OF FREQUEJsXY OF THE BAROMETRIC HEIGHT AT DIVERS STATIONS. 459 
or if 
that is, if 
For example, if the correlation between the second and third stations be 0v572, 
/• = V<R8786 = 0-9373. 
1 + /^’ 
7 - ^l( i + p). 
In other words, if three stations conld be found with coefficients 7\.2 = 0-9373 = 
and 7^3 = 0-7572 ; then the barometric height at the first would be exactly a linear 
function of the contemporaneous heights at the other two stations. . There seems no 
reason why stations should not be found with tliese correlations, or similarly related 
correlations. The correlation between Southampton and 'Lauclale is 0-7572 ; the 
correlation between Stonyhurst and Laudale and between Stonyhurst and 
Southampton must be about 0-94 to 0-95. We increase the distance and make it less 
perpendicular to the generalised isobars by moving across towards the East coast. 
Probably somewhere near Whitby the required correlation of 0-9372 would be reached, 
and at such a station we should expect the barometric height to be very nearly a 
linear function of the heights at Southampton and Laudale.''' 
Supposing the relation r (I -1- p) to hold, then it is easy to deduce from the 
expression for above, that if H^, Hg and Hg be the absolute heights of the 
barometer at the three stations. 
+ 
oy H, ^ C7-1 H3 
'2r a .2 '2i’ cr^ 
This passage of correlation into causal relationshipt is of such extreme importance, 
that it is worth while to see what approach we can find to it, even withi]i the somewhat 
narrow limits of the British Isles. We have no details available for the barometer 
* Let the reader imagine the heights at Southampton and Laudale replaced by the heights at two 
(or if necessary more) stations on the American continent, say, along the East coast, and the height at 
the Whitby station replaced by the height, after an interval of time, at a British station, say Valencia, 
and then he will grasp the sort of possibility—not the proven feasibility—of prediction, which the 
authors wish to lay stress upon. 
t [This expression is used advisedly to draw attention to the importance of the limit when a corre¬ 
lation passes into a causal relationship. If the unit A be always preceded, accompanied or followed by 
B, and without A, B does not take place, then we are accustomed to speak of a causal relationship 
between A and B. On the other hand, if when A occurs amounts, 6 ^, 60 , . . . hn of B are found with 
frequencies i? 2 >T 3 ■ ■ ■ Pn per cent, of the occurrences of A, we speak of a correlation between A and 
B. Now, if we approach the limiting case of = jjj = ^>3 = . . . = Pr-i = Pr+\ = . . . = 0, and 
pr = 100 per cent., it is clear that more and more nearly hr of B will occur whenever A occurs, f.e., a 
tixed amount of B on every occurrence of A. This is the transition of correlation into causal relation¬ 
ship. It is the construction of a ^^-dimensioned correlation surface, of vrhich a particular q — 1 
dimensioned section approaches indefinitely close to a frequency curve of zero standard deviation.] 
N 2 
o 
(j 
