PROGRESS IlSr ASTRONOMY. 137 



With reg'ard to masses: We naturally must first know that of the 

 earth; having- its size, if we can determine its density, the rest follows. 



The problem of determining the mean density of the earth has 

 occupied the minds of many workers during the closing century. 

 Newton (about 1728) pointed out how it could be deduced by observing 

 the deviation from the vertical of a plumb line suspended near a large 

 mass of matter — a mountain — the volume and densit}^ of which could 

 be previously determined. This method, which is very laborious and 

 requires the greatest skill and most delicate instruments, has been 

 employed several times — by Bouguer and Condamine in 1738 at Chim- 

 borazo; Maskelyne in 1774 at Schehallien, in Scotland, and James at 

 Arthur's Seat, near Edinburgh. 



At the beginning of the century another method was introduced by 

 Cavendish. This consists in measuring the attraction of two large 

 spheres of known size and mass, such as two balls of lead on two ver\' 

 small and light spheres, by means of a torsion balance constructed ])y 

 Mitchell for this purpose. 



The most recent determination by this method, and one which is 

 considered to give us perhaps the most accurate value, is that which 

 is due to the skill and ingenuity of Professor Boj's. His improvement 

 consisted in constructing a most delicate torsion lialance. The attracted 

 spheres consisted of small gold balls suspended Ijy a quartz fiber car- 

 rying a mirror to indicate the amount of twist. The whole instrument 

 was quite small and could easil}" be protected from air currents and 

 changes of temperature, while the use of the quartz fibers reduced to 

 a minimum one of the greatest difficulties of the Cavendish experiment. 

 The value of the mean density of the earth is now considered to be 

 5.6, which means that if we have a globe of water exactly the same 

 size as our own earth the real earth would weigh just .5.6 times this 

 globe of water. The earth \s weight in tons does not convey much 

 idea, but that it is six thousand trillions may interest the curious. 

 This determination has enabled the masses of the sun, moon, planets, 

 and satellites, and many sidereal systems to be accurately known in 

 relation to the mass of the earth. 



SOME ACHIEVEMENTS OF MATHEMATICAL ANALYSIS. 



Uranus, a planet unknown to the ancients, was discovered by its 

 movement among the stars by William Herschel in 1781. It was not 

 until 1816 that another major planet was added to the solar S3^stem, 

 and this discovery was one of the sensations of the century. 



The story of the independent discovery of Neptune by Adams and 

 Le Verrier, who were both driven to the conclusion that certain appar- 

 ent irregularities in the motion of Uranus were due to the attraction of 

 another body traveling on an orbit outside it, has been often told. The 



