ico CAUSES which affeff the ACCURACY 



and 



H+b 



Hence p(hg.b %. 



17. THESE feries will not converge faft, unlefs rg y Hg, and 

 hgt be all of them quantities much lefs than unity. Now, as m, 

 or the expanfion of air of the temperature r, for i of heat, is, 

 in fact, very fmall, being nearly .00245, an< ^ as g> or ^ Q ^g a - 

 rithm of I z, muft, of confequence, be nearly = m =. 

 .00245, it is plain, that, in all moderate temperatures, thefe 

 feries will converge with great rapidity ; though, in extreme 

 cafes, where z is fuppofed vaftly great, and where h may be ne- 

 gative, and alfo great, the feries in the denominator may con- 

 verge fo flowly that recourfe muft be had to the formula in 

 15. from which no quantities are rejedled. 



WHEN z, and, of confequence, g t are very fmall, and when 

 H and h do not differ much from r, the preceding formula, 

 agreeably to a remark in 6. will comprehend the cafe of uni- 

 form expanfion, and will give the fame expreffion for the height, 

 that would be derived from confidering only the equable de- 

 creafe of heat as we afcend in the atmofphere. Now, as in the 

 cafe fuppofed, we may rejecl all the powers of g but the firft, 

 and may alfo fuppofe g /, we have 



z = fC<4-~ r) (log.blog. (3). 



18. THIS 



