Astronomical and Nautical Collections. 369 



Dr. Young's theorem is p = — r + [ — — — 1) +d _ 



s \ mp 2ss mpz 



..s 



+ . . . When ?- vanishes, or near the zenith, the first term 



of the series only determines it, and it becomes simply proportional 

 to the refractive density p ; at a greater distance the second term 

 becomes sensible, depending on the total variation of the actual 



density in ascending a given height, ^ being := Ji : this coeffi- 



dz 



cient ought, therefore, to be the same in every hypothesis concern- 

 ing the constitution of the atmosphere, which professes to represent 

 correctly the initial diminution of temperature of density in ascend- 

 ing ; how this diminution may vary at greater heights cannot 

 easily be determined from direct observation, since we cannot 

 reason with certainty on the temperature of the open atmosphere 

 remote from the earth, from that of the surfaces of mountains, which 

 may very possibly be affected by their immediate contact with the 

 solid earth, and it seems necessary to obtain the subsequent coeffi- 

 cients from the phenomena of refraction, as observed in favourable 

 circumstances, taking also the mean of a great number of results. 



In the approximatory method of using four terms only, it may 

 become convenient to modify even the first two, in order to co- 

 operate the more perfectly with the succeeding ones ; but it is dif- 

 ficult to suppose that the actual constitution of the atmosphere can 

 be represented with great precision by a hypothesis like that of 

 Laplace, in which the initial variation of temperature is made 

 greater than the truth. That there is no actual necessity for such 

 a departure from observation, is shown by Mr. Ivory's table, and 

 by Dr. Young's latest solution of the problem, both of which begin 

 with assuming the initial variation of temperature equal to that 

 which is actually observed : while Mr. Ivory supposes the rate of 

 variation to become slower in ascending, and Dr. Young more 

 rapid, and yet the results agree very nearly with each other, and 

 with the French tables, except quite close to the horizon. 



The ridiculous accusations which were brought against Dr. 

 Young, and against the British Government, by au unfortunate 



