70 Royal Society : — 



Ex, 2. Rush's balloon ascent, September 10th, 1838 (see Meteo- 

 rological Papers by Admiral FitzRoy, No. 9, p. 19). 



A 60 B' 30-496 in. H 



a 5 b' 10-830 L 52 



836 B' + b' 41-326 I 0*64 



901 B'-b' 19-666 x 27 



q 17*3 



19*666 x 52400^-41-326 27116x901-2-900 



= 24935-8 =27146-1 



2198-8 c for 25000 34-9 h" for 27000 



181-4 diff.for-65 0'3 diff. for 100 



27116-0 "182-7 -q 



A-H=27164-0 



Laplace's formula gives the same result. 



As the British highlands do not exceed 5000 feet in altitude, and 

 lie near the parallel of 56° north latitude, the corrections will nearly 

 destroy each other. The following simple rule will therefore suffice 

 for calculating all British heights : — 



"Multiply the difference of the barometers by 524, and divide 

 the product by the sum of the barometers, retaining three decimal 

 places. Multiply this quotient by the sum of the temperatures of 

 the air increased by 836, and divide the product by 9, keeping one 

 decimal place. For aneroid and corrected mercurial barometers, the 

 quotient is the height in English feet. For uncorrected barometers, 

 subtract 2\ times the difference of the temperatures of the mercury." 



Ex. 3. Height of Ben Lomond (see Col. Sir H. James's Instruc- 

 tions for taking Meteorological Observations, App.). 



A 59-0 B 29-890 in. M 60-8 



a 47-8 b 26-656 m 49_"3 



836-0 B + b 56-546 M-m 11*5 



942-8 B-5 3-234 x 2j 



28-7 

 3-234 x 524^-56-546 x942-8-r-9-28-7=3110-5=A-H. 



The height by Laplace's formula is 3110-8, by levelling 3115*8. 

 The accuracy of the present formula is only intended to be tested by 

 Laplace's, and it will be wrong to at least the same extent. 



Very good results may also be obtained by neglecting H", which is 

 always very small, and transposing the terms h" and —2-35 (M— m) ; 

 thus 



A-H=(5240o|z^+ c + #'Y 



where 2\ is written for 2*35 to compensate for omitting to multiply 

 the latter by (836 + A-f a) -^900. This approximate form gives ri se 

 to the following practical rule for determining heights under 10,0^0 



