180 
HINTON. 
such a limitation to exist is by means of a material surface 
against which they slide. The existence of this surface could 
only be known to them indirectly. It does not lie in any 
direction from them in which the kinds of motion they know 
of leads them. If it were perfectly smooth and always in 
contact with every material object, there would be no differ¬ 
ence in their relations to it which would direct their atten¬ 
tion to it. 
But if this surface were curved—if it were, say, in the form 
of a vast sphere—the triangles they drew would really be 
triangles of a sphere, and when these triangles are large 
enough the angles diverge from the magnitudes they would 
have for the same lengths of sides if the surface were plane. 
Hence by the measurement of triangles of very great mag¬ 
nitude a plane being might detect a difference from the laws 
of a plane world in his physical world, and so be led to the 
conclusion that there was in reality another dimension to 
space—a third dimension—as well as the two which his or¬ 
dinary experience made him familiar with. 
Now, astronomers have thought it worth while to exam¬ 
ine the measurements of vast triangles drawn from one celes¬ 
tial body to another with a view to determine if there is 
anything like a curvature in our space—that is to say, they 
have tried astronomical measurements to find out if the vast 
solid sheet against which, on the supposition of a fourth di¬ 
mension, everything slides is curved or not. These results 
have been negative. The solid sheet, if it exists, is not 
curved or, being curved, has not a sufficient curvature to 
cause any observable deviation from the theoretical value 
of the angles calculated. 
Hence the examination of the infinitely great leads to no 
decisive criterion. It neither proves nor disproves the ex¬ 
istence of a fourth dimension. 
Coming now to the prosecution of the inquiry in the di¬ 
rection of the infinitely small, we have to state the question 
thus : Our laws of movement are derived from the examina¬ 
tion of bodies which move in three-dimensional space. All 
