62 DISSERTATION SECOND. [part n. 



to bend it, — all these were problems of the greatest interest, 

 and were now resolved for the first time ; the science of me- 

 chanics being sufficient, by means of the composition of for- 

 ces, to find out the fiuxionary or differential equations which 

 expressed the nature of the gradual changes which in all these 

 cases were produced, and the calculus being now sufficiently 

 powerful to infer the properties of the finite from those of 

 the infinitesimal quantities. 



The doctrine of Hydrostatics was cultivated in England 

 by Cotes. The properties of the" atmosphere, or of elastic 

 fluids, were also experimentally investigated ; and the ba- 

 rometer, after the ingenuity of Pascal had proved that the 

 mercury stood lower the higher up into the atmosphere the 

 instrument was carried, was at length brought to be a measure 

 of the height of mountains. Mariotte appears to have been 

 the first who proposed this use of it, and who discovered 

 that, while the height from the ground increases in arith- 

 metical, the density of the atmosphere, and the column of 

 mercury in the barometer, decrease in geometrical progres- 

 sion. Halley, who seems also to have come of himself to 

 the same conclusion, proved its truth by strict geometrical 

 reasoning, and showed, that logarithms are easily applicable 

 on this principle to the problem of finding the height of 

 mountains. This was in the year 1685. Newton two years 

 afterwards gave a demonstration of the same, extended to 

 the case when gravity is not constant, but varies as any 

 power of the distance from a given centre. 



To the assiduous observations and the indefatigable ac- 

 tivity of Halley, the natural history of the atmosphere, of 

 the ocean, and of magnetism, are all under the greatest 

 obligations. For the purpose of inquiring into these ob- 

 jects, this ardent and philosophical observer relinquished the 

 quiet of academical retirement, and, having gone to St. 

 Helena, by a residence of a year in that island, not only 



