On calculating Heights Barometrically without Logarithms, 71 



feet, embodying so much of the Table of corrections as is necessary 

 for that purpose. 



"Multiply the difference of the barometers by 52400, and divide 

 by the sum of the barometers. If the number of clear thousands in 

 the quotient be 



h 2, 3, 4, 5, 6, 7, 8, 9, 10, 



add 0, 0-5, 27, 7*2, 14-8, 26-1, 42-2, 63-6, 91*2, 125-6 

 and 0*2, 0*5, 0-8, 1*1, 1-6, 2-1, 2-9, 3'1 



for every additional hundred. Then multiply the result by the sum 

 of the temperatures of the air increased by 836, and divide the pro- 

 duct by 900. To this quotient 



add forkt 0, 10, 20, 30, 32, 34, 36, 38, 40, 42, 44, 



subtract for lat. 90, 80, 70, 60, 58, 56, 54, 52, 50, 48, 46 



the numbers 2'6, 2'5, 2*0, 1-3, 1*2, 1*0, 08, 0*6, 0*5, 0-3,^0-1 



for every clear thousand it contains. For aneroid and corrected 

 mercurial barometers this result is the height in English feet. For 

 uncorrected mercurial barometers, subtract 2\ times the difference of 

 the temperatures of the mercury. 



" The barometers may be expressed in any units. If the tempe- 

 ratures are expressed in 



degrees Centigrade, use 500, 500, A\, 



degrees Reaumur, use 400, 400, 5\, 



in place of 836, 900, 2£, 



which are only suited for degrees Fahrenheit. The rule and the 

 other numbers remain unaltered, and the result is in English feet." 

 Ex. 4. Height of Guanaxuato in Mexico. 



A 77*5 B 30-046 M 77'5 L 21 



a 70*3 b 23-660 m 7CK3 I 2-0 



836-0 B + 5 53-706 M— m "7-2 x 6-8 



983-8 B-6 6-386 __2| q 13-6 



p 18-0 



6-386 x 52400-r 53-706 6260-5 x 983-8^-900 



= 6230-7 =6843-4 



26-1 for 6000 13*6 q 



3-7 diff. for 230 \82-Q- p 



6260-5 A-H=6839'0 



Result by Laplace's formula 6838*2. 



These results are obtained by transforming Laplace's formula as 

 follows. The original expression in the Mec. Cel. vol. iv. p. 293, 

 reduced to English measures and the present notation, is 



