Of BAROMETRICAL MEASUREMENTS. 101 



1 8. THIS laft is precifely the formula of M. DE Luc, if we 

 give to />, r, and m, the proper values *. It was difcovered by 

 that ingenious and indefatigable obferver, without any enquiry 

 into the propagation of heat through the atmofphere, the prin- 

 ciple on which it depends ; and, that fo near an approximation 

 to the truth mould have been thus obtained, is to be confidered 

 as a fingular inftance of fagacity or of good fortune. -For if the 

 heat of the air diminifhed, not in the fimple ratio of the increafe 

 of the height, but in that of any power of it, fo as to be exprefs- 



ed by H A*", then, by computing as has been done above, we 

 mould find z = p(i+m(- : rp log. . Here the tempe- 

 rature from which r, or the fixt temperature, is to be fubtracl- 



. . H+b , nH+b . 



ed, is not , but : and this is a formula which con- 



2 7Z+I 



jefture or experiment alone would fcarcely have difcovered. 



IT is farther to be remarked of the formula 

 z p(i+m ^ rp log. - that it is rigoroufly juft, if we 



IT 1 L 



fuppofe the temperature - to be uniformly difFufed through 



the column of air, of which the height is to be meafured, as 

 is done by Dr HORSLEY in his theory of M. DE Luc's rules f ; 

 but that, on a fuppolition, more conformable to nature, of the 

 heat diminifhing in the fame proportion as the height increafes, 

 it is only an approximation to the truth, or the firft term of a 

 feries, whereof the other terms are rejected as inconsiderable. 



19. THE 



* If we take M. DE Luc's rule, as improved by the later obfervations of General 

 ROT and Sir GEORGE SHUCKBURGH, /> 4342.9448 :r the modulus of the tabular loga- 

 rithms multiplied by 10000 : r 32 and m .00245 nearly. It is unneceflary to re- 

 mark, that the logarithms underftood in all thefe formulas are hyperbolic logarithms, and 

 that the multiplication of them by p is faved, by ufing the tabular logarithms^ and ma- 

 king the firft four places of them, excluding the index, integers. 



f Phil. Tranf. vol. 64. part I. 



