442 
PROFESSOR K. PEARSON AND MISS A. LEE ON THE DISTRIBUTION 
as a rule, remarkably closer to the true mode than any application of methods such 
as (ii.) or (iii.). 
If we invert the process and calculate from Table IV. the median values at our 
three southern stations, we find ;— 
Mediau, St. Leonards. 29"-9976 
„ Southampton. .. 30''-0006 
„ Babbacombe. 29"-9986 
Thus we see that the median height of the barometer along the south coast of 
England approaches extremely closely to the 30", so commonly adopted by physicists 
as a measure of the “ standard atmosphere.” 
There is another convenient method of looking at this standard atmosphere of 30”. 
If we turn to the modal heights in Table IV., we notice that the mean modal 
height for all our stations is 29”-9902, with the very small probable error of 0'0051. 
Hence the mean modal height for the British Isles differs by less than twice its 
probable error from the customary standard atmosphere. On the other hand, the 
mean mean height differs by more than 12 times its probable error from the 
standard atmosphere. We may accordingly look upon the standard atmosphere of 
30 , either as corresponding very closely to the mean modal height of the barometer 
for the British Isles, or as representing the median height of the barometer along the 
English southern coast. 
Another interesting feature of tlie modal height is that it is less variable than the 
mean as we pass fi’om station to station, and the probable error in the determination 
of the mean of the modes is accordingly less than that of the mean of the means. 
Whereas up and down the British Isles we find a coefficient of variation of 0'14 per 
cent, for the mean barometric height, the corresponding quantity is only O'll per¬ 
cent. for the modes. On this account, and because the mode—as the most 
frequent barometric height—has a more direct physical interpretation than the 
mean, it seems to us that a record of local modes would be of greater significance 
than a record of local means. 
Owing to the property we have already noticed, fie., that the distribution of barometric 
frequency is constant along contour lines, differing, at any rate, not very widely from 
the isobars in the narrower sense of the word, it follows that mean and mode oscillate, 
although not without deviations, in general accordance. Thus, both mean and mode are 
least at Laudale and Hunrobin Castle, the most northerly stations we have dealt 
with ; both means and modes are greatest at the four southernmost stations, Margate, 
St. Leonards, Southampton, and Babbacombe, although it is characteristic of some 
peculiarity of observation or climatological individuality, that while out of the four 
the means are greatest at St. Leonards and Southampton, the modes are greatest at 
Southampton and Margate. In particular we look upon the modal value at Mai’gate 
(30”-0493) as standing geographically between Geldeston (30”-0047) and St. Leonards 
