18 The Astronomer- Royal on the [Feb. 2, 



attracted bodies, are in the same proportion as the masses of the 

 attracting bodies (a theorem which applies to gravitation, but does 

 not apply to magnetic and other forces). Into the evidence of these 

 portions of the law of gravitation, the speaker did not attempt to 

 enter : he remarked only that they rest upon very complicated 

 chains of reasoning, but of the most certain kind. His only object 

 was to show that tlie proportion of the masses of all bodies, which 

 have planets or satellites revolving round them, can easily be found — 

 (the proporfion for those which have no satellites is found by a very 

 indirect process, and with far less accuracy) ; and that if the absolute 

 mass of the earth be known, the absolute mass of each of the others 

 can be found. As their dimensions are known, their densities can 

 then be found. Thus it rests upon such inquiries as those on which 

 this discourse is to treat, to determine (for instance) whether the 

 planet Jupiter is composed of materials as light as water, or as light 

 as cork. 



The obvious importance of these determinations had induced 

 philosophers long since to attempt determinations of the earth's 

 density : and two classes of experiments had been devised for it. 



The first class (of which there was only one instance) is the 

 attraction of a mountain, in the noble Schehallien experiment. It 

 rests, in the first place, upon the use of the zenith sector ; and, in 

 the next place, upon our very approximate knowledge of the 

 dimensions of the earth. [The construction of the zenith sector was 

 illustrated by a model : and it was shown, that if the same star were 

 observed at two places, the telescope would necessarily be pointed 

 in the same direction at the two places, and the difference of direc- 

 tion of the plumb line, as shown by the different points of the 

 graduated arc which it crossed at the two places, would show how 

 much the direction of gravity at one place is inclined to the direction 

 of gravity at the other place.] Now, from our knowledge of the 

 form and dimensions of the earth, we know that the direction of 

 gravity changes very nearly one second of angle for every 100 feet 

 of horizontal distance. Suppose then, that two stations were taken 

 on Schehallien, one on the north side and the other on the south 

 side, and suppose that their distance was 4000 feet ; then, if the 

 direction of gravity had not been influenced by the mountain, the 

 Inclination of the directions of gravity at these two places would 

 have been about 40 seconds. But suppose, on applying the zenith 

 sector in the way just described, the inclination was found to be 

 really 52 seconds. The difference, or 12 seconds, could only be 

 explained by the attraction of the mountain, which, combined with 

 what may be called the natural direction of gravity, produced 

 directions inclined to these natural directions. In order to infer 

 from this the density of the earth, a calculation was made (founded 

 upon a very accurate measure of the mountain) of what would have 

 been the disturbing effect of the mountain if the mountain had been 

 as dense as the interior of the earth. It was found that the dis- 



