1817.) Scientific Intelligence. 251 
Should the above observations deserve a place in your philoso- 
phical journal, the insertion will much oblige, 
Sir, your obedient servant, 
Bishop-wearmouth, Feb. 10, 1817. Rosert PEnsEy. 
XV. Formulas for estimating the Height of Mountains. 
(To Dr. Thomson.) 
DEAR SIR, 
The perusal of Mr. Anderson’s very ingenious paper on baro- 
metric altimetry in your last number, brought to my recollection a 
couple of formule which I composed in one of the latter months of 
1815. Before sending them to you, I wished to ascertain if my 
discovery had been anticipated, but have had no opportunity of 
satisfying myself on that head. The formule of Sir G. Shuckburgh 
and Professor Leslie, I conclude, must be of general application ; 
if so, they are quite distinct from mine, which are exclusively 
adapted to the use of observers in countries of moderate inequality, 
like our own island. At all events, they have the merit of utility 
and convenience, whatever be the fate of their claims of originality ¢- 
and as, by every rule of probabilities, the present year ought to be 
favourable for making observations, you will perhaps deem this a 
favourable crisis for stimulating by discussion the spirit of curiosity 
which a long series of bad weather has torpified. 
1. If T, ¢, represent the temperatures of the air, taken at the 
bottom and at the summit of the mountain, by a detached thermo- 
meter; and B, 0, the heights of the mercury in the barometer in 
the same situations; the elevation, expressed in yards, will be 
equal to 
20(B — 3% 
ABH) x (808+ T+ 0) 
The result found from this theorem will not deviate from that 
obtained by logarithms, more than three or four feet in the height 
of Ben Nevis, estimated at 1450 yards. 
For altitudes of about 3640 feet, it is precisely equivalent to the 
logarithmic method. 
In lower elevations, the greatest error, about two or three feet, 
occurs at the height of 700 yards. 
These errors are so minute, particularly when compared with 
those which will arise from physical sources, that the observer who 
preserves this formula in memory, or in his memorandum book, 
need not regret the occasional absence of logarithmic tables. 
When the circumstances of the observation appear to admit of 
great accuracy, it will be proper to employ J + ch at 
of /, as a correction due to the diminished temperature of the 
mercury from 'T’ to ¢’, as shown by a thermometer attached to the 
instrument, 
instead 
