224 



perpetual snow, would have rendered futile any attempt to obtain a connected 

 series of levels by the use of the spirit level, and therefore not only the trial 

 levels, but those required for the location of the selected route were calculated 

 from barometric observations. 



" As this, however, involved a great mass of calculations, the author was 

 led to consider whether the reductions of the barometer observations could not 

 be effected by simpler means than those commonly used. It then occurred to 

 him that if the altitude corresponding to any reduced barometer reading were 

 divided by the difference in the height of the mercurial column at the sea level, 

 and at the given altitude, the resulting quotient woiild be a factor, which 

 might be used for calculating approximately the altitudes corresponding to 

 other barometric readings within a certain limited range. 



"Thus, assuming the height in inches of the mercurial column at the sea 

 level = 30, 



And taking a series of 



reduced barometric 



readings as . 

 The differences between 



these readings and 



that at the sea level 



are 

 And the corresponding 



altitudes at a mean 



temperature of 32° 



Fah. . 

 Which altitudes divided 



by the differences 



of pressures would 



give the factors 



29 



28 



27 



26 etc. 



1 



2 



3 



4 etc. 



ft. 

 886-9 



ft. 

 1804-8 



ft. 

 2756-2 



ft. 

 3743-5 etc. 



886-9 



902-4 



918-8 



935-9 etc. 



which could be used for calculating approximately the altitudes corresponding 

 respectively to the barometer readings between 30 and 29, 29 and 28, 28 and 

 27, 27 and 26, etc. 



" Following up this idea, it further became apparent, that as the differences 

 of mercurial pressure are expressed in inches and decimals, the decimal 

 division of the differences between these factors would supply the means of 

 calculating factors for all intermediate barometric readings, not, it is true, with 

 perfect accuracy, but within limits of error which may be practically disregarded; 

 the maximum error, from the employment of the factors in the calculations, 

 in the resulting altitudes, for elevations under 3250 feet, not exceeding four 

 inches. 



" It will be seen at once, that in this system of calculating altitudes, the 

 correction for the difference between the actual and the tabular mean tempera- 

 ture will be most readily made, not by reducing the barometer readings, but by 

 correcting the tabular altitudes ; and also that if each of the factors be divided 

 by 480, the resulting quotients will give the constants by which they must be 

 respectively altered, for each degree of difference between the actual and the 

 tabular mean temperature. The result of the above considerations was the 

 construction of the following table (calculated for a mean temperature of 

 32° Fah., and a mercurial pressure at the sea level of 30 ins.) by which the 

 calculation of altitudes from barometric observations may be effected rapidly, 

 and with the use of very few figures, without the necessity of referring to 

 a table of logarithms, and with a corresponding diminution in the liability to 

 numerical errors. 



