NEW WAYS OF MEASURING THE SUN* S DISTANCE. 69 



calculation the same unvarying estimate of his mean density. 

 It follows that the nearer any estimate of his distance places 

 him, and therefore the smaller it makes his estimated 

 volume, the smaller also it makes his estimated mass, and 

 in precisely the same degree. The same is true of the 

 planets also. We determine Jupiter's mass, for example (at 

 least, this is the simplest way), by noting how he swerves 

 his moons at their respective (estimated) distances. If we 

 diminish our estimate of their distances, we diminish at the 

 same time our estimate of Jupiter's attractive power, and in 

 such degree, it may be shown (see note), as precisely to 

 correspond with our changed estimate of his size, leaving our 

 estimate of his mean density unaltered. And the same is 

 true for all methods of determining Jupiter's mass. Suppose, 

 then, that, adopting a certain estimate of the scale of the 

 solar system, we find that the resulting estimate of the masses 

 of the planets and of the sun, as compared with the earth's 

 mass, from their observed attractive influences on bodies 

 circling around them or passing near them, accords with 

 dieir estimated perturbing action as compared with the 

 earth's, then we should infer that our estimate of the sun's 

 distance or of the scale of the solar system was correct 

 But suppose it appeared, on the contrary, that the earth took 

 a larger or a smaller part in perturbing the planetary system 

 than, according to our estimate of her relative mass, she 

 should do, then we should infer that the masses of the 

 other members of the system had been overrated or under- 

 rated ; or, in other words, that the scale of the solar system 

 had been overrated or underrated respectively. Thus we 

 should be able to introduce a correction into our estimate of 

 the sun's distance. 



Such is the principle of the method by which Leverrier 

 showed that in the astronomy of the future the scale of the 

 solar system may be very exactly determined. Of course, the 

 problem is a most delicate one. The earth plays, in truth, 

 but a small part in perturbing the planetary system, and her 

 influence can only be distinguished satisfactorily (at present, 



