NEWTON S PRINCIPIA. 321 



Hence, by eliminating p 



-- _ . 

 p x (1 + a T) 



Integrate this, on the supposition that r is constant, 



-n s 



x (1 -f a T) V 2 a 



Let h Q , A! be the heights of the mercury in the barometer 

 at the lower and upper stations, and T O , r p the temperatures 

 at those stations respectively. Therefore the above expres 

 sion gives 



The value of r being constant is taken as the mean of the 

 two observed values T O , T I( It is this fact that the decrease 

 of temperature is found by actual observation at every 

 application of the formula that renders the results so trust 

 worthy. If we neglect z 2 the above leads to 



in yards. The logarithms are in this formula the ordinary 

 tabular ones to base 10, and the temperatures are expressed 

 in degrees above 32 F. 



If very great accuracy be required, a variety of small 

 corrections for x, a, g Q are necessary. The correction for 

 the variation of gravity with the height may be found by 

 substituting the value of z thus found in 



and this is to be added to the former result. 



(2.) There is another very interesting application of these 



Y 



