THE RECOGNITION OF THE FOURTH DIMENSION. 
BY 
0. H. Hinton. 
[Read before the Society November 9, 1901.] 
There are two directions of inquiry in which the research 
for the pl^sical reality of a fourth dimension can be prose¬ 
cuted. One is the investigation of the infinitely great, the 
other is the investigation of the infinitely small. 
By the measurement of the angles of vast triangles whose 
sides are the distances between the stars astronomers have 
sought to determine if there is any deviation from the values 
given by geometrical deduction. If the angles of a celestial 
triangle do not together equal two right angles, there would 
be an evidence for the physical reality of a fourth dimen¬ 
sion. 
This conclusion deserves a word of explanation. If space 
is really four dimensional, certain conclusions follow which 
must be brought clearly into evidence if we are to frame the 
questions definitely which we put to Nature. If space is 
four dimensional, there must be a solid material sheet against 
which we move. This sheet must stretch alongside every 
object in every direction in which it visibly^ moves. Every 
material body must slip or slide along this sheet, not deviat¬ 
ing from contact with it in any motion which we can observe. 
The necessity for this assumption is clearly apparent if 
we consider the analogous case of a suppositionary plane 
world. If there were any creatures whose experience were 
confined to a plane, we must account for their limitation. If 
they were free to move in every space direction, they would 
have a three-dimensional motion; hence they must be phys¬ 
ically limited, and the only way in which we can conceive 
26—Bull. Phil. Soe., Wash., Vol. 14. 
(179) 
