452 PHYSICAL SCIENCES. 



the horizon, the angle H m E is the greatest possible, and is called the 

 horizontal parallax. It is clear that with regard to celestial bodies the 

 whole effect of parallax is in the vertical, or in the direction m m' Z ; 

 and as a person at H sees m' in the direction H m' A, when it really 

 is in the direction E m' B, it makes celestial objects appear to be lower 

 than they really are. The distance of the moon from the earth has 

 been determined from her horizontal parallax. The angle E m H can be 

 measured. E H m is a right angle, and E H, the radius of the earth, is 

 known in miles ; whence the distance of the moon E m is easily found. 

 Annual parallax is the angle under which the diameter of the earth's orbit 

 would be seen if viewed from a star. 



NOTE 131, p. 52. The radii wB, wG, &c., fig. 3, are equal in any 

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

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

 distance from the earth ; and when the 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 132, p. 52. WfienVenus is in her nodes. She must be in the line 

 N S n where her orbit P N A n cuts the plane of the ecliptic E N e n, fig. 12. 



NOTE 133, p. 53. The line described, $c. Let E, fig. 33, be the earth, 

 Fig. 33. 



S the 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 v a, and a person 

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



NOTE 134, p. 54. 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 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 ; 3 is 

 therefore the square root of 9, and the cube root of 27. 



NOTE 135, p. 55. Inversely, fyc. The quantities of matter in any two 



