 

 of high water, and vice versa, — a result hith- 

 erto unsuspected, and of prime importance. 



The next great step in the theory of the 

 tides was due to Airj-, in his article on ' Tides 

 and waves ' in the Encj-clopaedia metropolitana. 

 He gave in new and concise form a most use- 

 ful resume of Laplace's theory, and made an 

 original investigation of the effects of friction. 

 He also made valuable additions to the theory 

 as applied to shallow seas and rivers, a sub- 

 ject hitherto untouched. 



The labors of Lubbock and of Dr. Whewell 

 have added much to our knowledge of the re- 

 lations of the theory to the observed tides ; but 

 the two foremost cultivators of this branch of 

 science now living are Thomson and Ferrel. 

 The former, who is chairman of the committee 

 appointed bj- the British association for the ad- 

 vancement of science, for the purpose of the 

 extension, improvement, and harmonic analysis 

 of tidal observations, has done much, bj' his 

 improved methods of observing tides and" dis- 

 cussing them, to separate their components from 

 each other, and render the exact comparison of 

 theory and observed facts possible. Laplace 

 assumed that the fortnightly and semi-annual 

 tides due to the movement of the moon and sun 

 in declination move so slowly that the equilib- 

 rium theory applies to them with exactness. 

 But even if that be admitted, it can be shown 



