January 19, 1900.] 



SCIENCE. 



91 



the motion of solids in such media, have 

 been successfully woi'ked out to results 

 which agree fairly well with experiment. But 

 on the whole, notwithstanding the searching 

 investigations in this field of Stokes, Max- 

 well, Helmholtz, Boussinesq, Meyer, Ober- 

 beck, and many others, it must be said 

 that difficulties, both in theory and in ex- 

 periment, of a formidable character remain 

 to be surmounted.* 



Of all branches of hydromechanics there 

 is none of so great practical utility and 

 of such widely popular interest as the 

 theory of tides and waves. These phe- 

 nomena of the sea are appreciable to the 

 most casual observer ; and there has been 

 no lack of impressive descriptions of their 

 effects from the days of Curtius Eufus down 

 to the present time. The mechanical theory 

 of tides and waves is, however, a distinctly 

 modern development whose perfection must 

 be credited to the labors of the mathema- 

 ticians of the present century, f 



Here, again, progress is measured from 

 the advanced position occupied by Laplace, 

 who was the first to attempt a solution of 

 the tidal problem on hydrokinetic princi- 

 ples. After the fundamental contributions 

 of Laplace, contained in the second and 

 fifth volumes of the ' Mecanique Celeste, ' the 

 next decisive advance was that made by 

 Sir George Airy (1801-1892), in his article 

 on tides and waves, which appeared in the 

 Encyclopsedia Metropolitana in 1842. A 



*An extremely interesting method of experimental 

 investigation has been recently applied with success 

 by Professor Hele-Shaw. See a paper by him on 

 'Stream-line motion of a viscous film,' and an accom- 

 panying paper by Sir G. G. Stokes on ' Mathematical 

 proof of the identity of the stream-lines obtained by 

 means of a viscous film vpith those of a perfect fluid 

 moving in two dimensions. ' Report of British As- 

 sociation for the Advancement of Science for 1898. 



t An excellent summary of the history and theory 

 of tides, and of methods of observing and predicting 

 them, is given by Dr. Eollin A. Harris in his ' Manual 

 of Tides,' published as Appendices 8 and 9 of the Re- 

 port of the TJ. S. Coast and Geodetic Survey for 1897. 



quarter of a century later came the renais- 

 sance, started undoubtedly by the great 

 memoir of Helmholtz and by the Natural 

 Philosophy of Kelvin and Tait, along with 

 Lord Kelvin's inspiring communications 

 on almost every phase of wave and tidal 

 problems to scientific societies and journals. 

 Then followed the decided theoretical im- 

 provements in tidal theory of Professor 

 William Ferrel,* particularly in the de- 

 velopment of the tide generating potential 

 and in the determination of the effects of 

 friction. And a little later there appeared 

 the novel investigations of Professor G. H. 

 Darwin, who, in addition to furnishing a 

 complete practical treatment of terrestrial 

 tides, f has extended tidal theory to the 

 solar system and thrown an instructive 

 light on the evolutionary processes whence 

 the planets and their satellites have emerged 

 and through which they are destined to 

 pass in the future. J 



As we reflect on the progress which has 

 been thus summarily, and quite inade- 

 quately outlined, it will appear that the 

 mathematicians of the nineteenth century 

 have contributed a splendid aggregate of 

 permanent accessions to knowledge in the 

 domain of the more exact of the physical 

 sciences. And as we turn from the certain 

 past to the less certain future, one is prone 

 to conjecture whether this brilliant prog- 

 ress is to continue, and, if so, what part the 



* 'Tidal Researches.' Appendix to Report of U. 

 S. Coast and Geodetic Survey for 1874, Washington, 

 1874. 



t In article on tides in Encyclopsedia Britannica, 

 9th edition. 



X Darwin's investigations are published in a series 

 of papers in the Philosophical Ti-ansaciions of the Boyal 

 Society of London, Parts I., II., 1879 ; Part II., 

 1880 ; Part II., 1881 ; Part I., 1882. They are re- 

 published in part in Appendix G, Thomson and 

 Tait's Natural Philosophy, 2d edition. See also the 

 capital semi-poplar work, ' The Tides and Kindred 

 Phenomena in the Solar System,' by G. H. Darwin 

 Boston and New York, Houghton, Mifflin & Co., 

 1889. 



