1824.] Philosophical Transactions for 1823, Part II. 301 



Laplace's formula is made to extend to 74°, it is carried to its 

 utmost limit. However mutable we may suppose the condition 

 of the atmosphere to be, there must be a mean state equally 

 removed from the opposite extremes. Now, a table of refrac- 

 tions that should have this mean state of the atmosphere for its 

 basis would be the most advantageous of any. For although, 

 with respect to single observations, the errors of such a table 

 might be as great as in some other hypotheses, yet in a nume- 

 rous set of observations made at different times so as to embrace 

 all the usual changes, the inequalities of an opposite kind would 

 counterbalance one another. But to a certain distance from the 

 zenith, Laplace's formula is sufficiently exact for practical pur- 

 poses ; and it has the advantage of taking away the necessity of 

 having recourse to precarious suppositions respecting the consti- 

 tion of the atmosphere. 



There is no ground in experience for attributing to the grada- 

 tion of heat in the atmosphere any other law than that of an 

 equable decrease as the altitude increases. This law prevails to 

 the greatest heights to which we have been able to ascend. The 

 mean elevation for one degree of depression of the centigrade 

 thermometer is very nearly 90 English fathoms ; and in the 

 height ascended by Gay-Lussac, rather more than 4-1 miles, the 

 same quantity comes out equal to 95 fathoms. To this great 

 extent the law of a uniform decrease of temperature holds good 

 without much deviation from the truth. It therefore seems to 

 be the assumption most likely to guide us aright in approximat- 

 ing to the true constitution of the atmosphere. The very exact 

 coincidence in the properties of all the atmospheres compre- 

 hended in the formula assumed by Mr. Ivory, with the phaeno- 

 mena actually observed at the surface of the earth, accounts in a 

 satisfactory manner for the near approach of the refractions in 

 every case to the quantities determined by astronomers. It 

 appears that although the refractions near the zenith are affected 

 in a degree hardly perceptible by the peculiar constitution of the 

 atmosphere, yet near the horizon they depend upon the same 

 arrangement of the strata of air indicated by terrestrial experi- 

 ments. The causes in the irregularities observable in these last, 

 likewise disturb the celestial phenomenon in a more remarkable 

 manner. In measuring the height of a column of air, the acci- 

 dental disturbances to which the atmosphere is continually sub- 

 ject, are in some measure corrected by means of the tempera- 

 tures observed at both extremities of the column ; but in 

 computing the refractions, the astronomer has no guide but the 

 thermometer placed in his observatory. In the remote parts of 

 the atmosphere, there may occur innumerable changes deflecting 

 the light of a star from its proper course, of which he has no 

 intimation, and for which he can make no allowance. In com- 

 parison of this great source of error, we may reckon as of small 



