DISTANCE OF NEPTUNE. 



17. There is a remarkable astronomical law Fi s- 5 - 

 which was discovered, as a matter of fact, by 



Kepler, and shown by Newton to be a necessary 

 consequence of the principle of universal gravi- 

 tation, called the harmonic law; according to 

 this celebrated law, the successive distances of 

 the planets from the sun, have a certain fixed 

 relation to their times of revolutions, shortly 

 called their periodic times, by means of which 

 their relative distances can be easily computed, 

 when their periodic times are known. This 

 celebrated law is expressed as follows : 



The squares of the numbers zvhich express the 

 periodic times of any two planets, are in the 

 same proportion as the cubes of the numbers 

 which express their distances from the sun. 



This rule reduces the problem to determine 

 the distance of Neptune from the sun to a ques- 

 tion in the simple Rule of Three. 



The periodic time of the earth being a year, 

 will be expressed by 1, and that of Neptune will 

 be, as already shown, 164*6 ; now the squares of 

 these numbers are 1 and 27093. To find the 

 cube of Neptune's distance, is therefore a Rule 

 of Three question stated as follow : 

 1 : 27093 : : 1 : 27093. 

 Therefore this number 27093 is in fact the cube 

 of Neptune's distance from the sun, the earth's 

 distance from the sun being expressed by 1. 

 To find Neptune's distance, therefore, we have 

 only to find the number whose cube is 27093, and 

 by the ordinary processes of arithmetic, that 

 number is found to be 30-034. 



"We may, therefore, state in round numbers, 

 that Neptune is 30 times farther from the sun 

 than the earth. But the distance of the earth 

 from the sun being, in round numbers, 100 mil- 

 lions of miles ; it follows that the distance of 

 Neptune from the sun is, in round numbers, about 

 3000 millions of miles. Greater numerical pre- 

 cision than this has been attained by the com- 

 putations of astronomers, but the purpose of our 

 numerous readers will be best served at present 

 by adhering to these round numbers. 



18. To convey some notion of the prodigious 



185 



