368 THE POPULAR SCIENCE MONTHLY. 



difference of height, required. Before the barometer readings 

 can be used, this must be reduced to the same temperature 

 usually 33 F. 



Various formulee have been computed by eminent mathemati- 

 cians and physicists for calculating the difference of height be- 

 tween two points. These formulee depend on certain assump- 

 tions which, however, can not be considered as rigidly true. The 

 most important of these assumptions is that the atmosphere may 

 be supposed to be in a state of statical equilibrium. But owing 

 to the changes constantly taking place, due to differences of tem- 

 perature, humidity, winds, etc., this assumption can not be con- 

 sidered correct. The result will therefore be only an approxima- 

 tion to the truth. Assuming, however, a statical equilibrium of 

 the atmosphere, a formula can easily be deduced from known 

 jjrinciples. For this purpose we must first ascertain the w^eight 

 of a cubic inch of air and a cubic inch of mercury at a certain 

 temperature and pressure, and in a given latitude, say 45. Then, 

 by Boyle and Mariotte's law, connecting the weight of a gas and 

 the pressure, the formula can be obtained for determining the 

 height required. There are several elaborate formulee used for 

 this i^urpose. These include terms for altitude, latitude, temper- 

 ature, and humidity. A correction for altitude is theoretically 

 necessary owing to the diminution in the force of gravity and, 

 therefore, a decrease in the weight of bodies with increased dis- 

 tance from the center of the earth, but this correction is com- 

 paratively very small, and may, for all practical purposes, be 

 neglected. For the same reason a correction for latitude is 

 mathematically required, owing to the spheroidal figure of the 

 earth ; but this, too, is very small, and may be safely neglected. 

 The correction for temperature of the air is, however, very im- 

 portant. This term is easily computed. It is obtained for the 

 Fahrenheit scale by deducting 64 from the sum of the observed 

 temperatures at the upper and lower stations, dividing the differ- 

 ence by 900, and adding unity to the result. A correction for 

 humidity of the air is also necessary ; but it is doubtful whether 

 it is desirable to complicate the formula by a correction for 

 atmospheric moisture, the laws of which are so imperfectly un- 

 derstood. 



In all the barometric formulae which have been proposed the 

 first term is constant, and common to all. It is known as the 



"barometric coefficient," and is 5744 , where m is the "weight 



a 



of a cubic inch of mercury at the sea level in latitude 45 at 30 

 F. when the barometer reads 29"92 inches," and a the weight of a 

 cubic inch of dry air under the same conditions of latitude, tem- 

 perature, and pressure. Various values of this constant have 



