A NEW LAW OF GRAVITATION 121 



general law covers an infinite number of special cases. 

 The vanishing of the ten principal coefficients occurs 

 everywhere in empty space whether there is one gravi- 

 tating body or many. The other ten coefficients vary 

 according to the special case under discussion. This may 

 remind us that after reaching Einstein's law of gravi- 

 tation and formulating it mathematically, it is still a very 

 long step to reach its application to even the simplest 

 practical problem. However, by this time many hun- 

 dreds of readers must have gone carefully through the 

 mathematics; so we may rest assured that there has 

 been no mistake. After this work has been done it 

 becomes possible to verify that the law agrees with 

 observation. It is found that it agrees with Newton's 

 law to a very close approximation so that the main 

 evidence for Einstein's law is the same as the evidence 

 for Newton's law; but there are three crucial astro- 

 nomical phenomena in which the difference is large 

 enough to be observed. In these phenomena the obser- 

 vations support Einstein's law against Newton's.* 



It is essential to our faith in a theory that its predic- 

 tions should accord with observation, unless a reasonable 

 explanation of the discrepancy is forthcoming; so that 

 it is highly important that Einstein's law should have 

 survived these delicate astronomical tests in which New- 

 ton's law just failed. But our main reason for reject- 

 ing Newton's law is not its imperfect accuracy as shown 

 by these tests; it is because it does not contain the 

 kind of information about Nature that we want to 

 know now that we have an ideal before us which was 

 not in Newton's mind at all. We can put it this way. 



* One of the tests — a shift of the spectral lines to the red in the sun 

 and stars as compared with terrestrial sources — is a test of Einstein's 

 theory rather than of his law. 



