THE ASTRONOMICAL VIEW OF NATURE. 361 



former applying them to the measurement of the mag- 

 netic forces of the earth, the latter to that of the forces 

 exerted by currents of electricity i.e., by electricity 

 which is not at rest but in motion. As I have already 

 stated, the measurements of Coulomb confirmed the 

 prevalent notion that action at a distance, varying 

 inversely as the square of the distance, and directly in 

 the proportion of the quantities of the acting substance, 

 was a universal formula or law of nature. 1 The idea 



1 Coulomb's exact measurements 

 of the attraction and repulsion at a 

 distance of electrified bodies and of 

 magnets were published during the 

 years 1784 to 1789 in seven memoirs 

 presented to the Paris Academy of 

 Sciences. They are conveniently 

 collected, together with some other 

 memoirs of Coulomb, Poisson, and 

 others on kindred subjects, in the 

 first volume of the ' Collection de 

 Memoires relatifs a la Physique,' 

 published in 1884 by the Socie'te' 

 fran^aise de Physique. Coulomb 

 made use of the torsion-balance 

 and the proof-plane, the actions of 

 which he carefully examined. He 

 confirmed the law, which had been 

 vaguely or approximately expressed 

 by various writers before him, that 

 electrified bodies act on each other 

 with a force which is proportional 

 to the inverse square of their dis- 

 tances. This he did by direct 

 measurements of the repulsion of 

 small electrified bodies in the tor- 

 sion-balance (1785, 1st Me"moire). 

 He then extended his measure- 

 ments by an indirect method^ to 

 the action of electrified bodies of 

 larger size and to magnets (2nd 

 Memoire). He also defined what 

 is meant by quantity and density 

 of electricity and magnetism, and 

 showed how these could be meas- 

 ured and how the action of elec- 

 trified bodies and magnets depended 



on the more or less of these quan- 

 tities. Coulomb's researches con- 

 tain experiments of great delicacy. 

 Although the laws which bear his 

 name appear so simple when written 

 down, the phenomena they repre- 

 sent are most complicated, as in 

 the case of electricity the effect of 

 electrical influence, called by Fara- 

 day induction, and in the case of 

 magnetism the presence of the 

 earth's magnetism, and the fact 

 that we have never to do with one 

 kind of magnetism but always with 

 two states, destroys all chance of ex- 

 hibiting experimentally the simple 

 case represented by the mathemati- 

 cal formula. It was therefore ne- 

 cessary to consider this formula as 

 being merely a convenient descrip- 

 tion of the elementary action of 

 supposed isolated quantities of 

 electricity and magnetism, and by 

 a process of summation to deduce 

 mathematically the actual effects 

 for such cases of interaction as 

 are actually observable in the la- 

 boratory. It was especially the 

 phenomena of the distribution of 

 electricity on the surface of elec- 

 trified bodies of simple shape and 

 the distribution of magnetic forces 

 in the neighbourhood of magnets 

 which had to be calculated and 

 measured. In physical astronomy 

 a similar course of reasoning and 

 observation combined had verified 



