334 
MR. J. WELSH’S ACCOUNT OF METEOROLOGICAL 
In order to deduce from these numbers an approximation to the normal progression 
of temperature, freed from accidental irregularities, each series was m the first 
instance arranged in equations of the form^ 
T=X+YH, 
T beins the observed temperature at the height H ; Y the change in degrees of tem- 
perature due to 1000 feet of height; and X the temperature at the level of the sea 
which, with the addition of the quantity YH, would best represent the observed 
temperatures throughout the series, on the supposition of the change being uniform 
with the height. X and Y were eliminated by the method of least squares, and the 
following values obtained for the diflPerent series : 
Aug. 17. 
Aug. 26. 
Oct. 21. 
[Nov. 10. 
x~ 
7276 
64-98 
58-49 
50-02 
Y= 
- 3-097 
~ 2-617 
- 2-291 
— 2-496 
Mean error 
172 
2-16 
2-65 
2-56 
On the supposition that the rate of change is not constant, but that it varies with 
the height, the following interpolating equation was employed,— 

omitting higher powers of H than the second. When the same method of elimina- 
tion was 
adopted, the following values were found 
Aug. 17. Aug. 26. 
Oct. 21. 
Nov. 10. 
a,'— 
76-17 
64-11 
53-36 
44-69 
y- 
- 2-363 
— 2-346 
4 - 0-1132 
— 1-095 
— 0-03613 
- 0-01424 
- 1-868 
— O-O 6 O 7 O 
Mean error I* 30 
2-13 
1-35 
171 
In Table 11. will be found the differences between the observed temperatures, and 
those resulting from the two forms of equation employed. The progress of those 
differences in each series seems to follow a distinct law; there being in all cases a 
maximum of negative differences at a short distance from the earth, varying trom 
about 2500 feet on October 21, to 6000 feet on August 26, followed also in each by a 
maximum of positive differences at an additional height of 3000 to 5000 feet. Ims 
peculiar departure from a regular progression will be distinctly traced in the projected 
results (Plates XIX. — XXII.). It is there seen, in all the four series, that after a stead\ 
decrease of the temperature in the lower portion of the curve, this decrease becomes 
arrested, and, for a space of about 2000 feet, the temperature remains almost con- 
stant, or even increases by a small amount; the decrease being afterwards resumed 
and continued, without much variation, throughout the upper portion of the curve 
In the series of August 17 and 26 this fact is strikingly coincident with a large and 
abrupt diminution in the amount of aqueous vapour; the same coincidence being 
