324 TRANSACTIONS OF THE CANADIAN INSTITUTE. [Vov. VIII. 
stars, once according to apparent magnitudes and another time according 
to physical intensities, a striking example of a psychological experiment 
according to the method of mean or multiple gradations, though the ob- 
servation was made two thousand years ago in the time of Hipparchus, 
while we have only lately succeeded in measuring the physical stimulus? 
But, it might be said, just the fact that the measurement of the physical 
stimulus has another result than that of the psychical impression proves 
that there is a difference between physical and psychical intensities. But 
what is the physical intensity here? It is something not intensive. It is 
either (1) the angular width of an obscuring sector (a rotating disc) (2) 
or the turning angle of a Nicol prism, (3) or the thickness of an absorbing 
medium, (4) or a number indicating how many candles would give the 
same intensity, (5) or some other device to express intensity by some special 
or numerical equivalent. Thus we must come to the conclusion that what 
is called physical or objective intensity is either something not different 
from the subjective or psychical intensity or else it is not intensity at all. 
Having thus seen that a valid distinction between physical and psy- 
chical intensities cannot be drawn, our problem must necessarily read: can 
intensive magnitudes be measured? And _ this question must be uncon- 
ditionally answered in the affirmative. Science has for centuries succeeded 
in measuring intensive magnitudes, though we cannot admit that they 
were physical and objective. We measure pressure, electricity, heat, 
light, gravity, and other attracting and repulsing forces. But in every 
case we find on closer analysis, first, that the quantities measured are in 
the last instance psychical (intensities of light, pressure, effort, etc). 
Secondly, that all our measurement rests finally on the decision whether, 
(a) two intensive magnitudes are equal or not, or (b) whether or not 
the difference between the two intensive magnitudes is equal or not to the 
difference between two other intensive magnitudes. 
This is even so in the case of extensive i.e., spacial measurement. 
In fact if on the basis of the theoretical attainments of modern mathematics, 
and the experimental attainments of modern psychology, the question 
of the measurement of intensive or psychcal magnitudes is raised 
again, the tables will be turned and the question will then read: do we 
ever measure anything but intensive and psychical magnitudes? And 
further is extension, space, in first line magnitude, quantity? Let us test 
in the following, this radical reversal of the problem. 
First, there is no reason why the spacial properties of sensation 
should be regarded as less psychical and more physical than their intensity. 
No one who has studied Kant and has kept in touch with the results of 
