Sii Mr. Ivory un the 'I'keorj/ aj'lhe Aslyu)i(mlical RiJ'ruclioUs. 



))reservecl. He complains much of the great labour of llie 

 numerical calculations; but all difficulties were overcome, as 

 was to be expected: a table was computed and communicated 

 to Flanisleed in a triple form, for summer, winter, and the 

 intermediate seasons of spring and autumn. On mature re- 

 flection there occurred to him a serious objection to the sup- 

 posed scale of densities, on which account he writes to Flam- 

 steed that he does not intend to publish the tables. The fault 

 lies in this, that the centripetal force which continually in- 

 flects the light to the earth's centre, is the same at all the points 

 of the trajectoiy, or, in the words of Newton, the refractive 

 power of the atmosphere is as great at the top as at the bot- 

 tom, — than which nothing certainly can be more diffijrent 

 from what actually takes place in nature. 



Dismissing his first hypothesis, Newton next turned his at- 

 tention to the 22nd proposition of the third book of his Prin- 

 cipia. If the atmosphere consists of an elastic fluid gravi- 

 tating to the earth's centre in the inverse prooortion of the 

 square of the distance, and if it be admitted tnat the densities 

 are projjortional to the pressures, Newton, in the proposition 

 cited, pioves in eifect that the densities will ibrm a decreasing 

 geometrical series, when the altitudes are taken in arithme- 

 tical progression*. He writes to Flamsteed that an atmosphere 

 so constituted is certainly the truth. Newton evidently in- 

 tended by this assertion to mark a distinction between press- 

 ure, which is a cause of the variation of density that actually 

 exists in nature, and his first assumed law of the densities, 

 which is entirely arbitrary. Setting aside hypothesis, he now 

 advanced so far in the true })ath of investigation'; and if the 

 manner in which heat is diffused in the atmosphere and the 

 conse(]uent decrease of density were not known when he 

 wrote, he advanced as far as the existing state of knowledge 

 enabled him to do. It is certain from his letters, that, after 

 much time and labour, he at last succeeded in calculating a 

 table of refractions on the principle that the density is pro- 

 portional to the pressure. Such a table he communicated to 

 Flamsteed, although it is not found in the letters lately pub- 

 lished ; and there is every reason to think it the same which 

 he gave to Halley, and which that astronomer inserted in the 



* Newton demonstrates strictly that the densities will be in geometrical 

 proportion when the distances from the earth's centre are in musical or 

 hannonical proportion, that is, when they are tiie reciprocals of an arith- 

 metical progression; but in a series of this kind, if tiie first term bear an 

 almost infinitely great proportion to the differences of the following terms, 

 as is the case of the radius of the earth when comparcJ to elevations within 

 the limits of the atmosphere, the differences of the terms or the elevation;, 

 may, without sensible error, be reckoned in arithmetical progression. 



