SUN S DISTANCK FROM THK JiAKTH. 3 



of days required by the Earth (say) to go round the sun 

 squared, or multiplied by itself, be divided by the number of 

 days required by any other planet to go round the sun squared, 

 or multiplied by itself, the quotient so obtained will be the 

 same as that obtained by dividing the distance of the Earth 

 from the sun cubed, or multiplied by itself twice, by the dis- 

 tance of that other planet from the sun cubed, or multiplied 

 by itself twice. For example : — 



(Time of Earth) '^ (Distance of Earth) » 



(Time of Venus) ^ (Distance of Venus)'' 



The Earth's periodic time is (say) 365 days. 

 Venus' periodic time is (sa)^) 224 days. 

 As has been known for ages. Therefore : — 

 365 J 2 f D. E. ) 3 



224 ) ( D.V. 



Extract cube root from both members : — 

 365 li D. E. 



224 \ D. V. 



Applying logarithms : — 



5T.07 Distance of Earth 



36.88 Distance of Venus 



Which means that the distance of the Earth from the sun 

 • bears the same ratio to the distance of Venus from the sun 

 that fifty-one and seven one-hundredths does to thirty-six and 

 eighty-eight one-hundredths. Owing to neglect of fractions, 

 this is not precisely the proportion. It will in fact be quite 

 accurate enough for illustration and more convenient to say 

 that the Earth's distance from the sun is to Venus' distance 

 from the sun as 25 : 18. Very early observations gave this 

 proportion, and the calculations of Kepler have confirmed it. 

 In the present state of the inquiry, therefore, it is known that 

 if the Earth be at the distance twenty-five from the sttn, 

 \^enus will be at the distance eighteen, and the Earth will be 



