KEPLER'S THIRD LAW. ■ 495 
assert that T.5238 is the distance of Mars from the Sun, and re-assert that — the 
square of any planet's time is equal to the cube of its distance. Our reasons for 
saying that 1.5238 is the distance of Mars are, because we cannot find Mars' 
time without first finding the Earth's, nor its distance, Ukewise. Since we are 
forced to make the Earth's period i, we claim the right to make its distance i. 
Therefore, if we can find the distance of the Earth in miles, we have only to 
multiply this number by 1.5238 to find the distance of Mars in miles. But the 
Earth's distance is still unknown, so we assume the solar parallax to be 8". 8 
which makes the Earth's distance, 92,882,000X1-5238^141,534,000 miles=the 
distance of Mars. 
Thus, distances of all planets in miles can be found from their periods, with 
fifty times less labor than by any other process. And this is the only way in 
which Kepler's law should ever be used. We found the distance of Mars with 
little work, but will give the same case in the good old way, using numbers that 
appall the young student. We hear on all sides that — " the squares of times are 
j>A-^;>^r//(9;?«/ to cubes of distances. " We know it, and will show some of the 
proportions in the case of Mars and the Earth. Mars' time is 686.9766 days, 
whose square^47 1,940. The Earth's period is 365.2563 days, which squared= 
133,412, and 471,940-^-133,412=3.537. Now, as we know this to be equal to 
the cube of Mars' distance, we would like to take its cube root at once and end 
the matter ; but no, we must secure the same number by the proportional way. 
The Earth's distance, 92,882,000 miles, whose cube=8oi,834,445,oo6,ooo,ooo,- 
000,000. Mars' distance is 141,535,000 miles, and cubed=2,835,25i,23i,305,- 
000,000,000,000. To be proportional to squares of times, quotients must be 
equal, whence, 2,835,251,231,305,000,000,000,000-^801,834,445,006,000,000,- 
000,000=3.537 as before; but then this 3.537 is the cube of Mars' distance, and 
we must proceed as at first to extract its cube root. Using Kepler's law, in the 
proportional way, is like burning all the logarithmic tables in existence. We 
cannot concieve of dispensing with a unit of time in cosmical physics, and fail 
to find one better than the year. The earth revolves in a time which is equal to 
I ; now let us see if we have violated mathematical usage in calling the Earth's 
distance i, as we do its time. The ablest mathematicians make such statements. 
Thus : — in Newcomb and Holden's Astronomy, p. 228, it is said in formula that 
the force of gravity on the Earth's surface multiplied by the square of its radius 
■equals the mass of the Earth. 
Gravity on the Earth's surface=32.i feet per second; and radius=2o,899,- 
081 feet; and 20,899,081 squared and multiplied by 32.1=14,020,367,931,290,- 
408, which we are informed is the mass of the Earth. But it is not the Earth's 
mass in pounds, tons, or any other units. Is the assertion of such able astrono- 
mers false? By no means, — everybody at once understands that this vast num- 
ber is equal to i, that is, it is nothing but a ratio, for if we multiply gravity on 
the Sun's surface by the square of its radius in feet and divide the square by 
the above number, the quotient will be 333,426, an important number — the mass 
of the Sun, that of the Earth being i. Here, a string of seventeen figures was 
