204 Science Religion and Reality 



at the end than he did at the beginning. That does not matter. 

 He is asked to keep his attention fixed on the form of the explana- 

 tion rather than on the substance of the explanation ; we want to 

 indicate to him the train of ideas that he would have to exhaust if 

 he wished to get to the bottom of the significance of the new law. 



Einstein's law of gravitation is a statement that in empty space 

 ten quantities called potentials satisfy certain rather lengthy mathe- 

 matical equations which can be exactly specified. (The term 

 " potential " will be explained presently.) In other words, 

 whereas we might conceive a world in which the potentials at every 

 moment and at every place had entirely arbitrary values, the actual 

 world around us is not so unlimited. The statement that actual 

 phenomena are more limited in variety than imaginable phenomena 

 is evidently equivalent to the statement that the actual world is 

 governed by a law. The next question is. What are the " poten- 

 tials " which are governed by the law that has been specified .? 

 They are derived by simple mathematical calculations from certain 

 other quantities called intervals. If we know the values of the 

 various intervals through the world we can at once find the poten- 

 tials. What are these " intervals " ? They are relations between 

 pairs of events which are measured by a scale or clock. Instruc- 

 tions can be given describing exactly how the scale and clock are 

 to be employed, and the interval is merely the scale-reading or 

 clock-reading or a particular combination of the two readings. 

 Next question, What are " scales " and " clocks " ? It would 

 take a somewhat long description to prescribe exactly what con- 

 stitutes a perfect Scale or clock referred to here, but with patience 

 all the requirements can be stated ; we should, however, find it 

 necessary to introduce a new word which ought to be carefully 

 explained — the scales and clocks are made of matter. Next ques- 

 tion. What is " matter " ? That has often been asked, with 

 many diverse answers ; but here the answer is not so difficult. 

 Metaphysical properties of substantiality have no bearing on the 

 efficiency of a clock as an instrument of measurement, it is only the 

 mechanical properties of matter which concern us here ; and, so 

 far as mechanics is concerned, matter is merely the embodiment of 

 three measurable entities, mass, momentum, and stress. What are 

 " mass," " momentum," and " stress " ? It is one of the remark- 

 able (though comparatively little known) achievements of Einstein's 

 theory that it has succeeded in describing exactly what these are. 



