40 Mr, Nixon on the Measurement of Heights, 6fc, [Jan. 



To make the correction for the difference of temperature of 

 the mercury also additive, we have but to suppose that of /z' to 

 be at 100° F. Consequently as the interior thermometer of any 

 one of the inferior barometers will never indicate so elevated a 

 temperature, its perpendicular distance from h', as given in 

 Tables II. and III. must be augmented by multiplying the differ- 

 ence of its attached thermometer, and 100° by 2" 18 feet (the 

 value of 1° of the difference at 0° F,). Tabularly arranged, the 

 correction at 100° F. will be feet; at 99°, 2-18 feet, &c. (See 

 Table IV.) 



The height of // above the level of /* and H being obtained by 

 adding together for each the quantities given in the three tables, 

 their difference will be equal to the elevation of h above H at 

 0° F. Multiplying this approximate height by the sum of the 

 thermometers, and dividing the product by 836, we have the 

 correction in altitude additive for temperatures above 0° F. 



Multiplying •002837 by cosine of twice the latitude, we obtain 

 the fractional correction in altitude proper for that parallel. 

 Then as an addition to (or subtraction from) the sum of the 

 detached thermometers at 110°, equal to 1°, augments (or dimi- 

 nishes) the altitude '001057, we have but to substitute for the 

 fractional corrections their equivalents in degrees and quarters 

 of the sum of the thermometers. At the equator, the equivalent 



would be = ■:^5 = 2|°. (See Table V.) 



Having given the altitude and height of the thermometer at 

 the upper station, we find the mean temperature, the fall of the 

 thermometer being 2° in 500 feet, by dividing tlie difference of 

 level of the stations by 500, and adding the quotient, considered 

 as degrees to the temperature observed at the summit. At 55° 

 an increase of the mean temperature equal to 1° augments the 



altitude — . However as the fall of 2° in 500 feet may be con- 

 sidered in excess, we will call the mean dilatation — -. ; the cor- 



' 500 ' 



rection for altitudes computed with twice the height of the upper 

 thermometer substituted for the sum of the thermometers, will 



then be equal to the square of r^th part of the approximate alti- 

 tude. (See Table VI.) 



(To be continued.) 



