Mechanical Science. 371 



results, that one can never have a general rule by which to arrive 

 directly at the point required, and that the work is obliged to be 

 commenced with an hypothesis which, at a later period, is to be sub- 

 jected to criticism from the observations. At the same time, the 

 adoption of an hypothesis does not depend upon accident, but 

 requires the most intimate knowledge of mathematical forms in their 

 greatest extent, otherwise the progress would only be from error to 

 error. One rule, however, should be observed it is, to commence 

 by trying those formulae which require the determination of the 

 smallest possible number of arbitrary constants. 



4 Guided by these considerations, and by the relation between light 

 and heat so evident in the power which the solar rays possess of 

 producing heat by their passage through bodies but little transparent, 

 I commenced by supposing that the planetary space, with a perfect 

 transparency, would undergo no change of temperature, neither by 

 the effect of light nor radiant heat ; and that therefore the elevation of 

 temperature above that of the etherial regions can only commence at 

 the limits of the atmospheres of the planets. A necessary result is, 

 that the rate of change of temperature at a height infinitely above 

 the surface of the earth is always proportional to the rate of the cor- 

 responding change in the capacity which the atmosphere possesses 

 of absorbing light. Upon these considerations I expressed the tem- 

 perature of the atmosphere by means of a formula, which applies to 

 any height above the surface of the earth, and which contains only 

 two arbitrary constants ; one, which is also a function of the time, is 

 always determined by the immediate observation of the correspond- 

 ing temperature of the surface of the earth ; and the other, which 

 does not vary in relation to time, is the temperature of the planetary 

 space. 



* The numerical determination of these constants requires exact 

 observations of the temperatures of isolated points, up to a consider- 

 able height above the earth's surface; but, unfortunately, these 

 observations are so difficult, that at present I could take advantage of 

 one only, that made by M. Gay Lussac, in his aerial voyage. It is 

 very much to be desired that this observation should be repeated, 

 especially in the neighbourhood of the equator, where atmospheric 

 variations are small, and where, consequently, the influence of acci- 

 dental circumstances are less to be feared. Nevertheless, the single 

 observation of Gay Lussac has given me 4 9. 8 5 C., as the tempera- 

 ture of the planetary space, a number which only differs one-seventh 

 of a degree from that obtained by M. Fourier, according to the laws 

 of heat, radiating from the solid globe, supposed to have arrived at 

 its state of fixed and invariable temperature. 



* Without having much doubt as to the identity of light and heat, 

 or as to the accuracy of our photometrical knowledge, I thought it 

 would still be interesting to see the results which would be given by 

 setting out from the data of Lambert, on the absorption of light, 

 which, coming from the zenith, passes through the whole depth of 

 the atmosphere : establishing my calculation on the supposition that 



