APPENDIX. 299 



less, or 1. The following rule may be given ; as the square 

 of the distance of any planet from the sun is to I, which re- 

 presents the light and heat received at the earth, so is the 

 square of the earth's distance from the sun, to the degree of 

 light and heat received at the planet in question. 



The attraction of bodies dexreases as the square of the dis- 

 tance increases ; the attraction is mutual, and greater or less 

 according to their solid contents. 



The following is the rule for finding the distances of the 

 planets from the sun : — as the square of the earth's period of 

 revolution round the sun is to the cube of its disC-^nce, so is 

 the square of any other planet's annual period of revolution 

 to the cube of its distance ; and the cube root of the number 

 thus found will be the planet's distance from the sun. It 

 was ascertained by Kepler and demonstrated by Newton, 

 that from the combined forces of attraction and rectilinear 

 motion, the squares of the periodical times or revolutions of 

 the planets are, as the cubes of their distances. It was as- 

 certained by Kepler also, that if a line were drawn from the 

 sun to the earth, this line would, by the earth's motion, pass 

 over equal spaces, or areas in equal times. 



To such pupils as are sufficiently acquainted with Arith- 

 metic, the instructor should explain at large the particulars 

 mentioned in the above note. Questions may easily be pro- 

 posed, and worked out by the above rules : — for instance, if 

 the period of Mercury be 88 days, what is its distance from 

 the sun 1 — If the heat and light at the earth be 1, what is the 

 degree of heat and light at Mercury? and so of other planets. 



To find how many times one planet is greater than ano- 

 ther, the rule is, cube the diameter of each planet, and di- 

 vide the greater number by the less, the quotient will give the 

 proportional magnitudes, or the number of times the one is 

 greater than the other. 



LESSON 44. 



Fig. 40. Engraving V. S represents the sun, and N S is 

 the earth in different parts of its orbit. The white circle in 

 the dark space represents the ecliptic. The dark circular 

 space filled with stars extending eight degrees from each 

 side of the ecliptic represents the zodiac. The names of 

 the signs of the zodiac and the characters which represent 



