OF FREQUENCY OB' THE BAROMETRIC HEIGHT AT DIVERS STATIONS. 433 
Frequency annum. 
Height 
in inches. 
1 
Frequency per annum. 
\ 
Height 
in inches. 
Observed. 
Calculated 
Observed. 
Calculated 
B'rom (ii.). 
From (v.). 
From (ii.). 
From (v.). 
28-6 
0T9 
0 07 
0-09 
1 29-9 
41-27 
40-99 
40-99 
28-7 
0-42 
0-14 
0-17 
; 30-0 
45-92 
44-35 
44-37 
28-8 
0-38 
0-29 
0-32 
1 30-1 
46-96 
43-93 
43-64 
28-9 
0-46 
0-58 
0-60 
i 30-2 
38-88 
39-21 
38-66 
29-0 
0'69 
1-09 
1-09 
1 30-3 
30-19 
31-21 
30-16 
29T 
1-88 
1-99 
1-94 
30-4 
18-23 
21-79 
20-75 
29-2 
2-81 
3-50 
3-34 
i 30-5 
13-65 
13-08 
12-40 
29-3 
6-04 
5-86 
5-58 
30-6 
7-31 
6-61 
6-38 
29-4 
9-31 
9-31 
8-91 
30-7 
3-12 
2-76 
2-80 
29-5 
15T5 
14-21 
13-67 
30-8 
0-38 
0-87 
1-04 
296 
18-62 
-20-41 
19-82 
30-9 
0-31 
0-21 
0-3-2 
29-7 
26-85 
27-56 
27-11 
31-0 
0-08 
0-03 
0-09 
29-8 
36-12 
34-94 
34-64 
In view of the above remarks we shall confine our attention to curves of the 
form (ii.). We can now discuss the relations between the constants of this curve 
and the physical quantities associated with barometry. 
5. Constants of a Local Distribution of Barometric Frequency, 
It is convenient to term the height of the barometer, corresponding to the maximum 
frequency, the mode. This mode never coincides with the mean, and we shall represent 
them by and Mg respectively. The divergence of the mode from the mean marks the 
skewness of the frequency distribution, but it is fitting to measure this divergence in 
terms of some standard of variation of the local distribution. It is convenient to 
select as this standard, cr, the standard deviation of the distribution, or Uix,. We 
shall represent the skewness of the frequency by Sk. Another interesting physical 
constant of the distribution is indicated by the theoretical laAv of frequency—this is 
the maximum possihile of barometric height in the locality. It is directly obtained 
by adding to the mode or mean the possible range above either. This maximum 
height we will indicate by while shall indicate the maximum observed height. 
The following relations hold between the constants of the theoretical distribution 
and the above physical quantities 
o-= f \/p + l/y .(i.), 
1^0 hig — 1/y — /3i . 
Bj, — = a' = = 2o-/y^i = {p + l)/y .... (iii.), 
Sk. = (Mo — M,)/o- = i/xg/v//X 2 ^ = \ a//3i .(iv.). 
3 K 
VOL. CXC.-A. 
