132 



On the Mass of the Planet Jupitet. 



the expiration of one second. On de- 

 composing the motion a c, it evidently 

 results from the centrifugal force a b s 

 and the force of gravity d b;— d*h 

 being the sagitta to the curve, or 

 the versed sine of 1", to the radius 

 ao, or d, as found above. If we 

 comp ute db from the expression 

 ver. sin $ = 2 sin 2 & it comes out 

 ^00000000000951 =4,77 feet; that is 

 to say the fourth satellite, by reason 

 of the attraction of Jupiter, gravi- 

 tates towards him at the rate of 4,77 

 feet in one second of time. 



Were the mass of Jupiter one hundred times greater than it really 

 is, it is plain that he would attract his fourth satellite with one hun- 

 dred times the force ; and, consequently, produce one hundred times 

 greater velocity than the above, &c. &c. Let us now see, if J upiter's 

 fourth satellite were placed at the same distance from the sun, as 

 it is found to be from Jupiter, what would be the force of gravity exer- 

 cised upon it by the sun. By the second law stated above, we have 



3 3_ 2 



as 1 : ,012055 : ,* 365,25 : the square of the time, which would 

 be occupied by a body to revolve round the sun at this distance. 

 . • . j = 42031, 9 seconds 5 hence, in one second of time, the body thus 

 placed would perform 30", 834 5 and, decomposing this, we find the 

 gravitating force, or the versed sine of the angle, to be ,000000011 17000, 

 or 5600, 93. feet ; that is to say, the planet Jupiter's force of attraction, 

 is to the sun's force of attraction, or the mass of Jupiter to the mass 

 of the sun, as 4,77 :: 5600,93 or as 1 : 1174,2 i.e. the mass of 



Jupiter is 1174, 2- of the mass of the sun. This result would be a cor- 

 rect one, were it not that whilst the secondary is gravitating towards 

 Jupiter 1 he, (in proportion to his mass) is gravitating towards his 

 satellites ; but the neglect of this will affect the above by a very small 

 amount, whereas its introduction here, would tend much to lengthen 

 this communication, and to make it unintelligible. 



If we now assume the mass of the earth to be 354936 of the sun, as 

 has been found in a manner similar to the above, the mass of Jupiter 

 = 302 times that of the earth, and since the earth's weight can easily 

 be computed, it is evident we as easily obtain the weight of the planet 

 Jupiter. 



*** We have introduced the foregoing into our Journal, not because 

 we suppose it will inform the scientific Astronomer of any thing he was 



