412 NOTES. 



parallel of latitude, A a, B G ; therefore a change in the parallax ob- 

 served in that parallel can only arise from a change in the moon's 

 distance from the earth : and when tlie moon is at her mean distance, 

 which is a constant quantity equal to half the major axis of her orbit, a 

 change in the parallax observed in different latitudes, G and E, must 

 arise from the difference in the lengths of the radii n G and C E. 



NOTE 130, p. 52. When Venus is in her nodes. She must be in the 

 line N S n, where her orbit P N A n cute the plane of the ecliptic E N e n, 

 fig. 12. 



NOTE 131, p. 52. -The line described, $rc. Let E, fig. 33, be the earth, 



S the center of the sun, and V the planet Venus. The real transit of 

 the planet, seen from E the center of the earth, would be in the direction 

 A B. A person at W would see it pass over the sun in the line a, and 

 a person at O would see it move across him in the direction v' a'. 



NOTE 132, p. 53. 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 center 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 its 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 ; Sis therefore the square root of 9, and the cube root of 27. 



NOTE 133, p. 55. Inversely, <$-c. The quantities of matter in any two 

 primary planets are greater in proportion as the cubes of the numbers 

 representing the mean distances of their satellites are greater, and also in 

 proportion as the squares of their periodic times are less. 



NOTE 134, p. 55. 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 PO 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 attrac- 

 tion, 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 R 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 



