mid Levelling, §c. 331 



measurements of heights, and experiments on sound about 

 the years 1827, 1828, &c, I found that a given volume of 

 moist air in its mean state expanded from 1 to 1.4112 when 

 heated from the freezing to the boiling point. I shall call 

 this expansion for 1° centigrade 13", and equal to 0.004112. 

 The barometric measurements to which I here refer were 

 made on the Cheviot range, on the Pentland range of hills, on 

 Benlomond, Ben Nevis, &c, and the experiments on sound 

 were made in Fife by taking advantage of the reports of the 

 guns fired on Edinburgh Castle in honour of the royal birth- 

 days, coronation anniversaries, &c, thus turning, as far as I 

 could, these holiday rejoicings to the benefit of science, since 

 I had neither the means nor the influence to procure expe- 

 riments to be made expressly to serve my purposes. 



This co-efficient was introduced by me into a formula, 

 which I gave about that time in one of our public journals, 

 to determine the velocity of sound, and it almost uniformly 

 brings out results conformable to experience. It becomes 

 0.00230 for 1° of Fahrenheit's thermometer, and this was also 

 introduced into a set of tables published by me in 1838 for 

 the purpose of calculating heights by means of the mountain 

 barometer, which give correct results for all heights when the 

 barometric measurements have been accurately made under 

 favourable circumstances.* 



* Mr Francis Baily gave, among his collection of Astronomical Tables, 

 printed in 1827, Table xxxvi. to compute heights by the barometer. In 

 its application he neglected to state, that when subtracting the tempera- 

 ture at the higher station from that at the lower, if the result become nega- 

 tive, which it will be when the temperature at the higher station is greater 

 than that at the lower, a circumstance that may occur on some rare occa- 

 sions in small heights, then the logarithmic correction must be applied to 

 the higher barometer with the same or a negative sign, instead of an additive 

 as commonly happens. 



Though to a mathematician this could be of little consequence, as he 

 would naturally apply this correction according to its proper sign, yet to 

 guard against any misapprehension on the part of those little acquainted 

 with the use of signs, I carefully warned computers against any error from 

 this cause in the last sentence of Rule 3, page 10 of the explanation of these 

 tables. 



The same thing was done by Mr Ilowlett of the Ordnance Map Office 

 some years afterwards, among the professional papers published by the lioyal 

 Engineers in their first number. 



