MARS AS A WORLD. 173 



further suppose, with sufficient accuracy, that the dis- 

 tance between the earth and the sun is 400 times the 

 distance between the earth and the moon. The celebrated 

 law of Kepler tells us that if two satellites be revolving 

 around the same primary, the squares of the periodic 

 times will be proportional to the cubes of the mean dis- 

 tances. I must ask you, then, in order to conduct the 

 calculation, to assume the existence of a fictitious satellite 

 revolving around our earth at a distance which is 400 

 times as great as that of the moon at present. This would 

 move much more slowly than the moon, and it would 

 require a great many months indeed to complete one revo- 

 lution. How many months are required can be discovered 

 by Kepler's law just stated. As the moon goes round in 

 one month, the fictitious moon would require a number of 

 months, which is determined by first multiplying 400 by 

 itself twice, that is by obtaining the number 400 X 400 

 X 400, and then taking the square root of it. We for- 

 tunately find that for this particular problem the actual 

 nature of the work is materially facilitated. Each of the 

 several factors, 400, is itself found by multiplying 20 by 

 itself, or as we would say the square root of 400 is 20, 

 hence the square root of the cube of 400 is found by 

 merely multiplying 20 by itself twice over, and that gives 

 us the answer 8,000. Hence we learn that if there were 

 a fictitious moon revolving at a distance 400 times that 

 of our present moon, its periodic time would be 8,000 of 

 our present months. 



We have now placed the problem in the following 

 aspect. Our earth revolves around the sun in a year, or, 

 for our present purpose, we may, with quite sufficient 



