16 P>'°f- Leslie on Heat and Climate. [July, 



mometer to rise with great rapidity 3-1°, where it remained sta- 

 tionary some seconds, and then very slowly subsided. The same 

 experiment was performed on air three-fifths, two-fifths, and one- 

 fifth of the common density, and the excess of temperature was 

 found to be 56°, 7-7°, and 9-4°. After the air was much ex- 

 hausted, the quantity of rise hardly varied at all, so that it was 

 easy to fix the extreme point at 10*7°. All these experiments 

 were repeated at least twice with scrupulous attention. The 

 above numbers do not, however, express the proportional in- 

 crease of temperature of the rarefied air. The excess is not 3"! , 

 for example, in air of four-fifths the usual density, but£ x 3*1°= 

 3*9° ; because the heat contained in four parts of air is diffused 

 through five. In the same manner the computation may be 

 made for the other cases. The annexed table exhibits the ge- 

 neral results : 



Density. Rise of Temperature. 



Four-fifths 3-9° 



Three-fifths 9-3 



Two-fifths 19-7 



One-fifth 37-0 



Vacuum Infinite 



The intermediate quantities might be found by interpo- 

 lation ; but it will be more convenient to obtain a general 

 formula. For this purpose we shall recur to the former 

 numbers. Divide the straight line A F into five equal parts 

 in the points B, C, D, and E, erect the perpendiculars B G, 

 C H, D I, E K, and F L, equal to 3-1°, 5-6°, 7-7°, 9-4°, and 

 107°, and trace a curve through their extremities. Then if A F 



denotes the ordinary density, and O F any other density, the 

 ordinate O P will express the number corresponding to the 

 latter. But the differences between the equidistant ordinates are 

 2*5°, 2'1°, 1'7°, and 1-3°, forming a descending arithmetical pro- 

 gression, of which the last term is half the first. Hence, 

 producing the absciss till A F = F M, these differences will be 

 as the distances from M. Put AO = i', and OP=», and 

 suppose these finite differences to be proportional to the fluxions 

 of the ordinates, which will be very nearly true. Then y == 

 (2 - x) x, and?/ == 2 * - -\- a?» But when y as 1,,# = 107°; 



