310 Royal Institution, 



absolute mass of the earth would at once give determinations of the 

 absolute masses of the sun and planets. To show how this propor- 

 tion is ascertained, it is only necessary to remark, that a planet, if 

 no force acted on it, would move in a straight line ; that, therefore, 

 if we compute geometrically how far the planet moves in a short 

 time, as an hour, and then compute the distance between the point 

 which the planet has reached in its curved orbit, and the straight 

 line which it has left, we have found the displacement which is pro- 

 duced by the sun's attraction, and which is therefore a measure of the 

 sun's attraction. In like manner, if we apply a similar calculation 

 to the motion of a satellite during one hour, we have a measure of 

 the attraction of its primary. The comparison of these two gives 

 the proportion of the attraction of the sun, as acting upon a body, 

 at one known distance, to the attraction of a planet, as acting upon 

 a body at another known distance. It is then necessary to apply one 

 of the theorems of the laws of gravitation, namely, that the attrac- 

 tion of every attracting body is inversely as the square of the distance 

 of the attracted body, and thus we obtain the proportion of the at- 

 tractions of the sun and a planet, when the bodies upon which they 

 are respectively acting are at the same distance from both : and 

 finally, it is necessary to apply another theorem of the law of gravi- 

 tation, namely, that the attractions thus found, corresponding to 

 equal distances of the 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 Lecturer 

 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 the proportion of the masses of all 

 bodies, which have planets or satellites revolving round them, can 

 easily be found (the proportion 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 lecture 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 phi- 

 losophers 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 dimen- 

 sions 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. 



