PLANETS. 



that his satellites are opaque, and reflect 

 the Sun's light, is abundantly shown. 

 Wherefore, since Saturn, with his ring 

 and satellites, only yield a faint light, 

 fainter considerably than that of the fixed 

 stars, though these be vastly more re- 

 mote, and than that of the rest of the 

 planets, it is past doubt, he too, with his 

 attendants, are opaque bodies. 2. 

 Since the Sun's light is not transmitted 

 through Mercury and Venus, when plac- 

 ed against him, it is plain they are dense 

 opaque bodies; which is likewise evi- 

 dent of Jupiter, from his hiding the satel- 

 lites in his shadow ; and therefore, by 

 analogy, the same may be concluded by 

 Saturn. 3. From the variable spots in 

 Venus, Mars, and J.upiter, it is evident 

 these planets have a changeable atmo- 

 sphere ; which changeable atmosphere 

 may, by a like argument, be inferred of 

 the satellites of Jupiter, and therefore by 

 similitude the same may be concluded of 

 the other planets. 4. In like manner, 

 from the mountains observed in Venus, 

 the same may be supposed in the other 

 planets. 5. Since, then, Saturn, Jupiter, 

 both their satellites, Mars, Venus, and 

 , Mercury, are opaque bodies, shining 

 with the Sun's borrowed light, are fur- 

 nished with mountains, and encompass- 

 ed with a changeable atmosphere ; they 

 have, of consequence, waters, seas, .c. 

 as well as dry land, and are bodies like 

 the Moon, and therefore like the Earth. 

 And hence it seems highly probable, that 

 the other planets have their animal in- 

 habitants, as well as oar Earth. 



PLACETS, masses of. It would appear, 

 at first view, impossible to ascertain the 

 respective masses of the Sun and planets, 

 and to calculate the velocity with which 

 heavy bodies fall towards each when at a 

 given distance from their centres ; yet 

 these points may be determined from the 

 theory of gravitation without much diffi- 

 culty. It follows, however, from certain 

 theorems relative to centrifugal forces, 

 that the gravitation of a satellite to- 

 wards its planet is to the gravitation of 

 he Earth towards the Sun, as the mean 

 distance of the satellite from its prima. 

 ry, divided by the square of the time 

 of its sidereal revolution, or the mean 

 distance of the Earth from the Sun di- 

 vided by the square of a sidereal year. 

 To bring these gravitations to the same 

 distance from the bodies which produce 

 them, we must multiply them respective- 

 ly by the squares of the radii of the orbits 

 which are described : and, as at equal 

 distances the masses are proportional to 



the attractions, the mass of the Earth is 

 to that of the Sun as the cube of the 

 mean radius of the orbit of the satel- 

 lite, divided by the square of the time 

 of its side real motion, is to the cube of 

 the mean distance of the Earth from the 

 Sun, divided by the square of the side- 

 real year. Let us apply this result to 

 Jupiter. The mean distance of his fourth 

 satellite subtends an angle of 1530". 86 

 decimal seconds. Seen at the mean dis- 

 tance of the Earth from the Sun, it would 

 appear under an angle of 7964" .75 deci- 

 mal seconds. The radius of the circle 

 contains 636,619" .8 decimal seconds. 

 Therefore the mean radii of the orbit 

 of Jupiter's fourth satellite, and of the 

 Earth's orbit, are to each other as these 

 two numbers. The time of the sidereal 

 revolution of the fourth satellite is 16.6890 

 days ; the sidereal year is 365.2564 days. 



TTiese data give us -for the mass 



of Jupiter, that of the Sun being repre- 

 sented by I. It is necessary to add unity 

 to the denomination of this fraction, be- 

 cause the force which retains Jupiter in 

 his orbit is the sum of the attractions of 

 Jupiter and the Sun. The mass of Jupi- 

 ter is then The mass of Saturn 



lOO/.Oo 



and Herschel may be calculated in the 

 same manner. That of the Earth is best 

 determined by the following method : If 

 we take the mean distance of the Earth 

 from the Sun for unity, the arch describ- 

 ed by the Earth in a second of time will 

 be the ratio of the circumference to the 

 radius divided by the number of seconds 

 in a sidereal year. If we divide the 

 square of that arch by the diameter, we 



obtain 



1479565 

 10' 



for its versed sine, which 



is the deflection of the Earth towards the 

 Sun in a second. But on that parallel of 

 the Earth's surface, the square of the 

 sine of whose latitude is, a body falls in 

 a second 16*. feet. To 'reduce this at- 

 traction to the mean distance of the Earth 

 from the Sun, we must divide the num- 

 ber by the feet contained in that distance ; 

 but the radius of the Earth at the above- 

 mentioned parallel is 19,614,648 French 

 feet. If we divide this number by the 

 tangent of the solar parallax, we obtain 

 the mean radius of the Earth's orbit ex- 

 pressed in feet. The effect of the at- 

 traction of the Earth, at a distance equal 

 to the mean radius of its orbit, is equal to 



