366 Hydrostatics. 



the places at which the above result for the barometric pressure 

 at the level of the ocean was found, we shall have 51,9 as an- 

 swering to the temperature of the air at the lower station. Hence, 



48,8 + 51,9 _ . Q x 0^0223 = 



The correction, therefore, for difference of temperature, is 

 33 X 0,045 = 1 ,5 feet nearly, 



which added to 33 gives 34,5 for the elevation of the place of 

 observation at Cambridge above the level of the sea. Now the 

 actual elevation of the cistern of the barometer, as carefully 

 ascertained by levelling, is found to be 31 feet. In the calcula- 

 tion of very small heights near the level of the ocean, it is very 

 common to dispense with the formula and adopt the following 

 rule, namely, as 0,1 is to the difference in the barometric columns^ 

 so is 87 feet to the approximate difference of level required ; which 

 is to be corrected, if necessary, for the difference from 31 of the 

 mean temperature of the air at the two stations. Thus, 



0,1 : 0,038 : : 87 : 33,1, 

 a result agreeing very nearly with that derived from the formula* 



Thus, under a pressure of 30 inches of mercury at the tem- 

 perature of 50, 0,1 of an inch of mercury answers to 87 feet of 

 atmosphere. It will be seen moreover, that, as 0,1 of an inch of 

 mercury is equivalent to 87 feet of air, 0,01 answers to 8,7, 0,001 

 to 0,87, and j^ to 1,14. Hence in a good mountain barometer, 

 graduated to 500dths of an inch, there will be a sensible differ- 

 ence in the pressure of the air arising from a change of altitude 

 of less than two feet, or two thirds the length of the instrument. 



Formula (iv.) is essentially the same with that given by Laplace 

 in the 10th book of the Micanique Celeste^ but simplified after 

 the example of Poisson, and reduced to English measures. The 

 following example will serve to illustrate every part of this for- 

 mula. 



At the lower of two stations, the mercury in the barometer 

 was observed to be 29,4 inches, and its temperature 50, that of 



