92 THE PATH OF SCIENCE 



the sun attracted a planet by a force varying inversely as the 

 square of the distance, a line joining the planet to the sun 

 would sweep out equal areas in equal times. This assump- 

 tion—that there existed in the universe a force extending out- 

 ward to the planets and varying inversely as the square of 

 the distance to them— applied, of course, to all heavenly 

 bodies; and Newton applied it to the position of the moon 

 in its movement around the earth. He found, however, that 

 it did not agiee exactly with the observations, which involved, 

 of course, the diameter of the earth; and for sixteen years 

 Newton put the work aside. In 1682 it was discovered that 

 the diameter of the earth had been measured incorrectly and 

 was over 500 miles greater than the figure that had been 

 adopted.* Newton immediately repeated his calculations 

 and found that they agreed with the observed motion of the 

 moon. He then extended the work to include the motions of 

 the planets and their satellites, comets, and even the tides of 

 the sea. He stated his general law of gravitation: "Every 

 particle of matter in the universe attracts every other particle 

 with a force that varies directly as the product of the mass 

 and inversely as the square of the distance." 



The discovery of the fundamental laws of motion was a 

 challenge to philosophers to seek fundamental principles that 

 would supply laws of a general nature. The mathematicians 

 d'Alembert, Euler, Lagrange, and Laplace developed such 

 general principles, derived from the laws of motion, which 

 were applicable not only to material bodies but to the flow 

 of light, heat, and electricity. On the mathematical prin- 

 ciples that they established, the science of physics has been 

 built. Although the physical ideas themselves have changed 

 with the progress of experimental science, the new ideas have 

 been expressed in terms of the same fundamental principles. 

 In the nineteenth century, physicists thought that it might 

 be possible to reduce all laws to the laws of mechanics. 



* It is possible that Newton's difficulty arose instead from lack of 

 proof that the mass of a spherical body would behave as if it were 

 concentrated at the center. 



