300 



On Barometric Heights. 



[No. 136. 



as follows : To 522 add twice the number expressing the mean tem- 

 perature in degrees cent., and we have the correct height corresponding 

 to a difference of 1° cent, and on Fahr. multiply the mean tempera- 

 ture above 32 by 0.6 and add it to 290, the sum is the correct height 

 giving a difference of 1° Fahr. 



The following Table may be convenient for reference. 



I may perhaps have occasion 

 to refer again to this subject. 



Mean 

 Temp. 

 Cent. 



Height 

 for 1°. 



Mean 

 Temp. 

 Fahr. 



Height 

 for 1°. 





 5 



10 

 15 

 20 

 25 

 30 



522 

 532 

 542 

 552 

 562 

 572 

 582 



30 

 32 

 40 

 50 

 60 

 70 

 80 



289 

 290 

 295 

 301 

 307 

 313 

 319 



There is a formula for finding the approximate height in barometric 

 operations of the same general form as that of Leslie, for diminution 

 of temperature. The formula is Q—~) 1 3050=Approx. Ht* (E) 

 The co-efficient in this formula is half the height of the equiponderant 

 column. The co-efficient of formula (A) before given is 52,200, being 

 double the height of the equiponderant column, or just 4 times the co- 

 efficient of formula (E). Now as in Leslie's formula the co-efficient is 

 25 cent, or just J of the interval from freezing to boiling, we may 

 therefore transform it into another of the form (A) and It becomes 

 (b"5D 100=diminution in degrees cent, or (j^S) 180= diminution 

 in deg. Fahr. which may be thus expressed : " The sum of the baro- 

 meters at the two stations is to their differences, as the No. of degrees 

 in the interval from boiling to freezing is to the diminution of mean 

 temperature by ascent." This rule will give results not sensibly 

 differing from those of the logarithmic formula (C and D) at intervals 

 of 4000 feet, or even at a mile. 



* The formula, (|-g) 13,000 and (|r^)52,200, for the approximate height, 

 ly close approximations to the truth, and are not absolutely identical : the former 



, are 

 only close approximations to the truth, and are not absolutely identical : the former errs 

 in excess, and the latter a little in defect. If they were absolutely identical, we should 



have B b_ =4 B— b B-b_ B 2 — b 2 (B+b ) (B— b), from which by transposition and 



b B B+b' 0F li- r -b — " 4Bb 4Bb 



division we get 4 B b=,B- r -b, 2 =B 2 +2Bb+b 2 hence 2 Bb=B J +b 8 , which however 

 do not differ much from the truth when B and b are nearly equal. 



