i 3 6 GRAVITATION— THE LAW 



call (rather loosely) the extended geometry Euclidean; 

 or, if it is necessary to emphasise the distinction, we 

 call it hyperbolic geometry. The term non-Euclidean 

 geometry refers to a more profound change, viz. that 

 involved in the curvature of space and time by which 

 we now represent the phenomenon of gravitation. We 

 start with Euclidean geometry of space, and modify it 

 in a comparatively simple manner when the time-dimen- 

 sion is added; but that still leaves gravitation to be 

 reckoned with, and wherever gravitational effects are 

 observable it is an indication that the extended Euclidean 

 geometry is not quite exact, and the true geometry is a 

 non-Euclidean one — appropriate to a curved region as 

 Euclidean geometry is to a flat region. 



Geometry and Mechanics. The point that deserves special 

 attention is that the proposition about time-triangles is 

 a statement as to the behaviour of clocks moving with 

 different velocities. We have usually regarded the 

 behaviour of clocks as coming under the science of 

 mechanics. We found that it was impossible to confine 

 geometry to space alone, and we had to let it expand a 

 little. It has expanded with a vengeance and taken a 

 big slice out of mechanics. There is no stopping it, and 

 bit by bit geometry has now swallowed up the whole of 

 mechanics. It has also made some tentative nibbles at 

 electromagnetism. An ideal shines in front of us, far 

 ahead perhaps but irresistible, that the whole of our 

 knowledge of the physical world may be unified into a 

 single science which will perhaps be expressed in terms 

 of geometrical or quasi-geometrical conceptions. Why 

 not? All the knowledge is derived from measurements 

 made with various instruments. The instruments used 

 in the different fields of inquiry are not fundamentally 



