482 NOTES. 



NOTE 131, p. 60. The line described, <ff. Let E, fig. 33, be the earth, S the 

 Fig. 33. 



centre of the sun, and V the planet Venus. The real transit of the planet, seen 

 from E the centre of the earth, would be in the direction A B. A person at W 

 would see it pass over the sun in the line t> a, and a person at O would see it 

 move across him in the direction v< a 1 . 



NOTE 132, p. 61. Kepler's law. Suppose it were required to find the 

 distance of Jupiter from the sun. The periodic times of Jupiter and Venus 

 are given by observation, and the mean distance of Venus from the centre of 

 the sun is known in miles or terrestrial radii ; therefore, by the rule of three, 

 the square root of the periodic time of Venus is to the square root of the 

 periodic time of Jupiter as the cube root of the mean distance of Venus from 

 the sun, to the cube root of the mean distance of Jupiter from the sun, which 

 is thus obtained in miles or terrestrial radii. The root of a number is that 

 number which, once multiplied by itself, gives it square ; twice multiplied by 

 itself, gives its cube, &c. For example, twice 2 are 4, and twice 4 are 8; 2 is 

 therefore the square root of 4, and the cube root of 8. In the same manner 3 

 times 3 are 9, and 3 times 9 are 27 ; 3 is therefore the square root of 9, and the 

 cube root of 27. 



NOTE 133, p. 63. Inversely, $c. The quantities of matter in any two pri- 

 mary planets are greater in proportion as the cubes of the numbers represent- 

 ing the mean distances of their satellites are greater, and also in proportion as 

 the squares of their periodic times are less. 



NOTE 134, p. 63. As hardly anything appears more impossible than that 

 man should have been able to weigh the sun as it were in scales and the earth 

 in a balance, the method of doing so may have some interest. The attraction 

 of the sun is to the attraction of the earth as the quantity of matter in the 

 sun to the quantity of matter in the earth; and, as the force of this reciprocal 

 attraction is measured by its effects, the space the earth would fall through in 

 a second by the sun's attraction, is to the space which the sun would fall 

 through by the earth's attraction, as the mass of the sun to the mass of the 

 earth. Hence, as many times as the fall of the earth to the sun in a second 

 exceeds the fall of the sun to the earth in the same time, so many times does 

 the mass of the sun exceed the mass of the earth. Thus the weight of the sun 

 will be known if the length of these two spaces can be found in miles or parts 

 of a mile. Nothing can be easier. A heavy body falls through 16'0697 feet 

 in a second at the surface of the earth by the earth's attraction ; and, as the 

 force of gravity is inversely as the square of the distance, it is clear that 



