376 



SCIENTIFIC THOUGHT. 



phenomena, or even for such processes as happen con- 

 tinually under our eyes and our hands, this universal 

 law of gravitation has practically done nothing. The 

 action of gravitation alone between masses which we 

 can manipulate directly is so weak that it takes the very 

 finest instruments to detect it at all, and at molecular 

 distances it is so immeasurably small that it is hardly 

 conceivable how it can explain the existence of those 

 enormous forces with which we here have to deal. 1 If 



&c. more or less in the dark (see 

 ' Mathematische Annalen,' vol. xi. 

 p. 323). From a philosophical point 

 of view these discussions, in which 

 many other eminent leaders of 

 scientific thought took part, are 

 of great interest and importance, 

 as they bear upon the value of 

 mathematical formulae in physical 

 research, upon the definition of 

 laws of nature, the extent of their 

 applicability, the correct lines of fut- 

 ure research, the use of analogies in 

 the formation of physical theories, 

 &c. I therefore refer here to the 

 literature of the subject : Tait, 

 ' Sketch of Thermodynamics' (1868, 

 pp. 57, 76); Thomson and Tait, 

 'Natural Philosophy' (1st ed., p. 

 311); Carl Neumann, 'Die Prin- 

 cipien der Electrodynamik ' (Tub- 

 ingen, 1868); Helmholtz in various 

 memoirs from 1872 onwards, all 

 collected in ' Wissenschaftliche Ab- 

 handlungen ' (vol. i. pp. 545, 636, 

 774, &c.) and in 'Vortrage und 

 Reden ' (voL ii. Faraday Lecture) ; 

 Carl Neumann, ' Mathematische 

 Annalen' (voL xi. p. 318). See 

 also Riecke on ' Wilhelm Weber ' 

 (Gottingen, 1892), and Clerk Mas- 

 well, 'Electricity and Magnetism,' 

 (vol. ii. last chapter) ; ' Elementary 

 Treatise on Electricity' (p. 51). 



1 An interesting speculation as to 

 whether the Newtonian formula of 

 gravitation is capable of explaining 



cohesion and capillary attraction 

 will be found in Thomson's (Lord 

 Kelvin's) paper to the Royal Society 

 of Edinburgh (1862), and in his lec- 

 ture before the Royal Institution 

 (1866), on Capillary Attraction, both 

 reprinted in the first volume of 

 ' Popular Lectures and Addresses.' 

 He there shows that if we combine 

 Newton's law with the assumption 

 of an ultimate heterogeneousness of 

 matter, as is demanded in the so- 

 called atomic theory used in chem- 

 istry, the mass of ultimate por- 

 tions of matter at vanishing dis- 

 tances, or what is called in contact, 

 may give rise to molecular forces of 

 attraction of any magnitude ; since 

 the Newtonian attraction depends 

 on two data the distance and the 

 density (or mass) of attracting par- 

 ticles. He concludes by saying that 

 " it is satisfactory to find that, so 

 far as cohesion is concerned, no 

 other force than that of gravitation 

 need be assumed ; ' (p. 63). It does 

 not seem that this view, which was 

 also held by Sir John Herschel, is 

 generally adopted by physicists (see 

 Todhunter and Pearson, ' History 

 of the Theory of Elasticity,' vol. i. 

 p. 418, &c. ; vol. ii. art. 1650). An- 

 other interesting speculation arose 

 out of the discussion over Weber's 

 law. One of the objections started 

 by Helmholtz against Weber's law 

 was that, under certain conditions, 



