on the Formula for measuring Heights by the Barometer. 233 
in taking the corresponding observations at the upper one, I had 
recourse to a method of obviating that disadvantage by interpo- 
lation, which, on account of the shortness of the interval be- 
tween the two sets of observations, could not err much from the 
truth. The method to which I allude, consisted simply in tak- 
ing the observations at the lower station twice, with the exact 
time at which they were finished ; namely, before ascending the 
hill, and, again, after coming down. If any change was ob- 
served to have taken place in the state of the barometer, on 
making the second observation (the mercury in both cases being 
reduced to the same temperature), the difference was ascribed to a 
change in the barometrical pressure, during the interval between 
the two observations ; and, on the supposition that the change 
had been uniform, it was easy to determine the height of the 
mercurial column at the lower station, for the instant of time 
when the observation at the top was completed. Similar cor- 
rections were applied to the temperature and humidity of the 
air. By this mode of proceeding, the necessary data at the 
lower station were obtained, probably with as much precision as 
if they had been actually procured by observations made at the 
exact instant when those at the upper station were taken ; with 
this advantage, that the chance of error arising from the use of 
different instruments by different observers, was, in a great mea- 
sure, avoided. The instruments, it may be added, were all of 
the best construction, and, with great delicacy, conjoined the ut- 
most exactness of graduation. The barometer was furnished 
by Mr Adie of Edinburgh, and read off to the thousandth part 
of an inch. 
But, instead of illustrating the correctness of the coefficients 
I have proposed, by an appeal to my own observations, it will 
perhaps be more satisfactory to apply the formula to the ob- 
servations of Sir George Shuckburgh, and General Roy, for 
the measurement of heights, which they had determined geo- 
metrically, with greater precision, it may be presumed, than the 
less perfect instrument I possessed enabled me to attain. At 
any rate, this will remove all grounds for suspecting that any 
perversion of facts has been made to accommodate the barome- 
trical results to the geometrical measurements. I shall accord- 
