20 



MATHEMATICAL AND PHYSICAL SCIENCE. 



[Diss. VI. 



culty of treating the motions of fluids ; thirdly, the 

 peculiar difficulty of treating the motions when the 

 fluids cover an area which is not plane but convex ; 

 and, fourthly, the sagacity of perceiving that it was 

 necessary to consider the earth as a revolving body, 

 and the skill of correctly introducing this considera- 

 tion. The last point alone, in our opinion, gives a 

 greater claim for reputation than the boasted explana- 

 tion of the long inequality of Jupiter and Saturn." 1 

 We must, however, qualify this eulogy by adding, in 

 the words of the same writer, that Laplace's theory, 

 though based on sounder principles than the equili- 

 brium theory, " has far too little regard to the actual 

 state of the earth to serve for the explanation of even 

 the principal phenomena of the tides." It is, in fact, 

 like many other productions of the same age and 

 school, a great display of ingenuity and mathemati- 

 cal skill, which hardly yields a single result worthy 

 of confidence, or agreeing with nature, except by the 

 abandonment of its deductive rigour, or a concealed 

 induction backwards from the phenomena to be ac- 

 counted for. The same amount of skill and resource 

 which Mr Airy has shown in adapting it to his own 

 views, and to recent observations, would probably 

 have sufficed to construct a theory from the founda- 

 tion. By others the attempt seems to have been 

 abandoned as hopeless. 



( 79 Since our limits will not permit us to return to 



Tides Dr * ne subject of tides, we shall here briefly state the 

 Wheweli progress of the subject since the time of Laplace. 

 Sir J. Lub- The chief steps have consisted in co-ordinating the 

 bock. results of observation and analyzing them into their 

 partial phenomena, by the help of Newton's and 

 Bernoulli's theory. This labour has been greatly 

 advanced by Dr Wheweli, and also by Sir John Lub- 

 Cotidal bock. The former has constructed maps of " cotidal 

 lines. lines," which, indicating the relative time of high 

 water in different parts of the globe, give us a gra- 

 phic conception of the course and propagation of the 

 tidal wave. The tides of the Eastern Pacific are but 

 little known ; but a vast wave advances northwards 

 between Australia and Africa, diverted or retarded 

 by the obstacles it meets with in the Indian Archi- 

 pelago. Another (and to us the most important) 

 branch sets from south to north up the vast canal of 

 the Atlantic, where it is gradually complicated by 

 local tides, having their origin in the wide expanse 

 between Africa and the Gulf of Mexico. The two 

 sets of waves sometimes reinforce, sometimes oppose, 

 one another ; they are prolonged to the western 

 shores of England and Norway, where the tidal im- 

 pulse arrives 24 hours after it passed the Cape of 

 Good Hope. It is propagated most rapidly at a dis- 

 tance from coasts, and is retarded in narrows and 

 shallows. It sends offshoots into every bay and 

 strait, always greatly retarded in point of time (ap- 



parently by friction), but often increased in elevation 

 by concentration of the effect in a gradually narrow- 

 ing channel, as we see in the exaggerated tides of the 

 river Amazon, the Severn, and the Bay of Fundy. 

 The same place may be the seat of several tides at 

 once, which may increase or destroy one another ; 

 thus, a small tide is propagated through the Straits 

 of Dover as far as the Dutch coast, where it only 

 arrives simultaneously with the principal wave, 

 which has made the entire tour of Great Britain. 



As regards the progress of theory, Dr Thomas 

 Young, whose character as one of the greatest Dr Young 

 philosophers of the past age we shall have to con- 

 sider in another chapter, next after Laplace grappled 

 with the difficulties of this arduous subject. Em- 

 ploying mathematical methods of inferior power but ' 

 greater directness, and taking into account causes of 

 local action which Laplace had not ventured to in- 

 clude in his analysis, he gradually matured a theory 

 adequate to represent many of the results of ex- 

 perience, of which Laplace gives no account. 



He distinguishes the results of ihe forced and/ree ?*"^ 

 oscillations of the sea ; the former resulting from the f orce d 

 direct action of the sun and moon combined with the waves, 

 rotation of the earth, and whose periods of rise and 

 fall are determined solely by those external causes 

 (external, I mean, to the mass of the ocean) ; the 

 free waves, on the contrary, derived from the former, 

 are transmitted with velocities depending on the me- 

 chanism of the fluid itself, on its depth, and on the 

 resistances arising from friction to which those mo- 

 tions are exposed. These all-important modifications 

 of the dynamical Theory of the Tides were deduced 

 by Dr Young from the general theory of oscillations 

 and resistances, and from the laws of fluids detected 

 by Dubuat, 2 and he applied them with no ordinary 

 skill to the solution of the problems of tides in 

 oceans, estuaries, and rivers. It is an extraordinary 

 fact, and not without significance, in the history of 

 science, that these researches of Young, published 

 anonymously in the Supplement to the Sixth Edition 

 of the Encyclopaedia Britannica, and in the Seventh 

 Edition of this work, and likewise in several jour- 

 nals and reviews, so generally escaped notice as to 

 have been almost unknown till Dr Peacock, in his 

 recently published " Life and Miscellaneous Works 

 of Dr Thomas Young" has fortunately recalled 

 attention to their existence and their important 

 results. 



In doing so, Dr Peacock has communicated with 

 Mr Airy, whose very valuable article on Tides and 

 Waves has been above referred to (78), and has Waves, 

 ascertained from him that Dr Young's researches 

 had escaped his notice when he undertook that 

 elaborate recension of Laplace's theory, and made 

 those important additions to it to which I have 



1 Encyclopaedia Metropolitana, " Tides and Waves," art. 117. 



2 See Chapter IV., Section 6, where we shall return to some portion of this subject. 



