Bauhaus-Universität Weimar

Experimental Psychology: A Manual of Laboratory Practice, Vol. II: Quantitative Experiments, part 1: Student's Manual
Titchener, Edward B.
§ 2. Mental Measurement xxi 
the beginning. In weighing our package, we had the zero point 
upon the scale bar ; the limiting point at which the sliding weight 
was just counterbalanced ; and the mark that lay I oz. (or i lb.) 
from the zero point. There are various devices—the introduc¬ 
tion of submultiples of the unit, the use of. the vernier—for in¬ 
creasing the accuracy of measurement ; there are other devices 
for standardising the conditions (temperature, stress) under 
which a measurement is made ; there are mathematical rules for 
calculating the ‘ probable error ’ of a given measurement. These 
are all refinements of the art of measuring. The essential thing 
is that we have our three terms : the limiting points of the mag¬ 
nitude to be measured, and a point lying at unit distance from 
the one or the other limiting point. 
The third term, without which measurement is impossible, 
need not, however, be expressed. Suppose that two black strokes 
are made upon a sheet of paper, and that you are asked to say 
how far the one is above the other, or to the right of the other. 
You reply, without difficulty, “Two inches’’ or “Five centi¬ 
metres.” But that means that you have mentally introduced a 
third term : the unit mark, inch or cm., with which you have be¬ 
come familiar in previous measurements. Without this, you 
could only have said : “ The one mark is above the other ” or 
“to the right of the other” ; you could not have answered the 
question “how far.” How long is a given stretch of level road ? 
Two hundred and fifty yards? A quarter of a mile ? Most 
people have no mental unit for such a measurement. Either 
they say “ It looks about as long as from so-and-so to so-and-so,” 
—comparing it with a familiar distance ; or they make a rough 
determination by pacing the distance itself. How deep is this 
well ? Very few people can say, even if they can see the water. 
So a stone is dropped in, and the seconds are counted until the 
splash is heard. The pace or the familiar distance gives a third 
term for the measurement of the road ; and we know that the 
distance traversed by the stone in falling is the product of the 
distance traversed in the first second (about 490 cm.—our third 
term) into the square of the time. Where there is no such third 
term, there is no measurement. This rule is universal. 
§ 2. Mental Measurement.—There can be no question but that,


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