€68- 



6n ths coflEsroN or fluids. 



For rcpresen ling the depression, thus de- 

 termined, in a formula capable of expressing 

 it at. once, in terms of the diameter of 

 the tube, I have deduced an approximate 

 determination from the supposit on of a sphe- 

 rical surfiice, and corrected it, by compa- 

 rison with the results of these calculations, 

 so as to agree with them all, without an error 

 of one two thousandth of an inch, in the 

 most unfavourable of the five cases com- 

 pared. The theorem is, first, c = 



.0\5d 



dd+. 16 



which is nearly half the versed sine of a 

 spherical surface, and then /=-— — |- e — 



14.5e', which shows the central depression 

 without any sensible error. 



I have also found a formula, which ex- 

 presses the difference between the central 

 and marginal depression, so that an obser- 

 vation on the height of the barometer may " 

 be corrected, with equal accursfcy, whe- 

 thCT the elevation of the highest or lowest 

 point of the surface has been measured, pro- 

 vided that the tube be of moderate dimen- 

 sions. This formula is s=: — 5f +100 



° 15{5d-l-100d'J + 18. 



If d were very large, it would require some 

 further correction, g being ultimately too 

 great by .OO69. The results of these for- 

 mulas are compared, in the first of the fol- 

 lowing tables, with those of the calculations 

 at large ; and in the second, they are re- 

 duced into a form more immediately appli- 

 cable to practice, and are compared also 

 with the table pubhshed by Mr. Cavendish. 



