at very loiv Temperatures and Altitudes. 1 79 



from a certain limit through all degrees of magnitude, and 

 even to change from positive to negative. It seems to be of 

 little avail to talk of a mean value, when there occur such ex- 

 cessive variations depending upon circumstances mostly hid- 

 den from our knowledge. Such being the fact, we may inquire 

 whether it can be satisfactorily accounted for. Now the re- 

 fractive power of air depends upon its density, or upon its 

 pressure and temperature which determine its density ; and all 

 experimenters have uniformly found that the distribution of 

 heat in the stratum of air in contact with the earth is ex- 

 tremely irregular. Sometimes the same degree of heat which 

 is observed at the earth's surface continues to prevail without 

 variation to a great height ; at other times, contrary to what 

 usually happens, the heat increases as we ascend ; and even 

 when the heat decreases in ascending, the rate at which it will 

 vary cannot be predicted with any degree of certainty. As far 

 as the refractions are affected by the stratum of air subject to 

 such vicissitudes, they must be irregular, as observation proves 

 them to be. But above this first stratum of air, the vicinity 

 of the earth has little influence on the propagation of heat, 

 which is distributed by laws depending alone upon the nature 

 of the aerial fluid. The atmosphere now assumes a more re- 

 gular constitution ; and the refractions, at elevations which 

 exempt them from the inequalities in the stratum at the earth's 

 surface, become subject to calculation founded on a few ele- 

 ments. The boundary which separates the refractions irre- 

 ducible to any degree of regularity, from 'those that can be 

 theoretically computed, at least with tolerable accuracy, must, 

 it is evident, be ascertained experimentally ; and it seems to 

 be placed at an elevation of 2° or 1°^ above the horizon. 



2. We are next to examine whether the tables in the hands 

 of astronomers have nearly the same accuracy at very low de- 

 grees of heat which they possess within the usual range of 

 temperature. And here I shall confine myself to Dr. Brink- 

 ley's table, and the table published in the Phil. Transactions 

 for 1824, and there called the New Table. In such arithmetical 

 examinations the head must follow the fingers ; and it is easy, 

 by a well-devised collection of instances and a little manage- 

 ment, to establish any conclusion wished for ; on which account 

 I have included in the following table all the observations be- 

 tween 2° and 10°, without omitting one. 



Z 2 App. 



