Of BAROMETRICAL MEASUREMENTS. 103 



20. THE term involving m * , that has now been computed, 

 will rarely amount to any thing confiderable. The coefficient 

 of it vanifhes when both H and b are equal to r, but increafes 

 as thefe two quantities recede from r on either fide. In no in- 

 ftance where the barometer is to be applied to actual meafure- 

 ment, will the correction probably be found greater than in de- 

 termining the height of Cora9on above the level of the South 

 Sea, where If, or the height of the thermometer at that level, 

 was 84!, and , or the height of the thermometer at the top 

 of the mountain, 43 i ; the coefficient of m 2 comes out, in 

 this cafe 4-426, and m 3 being = .000006 (.00245)% the cor- 



rection = .00259, or nearly of the height of the moun- 



tain, as found before any correction was applied, or = 40 feet 

 nearly. It is to be remarked, too, that, for every value of H, 

 or of the temperature at the lower flation, there are two values 

 of b, or the temperature at the upper ftation, that make the co- 



r 



efficient, ---- --- 1 -- , and, of confe- 



242 12 



quence, the correction depending on it equal to nothing. This 

 is evident from the nature of the coefficient ; but, as the law by 

 which this laft increafes and decreafes is, by no means, fimple, 

 it were convenient to have it reduced into a table, for the dif- 

 ferent values that might be affigned to H and b, from which it 

 would be immediately obvious in what cafes it was to be taken 

 into account, and when it might fafely be omitted. 



BUT though this correction may fometimes be of confe- 

 quence enough to be included in the meafurement of heights, 

 it is certain that it may be fafely neglected in the computation 

 of the other corrections. For the error thereby committed in 

 the eftimation of a new correction, will be nearly the fame part 

 of the former correction, that the new one is of the whole 



height. If, for inftance, the new correction be of the 



whole 



