3i Mr. Ivory in reply to the Historical Sketch 



Now in all this it is presumed that the substituting of one 

 density tor the other will produce no material alteration in 

 the atmosphere in other respects ; not reflecting that a change 

 in the expression of the density, although numerically insensi- 

 ble, by varying both the pressure and the function for heat, 

 may entirely aker the nature of an atmosphere, as happens in 

 the present instance. When the density is c ~'>^~'^^*", the 

 rigorous expressions of the pressure and the function for heat 

 are respectively, 



\-e ~ \—e 



1 ec ^ ' 



l—e ~ 1-e ' 



by which it is proved that the properties of the new atmo- 

 sphere are entirely different from those of the one originally 

 assumed. 



Thus there is neither mistake nor paradox in my paper, 

 although there is some inconsistency in the calculations of 

 Kramp and Bessel. 



3. It is said, p. 377, that my table of refractions has been 

 examined in a former Number of the Journal. Now here the 

 word examine must be understood in a sense different from its 

 usual import in the English language, 'i he author selects a 

 set of observations by Mr. Groombrids;e; he then alters his 

 table m various respects so as to reduce the errors of the ob- 

 servations to the least possible quantities, that is, so that the 

 errors with opposite signs may be equal in amount. Having 

 made the most of his table, he compares his manufactured re- 

 sults with the errors of the same observations computed simply 

 by my table ; and in this manner he makes out that one table 

 has little to boast of over the other. But, since they cannot 

 be compared when put on a par, every candid examiner, fol- 

 lowing the rules of an unsophisticated logic, must conclude 

 that there is no comparison between them. What he is pleased 

 to call an examination, is an attempt, per fas ct nefas, to raise 

 up his table to the same level with mine. 



4. I must now advert to a more disagreeable point. What 

 Dr. Young calls his latest solution of the problem, published 

 in the Philosophical Tranactions 1824, and another particular 

 solution mentioned at the end of the XlVth Number of the As- 

 tronomical Collections in the .Journal of Science, are both taken 

 from my paper. First, it is certain that the solutions in 

 question are particular cases of my general formulae, when 



a certain 



