ATTEMPTS TO EXPLAIN GRAVITATION 253 



according to a definite law (the attraction between two bodies being 

 directly proportional to the product of the masses and inversely as the 

 square of the distance, if the dimensions of the bodies are small com- 

 pared with the distance between them). Having enunciated this law 

 he proceeded to verify it by studying the motion of the moon. The 

 moon revolves in an orbit that is nearly circular and to keep it in this 

 orbit there must be an acceleration toward the earth equal to V 2 /r 

 where V is the moon's orbital velocity and r is the distance from the 

 earth to the moon (approximately 240,000 miles). In place of V we 

 may put 2-n-r/t, where t is the time of one revolution (27.3 days). 

 Hence the acceleration toward the earth equals 



(— Y 



V 2 \ t J Arf-r 4 x 9.86 x 240,000 x 5280 "" . 



T = ~~T' = ~f~ = - (27.3 x 86,400) 2 ~= -0089 feet/sec 2 . 



The acceleration the earth should exert, if Newton's law be true, at a 

 distance of 240,000 miles (60 times the earth's radius) = 32.16/60 2 

 = .0089 feet/sec 2 where 32.16 feet/sec 2 is the acceleration at the surface 

 of the earth. The verification in the case of the moon is complete. 

 Hence we have the mathematical statement of the law: F (the force) 

 =1 Mm/r 2 ■ G where G is a constant depending upon units only. We 

 say nothing about the quality of the matter but only the quantity, and 

 the distance. Notice also that there is no factor in the equation refer- 

 ring to the nature of the intervening medium. 



It may not be out of place to call attention to the universality of the 

 law. There are a few slight discrepancies between observed and calcu- 

 lated values, but as a whole it is fully attested by observation. 



In referring to the magnitude of gravitational force consider first 

 small bodies and later astronomical bodies. We know to-day that the 

 radiation from the sun exerts a pressure. Kepler suggested this three 

 centuries ago and one hundred and fifty years later the great mathe- 

 matician Euler adopted his suggestion in accounting for the repulsion 

 of comets' tails. So delicate is this pressure that it was not discovered 

 until recently (1900). Albeit this pressure is very small as bodies 

 diminish in size, we reach a limit at which it predominates over gravita- 

 tion. This is due to the fact that gravitation is proportional to the 

 mass (the cube of the linear dimension) while radiation-pressure is 

 proportional to the surface (the square of the linear dimension). 



When we consider electrons we find that the gravitational attraction 

 between two electrons is insignificant compared with electrical attrac- 

 tion. The electrical force in air between two negative electrons one 

 centimeter apart is equal to (4.5 X 10" 10 ) 2 = 20 X 10" 20 dynes, if we 

 take the charge on an electron to be 4.5 X 10 -10 c.g.s. electrostatic units. 



The gravitational attraction between two electrons at a distance of 

 one centimeter = 10" 27 X lO" 27 X 6.6 X 10" 8 = 6.6 X 10" 62 dynes, 



