320 



SCIENTIFIC THOUGHT. 



matical formula which expresses the existing relations 

 of natural things acts in a similar way, but probably few, 

 if any, subsequent discoveries have given scientific minds 

 so much fruitful work to do as the gravitation formula. 

 An analysis of it will serve us as a guide through a very 

 large portion of the scientific work of our period : it will 

 serve also as an example of the great service which the 

 mathematical mode of dealing with conceptions renders to 

 the progress of science and of thought. 



The so-called law of gravitation states that every two 

 portions of matter, placed at a distance from each other, 

 exert on each other an attractive force, 1 which depends 

 on the masses of each, and on their distance from 

 each other. The attractive force varies in the direct 

 proportion of the mass of each, and in the inverse 

 duplicate ratio of the distance. Three distinct lines of 



1 The gravitation formula gives 

 no indication of the actual or abso- 

 lute amount of the force in ques- 

 tion ; it only establishes a relation. 

 It was fully three-quarters of a 

 century after the publication of the 

 ' Principia ' that experiments were 

 suggested in order to determine the 

 actual magnitude of the force of 

 gravitation i.e., the constant c in 



the formula f=c \ . Michell in 



7~" 



1768 devised an apparatus, em- 

 ployed later (1797) by Cavendish, 

 and Maskelyne made measurements 

 towards the end of the last century. 

 More and more accurate determin- 

 ations were made all through the 

 present century, and latterly by 

 Prof. Boys. Few persons have an 

 idea of the extreme feebleness of the 

 force, which nevertheless, through 

 the magnitude of the earth, ac- 

 quires in our daily experience such 

 ormidable proportions. As it ia 



desirable, in accordance with one of 

 the principal scientific tendencies of 

 our age, to place the knowledge of 

 absolute physical quantities in the 

 place of merely relative numbers, 

 I mention here that the force with 

 which two units of matter (i.e., 2 

 grammes) placed at unit distance 

 (i.e., 1 centimetre) apart attract 

 each other is such that they would 

 approach each other with a velo- 

 city of nearly 7 hundred millionths 

 of a centimetre in the first second 

 of time. As a pound is a more 

 familiar quantity, we may also say 

 that two masses, each containing 

 415,000 tons of matter, and situ- 

 ated at a distance of one statute 

 mile apart, will attract each other 

 with the force of 1 Ib. (see Sir 

 R. S. Ball, 'Ency. Brit,' 9th ed., 

 art. " Gravitation ") See also Sir 

 R. S. Ball, 'The Story of the 

 Heavens,' p. 106, and Prof. Boys 

 in 'Nature,' vol. 50, p. 330, &c. 



