392 Dr. J. R. Mayer on Celestial Dynamics. 



axis of its orbit ; whence it is apparent that a planet, on arriving 

 at the sun, moves at least as quickly as a weight which falls freely 

 towards the sun from a distance as great as the solar radius, or 

 96,000 geographical miles. 



What thermal effect corresponds to such velocities ? Is the 

 effect sufficiently great to play an important part in the immense 

 development of heat on the sun ? 



This crucial question may be easily answered by help of the 

 preceding considerations. According to the formula given at 

 the end of Chapter II., the degree of heat generated by percus- 

 sion is 



= 0-000139° xc 2 , 

 where c denotes the velocity of the striking body expressed in 

 metres. The velocity of an asteroid when it strikes the sun 

 measures from 445,750 to 630,400 metres ; the calorific effect 

 of the percussion is consequently equal to from %7\ to 55 millions 

 of degrees of heat*. 



An asteroid, therefore, by its fall into the sun develop es from 

 4600 to 9200 times as much heat as would be generated by the 

 combustion of an equal mass of coal. 



V. The Origin of the Sun's Heat (continuation) . 



The question why the planets move in curved orbits, one of 

 the grandest of problems, was solved by Newton in consequence, 

 it is believed, of his reflecting on the fall of an apple. This story 

 is not improbable, for we are on the right track for the discovery 

 of truth when once we clearly recognize that between great and 

 small no qualitative but only a quantitative difference exists — when 

 we resist the suggestions of an ever active imagination, and look 

 for the same laws in the greatest as well as in the smallest pro- 

 cesses of nature. 



This universal range is the essence of a law of nature, and the 

 touchstone of the correctness of human theories. We observe 

 the fall of an apple, and investigate the law which governs this 

 phenomenon ; for the earth we substitute the sun, and for the 

 apple a planet, and thus possess ourselves of the key to the me- 

 chanics of the heavens. 



As the same laws prevail in the greater as well as in the 

 smaller processes of nature, Newton's method may be used in 

 solving the problem of the origin of the sun's heat. We know 

 the connexion between the space through which a body falls, the 

 velocity, the vis viva, and the generation of heat on the surface 



[* Throughout this memoir the degrees of heat are expressed in the 

 Centigrade scale. Unless stated to the contrary, the measures of length 

 are given in geographical miles. A geographical mile = 7420 metres, and 

 an English mile == 1608 metres, — Tr.] 



