November 11, 1898.] 



SCIENCE. 



649 



He concludes that for big slow currents — 

 such as the Gulf Stream — the friction of the 

 ocean bed is bj' far the most important fac- 

 tor in the dissipation of the energy of mo- 

 tion, while for the short waves in deep 

 water viscosity becomes paramount. The 

 continued existence of ocean currents is a 

 problem not satisfactorily explained. They 

 are usually attributed principally to the 

 tendency of the winds to blow on the aver- 

 age mainly in one direction. Against this 

 is urged the dissipation of the energy thus 

 acquired, by the viscosity of the fluid. 

 Hough concludes that too much effect has 

 been attributed to viscosity. Such currents 

 will doubtless take a long time to start, but 

 when once set in motion the modulus of 

 decay is so large that energy is dissipated 

 very slowly and the winds are sufficient to 

 supply the energy lost by viscosity. The 

 long-period tides, again, are supposed to be 

 greatly affected by viscosity. If, however. 

 Hough's conclusion that the modulus of 

 decay is comparable more nearly with 20 

 years than with a few months those tides 

 whose periods are as great as one or even 

 six months will be but little affected. 

 Hence the differences between observation 

 and the results of the equilibrium theory of 

 the tides, originally attributed to viscosity, 

 cannot be explained in this way. 



A few special problems of motions of 

 solids have been solved, the squares of the 

 velocities being neglected. The motion of 

 a sphere and the linear motion of an ellip- 

 soid in an infinite fluid had been solved. 

 Edwardes, in 1892, added the rotational mo- 

 tion of an ellipsoid and the motion of fluid 

 through a channel bounded by a hyper- 

 boloid of revolution. As before stated, the 

 results have little more than a mathemat- 

 ical interest. 



To attempt to give any idea of the possi- 

 ble directions in which future progress is 

 likely to be made is a dangerous task. One 

 can, however, do something by mentioning 



the problems in which a little progress has 

 been made and also those which have been 

 before the scientific world for some time 

 and remain j'et unsolved. For some of the 

 indications given below I am indebted to 

 friends who have themselves contributed to 

 recent progress. 



Problems in discontinuous motion in two 

 dimensions in an infinite, frictionless, in- 

 compressible fluid are now without funda- 

 mental difliculties. In fact, they are mainly 

 exercises iu conform representation. The 

 problem is reduced to that of finding a 

 function to satisfy Laplace's equation for 

 two dimensions with given boundary con- 

 ditions. ISTo special service will be gained by 

 hydrodynamics, by solving for new forms 

 of boundaries, unless the cases arise in ex- 

 periment. But I have mentioned the fact 

 • that no problem of discontinuous motion in 

 three dimensions has yet been solved. The 

 difficulty is one which can easily be ap- 

 preciated. The theory of functions deals 

 with a complex of the form x + iy, and this 

 suits all problems in two dimensions. But 

 little has been done with a vector in three 

 dimensions, and certainly nothing has been 

 built up concerning it which corresponds to 

 the results obtained for the two dimensional- 

 vector. The subject of discontinuous motion 

 was set for the Adams prize in 1895 ; this is 

 the prize which has produced Maxwell's es- 

 say on Saturn's Rings and J. J. Thomson's 

 on Vortex Motion. A solution for a solid of 

 revolution was asked for, and it was gen- 

 erally supposed that the circular disc would 

 be the easiest to attempt. N^o essay was 

 sent in. One prominent mathematician, 

 who has aided considerably in the develop- 

 ment of hydrodynamics, mentioned that 

 he had worked for six months and had ob- 

 tained absolutely nothing. A magnificent 

 reception, therefore, awaits the first solu- 

 tion ! 



Some mention has been already made of 

 difiSculties awaiting solution in tide and 



