tion is limited: the frequency of movement cannot be
inferred from it; two series might have quite different average
oscillations and yet the same standard deviation; and the range of
movement, or spread of the variations from the average price (though
allowed for in the standard deviation more than in the average error),
is hidden. Now frequency of movement, average daily price variation, and
range of price movements are matters of fundamental importance to the
public. Hence for practical purposes we require several kinds of
measurement of price movements, and it is impossible to weigh exactly
the one against the other in respect of importance. Observe that an
increase of the frequency of movement, or even of the average daily
movement, is not necessarily objectionable, since changes are less
harassing when they take place by small increments than when they are
brought about by a few big variations. The difference between the
highest and lowest price, we may observe, is a very imperfect indication
of the range of movement (though, taken in conjunction with the standard
deviation, it is the best at our disposal), because either of the
extreme prices might be accidental and quite out of relation to all
others. An investigator must be on his guard against using quotations of
this kind. There is also a difficulty about the frequency of movement,
because as a rule many movements take place in one day the total over a
period sufficiently lengthy to yield general results is enormous, and
many are unrecorded. In one day, for instance, when the net drop was 33
points and the range of variation 59 points (namely, 8.45 to 7.86), 150
price fluctuations were recorded. However, the count of frequency of
movement from daily closing prices would probably afford a roughly
satisfactory comparative measurement in markets in which prices
sometimes remain the same for a day or two together. The points just
noted apply also to the average fluctuation and the standard deviation,
but it is probable in these cases that daily or even weekly quotations
would be sufficient to yield the information sought for with sufficient
exactness for purposes of comparison.

Effect of speculation on steadiness of prices.

Now, supposing dealing to be confined to experts, what effects upon the
course of prices would one expect from the specialism of the cotton
market and improved facilities for dealing, on the assumption that
dealers were governed wholly