132	THE  FACTORS OF THE MIND
grounds for dismissing the whole proposal, they shed a most
instructive light on the nature of the process by which such
judgments are reached, and thus help to indicate how that
process may be made more trustworthy.
All measurement is in some degree inexact and unreliable.
When we say that a child is x years old or x feet high, that
merely means that his c true ? measurement, JT, is such that
(x — |)& < % < (x + £)«• The physicist himself is always
ready to distinguish between 'orders of magnitude', and
to * neglect small quantities.5 Thus the more important
task that confronts the applied psychologist is, not so much
to prove that his variables obey the postulates of measure-
ment, but to show that the errors entailed by his tentative
methods are smalll compared with the measurements so
obtained.
The same principles and procedure may be applied when our
interest lies in comparing, not the mental productions of different
persons, but the mental characteristics of the same person. In
motivating human behaviour, particularly in the social and
economic world, an important part is played by what may be called,
in a broad sense of the term, relative preferences. The recent effort
to extend factorial measurement into this new field has met with
strenuous criticism. To a large extent the objections urged are
much the same as those raised sixty years ago against the c dismal
science' of economics. The factorist is warned that, since the
interval of 10 seconds, and yet after 6 sucli imperceptible movements, is
seen to be at an obviously different place, (ii) Again, given two scripts, 10
and 6, the observer can find a third bisecting their distance, i,e« such that
(10 — 8) = (8 — 6), and two more such that (10 — 9) = (9 — 8) and
(8 — 7) = (7 — 6). He is now asked to find another script, 8', such that
(9— 8') as (8' — 7). Then 8' and 8 should not be perceptibly different.
Not infrequently they are. Such inconsistencies merely illustrate the effect
of allowing small deviations, lying within the margin of experimental error,
to accumulate.
1 If the research student asks how small, I suggest, to begin with, the rough
convention often adopted by the physicist: " two quantities are of the same
order of magnitude when their ratio does not exceed to " (Jeffreys, loc, cit.,
p* 217). The weight of the copy of the standard kilogram at the Standards
OfHce at Westminster is certified to be I -ooo ooo 070 ± *ooo ooo 002 times
the weight of the original in the Standards Bureau at Sevres. But the
educational psychologist seems happy when two copies of his unit differ
by no more than 10 per cent.