330 



SCIENTIFIC THOUGHT. 



an almost unique instance of the combination of abstract 

 reasoning and practical inventiveness. An almost equally 

 important problem, having both scientific and practical 

 interest, arising out of the Newtonian gravitation formula, 

 is the problem of tides. Here also the first suggestions 

 towards a theory were given in the ' Principia,' whereas 

 the first attempt at a solution is contained in Laplace's 

 great work. A closer approximation was reached by Sir 

 W. Thomson in his extensive theoretical and practical use 

 of Fourier's mathematics. 



I shall have frequent opportunity to refer to the bene- 

 ficial and fructifying influence which practical problems 

 have exerted on scientific thought ; x in fact, in spite of 



has since been in use in submarine 

 telegraphy. The best account of 

 these discoveries and inventions is 

 to be found in Lord Kelvin's own 

 papers, a good summary being given 

 in his short article in Nichol's ' Cy- 

 clopedia,' reprinted as No. 82, vol. 

 ii. p. 138. 



1 How much science owes to the 

 practical interests of navigation can 

 be seen by a glance at the subjects 

 contained in the third volume of 

 Lord Kelvin's ' Popular Lectures 

 and Addresses.' The Tides, Deep- 

 Sea Sounding, Cable-Laying, and 

 Terrestrial Magnetism all furnish 

 important practical as well as high- 

 ly abstract theoretical problems, 

 the solution of which demands new 

 instruments and new methods of 

 calculation. The phenomena of 

 tides and those of terrestrial mag- 

 netism are intimately connected 

 with two of the most refined 

 mathematical theories which this 

 century has developed. The for- 

 mer was first attacked by the so- 

 called equilibrium theory the pro- 

 blem being to find the figure of 

 equilibrium of a rotating ellipsoid 



covered with water under the in- 

 fluence of various attracting forces. 

 Laplace, followed by Airy and 

 Thomson, showed how it is much 

 more a question of dynamics than 

 of statics, and that it resolves itself 

 into the analysis and subsequent 

 synthesis of a number of periodic 

 movements, dependent upon the 

 several periodic changes of the ro- 

 tation of the earth and the revo- 

 lutions of the moon round the 

 earth and the sun. A general 

 method of dealing mathematically 

 with the superposition of several 

 periodic changes had been invented 

 by Fourier in the early part of 

 this century, and it was this which, 

 especially in the hands of Lord 

 Kelvin and his brother the late 

 Prof. James Thomson led to the 

 harmonic analysis of tide motion 

 and the subsequent invention of 

 tide-predicting apparatus (see the 

 above volume, p. 177 sqq.) The 

 observation of the magnetism of 

 the earth is connected with great 

 improvements in the theory and 

 construction of the mariner's com- 

 pass, suggested and carried out by 



