Neiv Tables for Finding Heights by the Barometer. 69 



heights, and if its density was throughout the same as at tlie 

 surface of the earth, it would be all contained within a limit 

 of about five miles. Air, however, is an elastic fluid, subject 

 to Mariotte's law, and has therefore its density proportional 

 to the pressure to which it is subjected, and if there were no 

 disturbing elements, the law would still be a simple one. 

 The heights would be in arithmetical progression, while the 

 pressures would be in geometrical progression, thus having 

 the nature of a table of logarithms, and the difference in 

 height would be equal to a certain constant distance, 

 multiplied by the difference between the logarithms of the 

 heights of the barometer at the two places. The principal 

 disturbing element is temperature, which varies the density 

 of the air by its changes. If we could obtain the tempera- 

 ture of the column of air between the two places, the 

 ])roper correction could be obtained ; but as we can only 

 apply the thermometer to the air near the surface of the 

 earth, where it is greatly affected by radiation, and have to 

 assume, as Laplace has done, that the temperature of the 

 column of air between tlie two stations is the mean of that 

 near the ground at each station, we sometimes get very 

 anomalous results. This has been proved by observing 

 barometers at two stations, not very distant, though con- 

 siderably differing in altitude, whose difference of height had 

 been well determined by careful levelling. Having now the 

 height and the barometer readings, we can substitute them 

 in Laplace's formula, and work out the temperatures. An 

 extensive series of such observations was made by Professor 

 Plantamour, using for his stations, Geneva and the Hospice 

 of St. Bernard. From the mean of the 8 a.m. observations, 

 the correction to the observed mean temperature varied from 

 -|-4<'5° in December to — 4*3° in July. The 4 p.m. observa- 

 tions gave -i-2'3° in December, and — 6"5° in July, and the 

 10 p.m. observations had a range of from + 47° in December 

 to — 0'2^ in July. Similar observations in the United 

 States, between Mount Washington in New Hampshire and 

 Portland, Maine, gave the following ranges : 8 a.m., +1'7'' 

 in August, and — 1"9° in November ; 5 p.m., — 3"2° in 

 December, and — 1'1° in September ; and 11 p.m., + 3'4° in 

 August, and — 2*1° in November. As the effect of an error 

 of one degree in the mean temperature is about 2 feet in 1000, 

 the greatest of the above corrections, the — 6 "5° in July, 

 would amount to 13 feet in 1000. Attempts have been made 

 to determine the law of decrement of the temperature of the 



