98 
Proceedings of the Royal Society of Edinburgh. [Sess. 
quantities, we get for the northward and westward components of the 
pressure-gradient per hundred kilometres 
A N y=l|-(WtoE) 
and 
AwP = l^ T( S to N), 
where (W to E) and (S to N) indicate the components of the wind- velocity 
resolved in those two directions. 
Now from a pilot balloon ascent we cannot get the value of p/0 for the 
special occasion of the ascent, but there is really little variation from time 
to time of this ratio. For the greater part of the troposphere variations of 
pressure and temperature go together, and the whole range of variation 
of 0 for any particular time of year is less than 10 per cent., and the whole 
range of variation of p is of the same order. Consequently a mean value 
of p/0 may be taken as a first approximation for the purposes of the 
calculation. 
The following is a table of average values of p/0 : — 
Table II. — Table for Values of p/e at Different Levels — 
Average of Results in “Geophysical Journal,” 1912. 
Height, 
kilo- 
metres. 
p/e. 
Height, 
kilo- 
metres. 
Pie. 
Height, 
kilo- 
metres. 
p/e. 
Height, 
kilo- 
metres. 
pie. 
20 
•26 
15 
•53 
10 
1*18 
5 
2-11 
19 
•28 
14 
•64 
9 
1-35 
4 
2-35 
18 
•32 
13 
•75 
8 
1-52 
3 
2-61 
17 
•39 
12 
•87 
7 
1-70 
2 
2-91 
16 
•46 
11 
1-02 
6 
1-90 
1 
Gd. 
3*24 
3-55 
Having thus computed the pressure-difference for 100 kilometres, in 
two directions at right angles, for the level of each kilometre, we may next 
obtain by subtraction the change of pressure-difference for each kilometre. 
The use of the mean value for p/0 will not altogether invalidate the process, 
because the variation from kilometre to kilometre depends generally on the 
ordinary diminution of pressure with height rather than on any extra- 
ordinary distribution of temperature. 
Substituting the value of the rate of increase of pressure-difference per 
kilometre of height in the equation 
dA P_oA.oP(M A P 
dh~ “ 6\0 p 
