434 PHYSICAL SCIENCES. 



NOTE 26, p. 5. Kepler discovered three laws in the planetary motions 

 by which the principle of gravitation is established : 1st law, That the 

 radii vectores of the planets and comets 

 describe areas proportional to the time. 

 Let fig. 9 be the orbit of a planet ; then, 

 supposing the spaces or areas PSp, pSa, 

 a!S6, &c., equal to one another, the radius 

 vector S P, which is the line joining the 

 centres of the sun and planet, passes over 

 these equal spaces in equal times ; that is, if 

 the line S P passes to Sp in one day, it will 

 come to S a in two days, to S 6 in three 

 days, and so on. 2nd law, That the orbits 

 or paths of the planets and comets are conic sections, having the sun in 

 one of their foci. The orbits of the planets and satellites are curves like 

 fig. 6 or 9, called ellipses, having the sun in the focus S. Several comets 

 are known to move in ellipses ; but the greater part seem to move in 

 parabolas, fig. 7, having the sun in S, though it is probable that they 

 really move in very long flat ellipses ; others appear to move in hyper- 

 bolas, like fig. 8. The third law is, that the squares of the periodic times 

 of the planets are proportional to the cubes of their mean distances from 

 the sun. The square of a number is that number multiplied by itself, 

 and the cube of a number is that number twice multiplied by itself. For 

 example, the squares of the numbers 2, 3, 4, &c., are 4, 9, 16, &c., but 

 their cubes are 8, 27, 64, &c. Then the squares of the numbers repre- 

 senting the periodic times of two planets are to one another as the cubes 

 of the numbers representing their mean distances from the sun. So that, 

 three of these quantities being known, the other may be found by the rule 

 of three. The mean distances are measured in miles or terrestrial radii, 

 and the periodic times are estimated in years, days, and parts of a day. 

 Kepler's laws extend to the satellites. 



NOTE 27, p. 5. Mass. The quantity of matter in a given bulk. It 

 is pi-oportional to the density and volume or bulk conjointly. 



NOTE 28, p. 5. Gravitation proportional to mass. But for the resist- 

 ance of the air, all bodies would fall to the ground in equal times. In 

 fact, a hundred equal particles of matter at equal distances from the sur- 

 face of the earth would fall to the ground in parallel straight lines -with 

 equal rapidity, and no change whatever would take place in the circum- 

 stances of their descent, if 99 of them were united in one solid mass ; for 

 the solid mass and the single particle would touch the ground at the same 

 instant, were it not for the resistance of the air. 



NOTE 29, p. 5. Primary signifies, in astronomy, the planet about 

 which a satellite revolves. The earth is primary to the moon. 



NOTE 30, p. 6. Rotation. Motion round an axis, real or imaginary. 



NOTE 31, p. 7. Compression of a spheroid. The flattening at the 

 poles. It is equal to the difference between the greatest and least dia- 

 meters, divided by the greatest, these quantities being expressed in some 

 standard measure, as miles. 



