126 THE FACTORS OF THE MIND

interval) which separate the extremes and which the three notes
mark off.1

If the formulae of correlational and factorial analysis
are to be applied to such magnitudes,, it will be necessary
to show that the differences, distances, or intervals are
subject to the operation of addition. This holds in attempt-
ing to measure both the factors themselves and the empirical
variables from which they are derived. The possibility of
finding a unit of measurement follows from this, not vice
versa^ as Stephenson's criticisms seem to imply.

First of all, however, let us see what procedures have
actually been employed in attempting to replace crude
ordinal results (which are all that the teachers' usual method
of marking really supplies) by a set of additive measure-
ments. The construction of mental and scholastic tests
exemplifies the expedients most commonly adopted. For
the measurements in individual psychology four main types
of scale may be distinguished : the student will find con-
crete illustrations of each in the L.C.C. Report already
cited [41].

(i) Speed or frequency scales, For these the initial measure is
generally either (a) the time taken for a specified number of reactions
(amount-limit method) or (b) the number of reactions performed in a
stated time (time-limit method)—the stated time being either a
short period measured in minutes, or a longer period measured in

1 The distinction is clearly drawn by Meinong (Uber die Bedeutung des
Weber*schen Ges sizes, p. 22), who distinguishes the UntersMed from the
Verschiedenheity e.g. the Strecke (or c stretch J) between two points from the
< distance' between them ; the former is itself a line; the latter is not.
The psychologist will recollect Delboeuf s proposal to measure sensory
intensity in terms of * sense-distance ' (contrasts sensible), instead of in terms
of the sensations themselves as Fechner had proposed (Revue fhilosophique,
1878, V, pp. 53 f.). What I may call Fechner's fallacy constantly reappears in
criticisms of psychological measurement; e.g. in the British Association
Report the " measurability of sensation intensity " is denied because a sensa-
tion " cannot be analysed into parts from which it can be resynthetized by a
defined operation of addition " (loc. cit.9 App. IV, p. 15). Nevertheless, as
the instance cited in the text suggests, it may be adequate for practicable
purposes to estimate distance by the corresponding * stretch,' the abstract
interval by the number of concrete things we can interpolate within it,