without the Equivalence Hypothesis. 95 



present paper. And its scope will be a limited one, viz. to 

 treat only some chief aspects of the physical implications of 

 the Principle and to illustrate them to a certain extent, but 

 by no means to try to embrace in a few generally coyariant 

 formulae all the marvels of Nature. The strength of the 

 " strong " point is indisputable and does not call for lengthy 

 remarks ; it amounts, in its ultimate analysis, to claiming 

 that real, phenomenal, contents should be expressed, or 

 expressible at least, in a way showing their independence of 

 the particular language or scaffolding adopted. The weak- 

 ness of the " weak " point, however, does require some 

 explanations. First of all, then, independently of agreement 

 or disagreement with experimental facts, the equivalence 

 hypothesis is a vulnerable point because of its very special 

 nature and of the great number of assumptions which 

 it tacitly implies. In the next place, however, serious 

 doubts with regard to its acceptability arise, according to 

 my opinion, from the obstinately negative results quite 

 recently obtained by St. John at the Mount Wilson Obser- 

 vatory *. The mean displacement (which according to 

 Einstein should be about t Jq A.U. towards the red) is at 

 the sun's centre for 25 lines — *001, and for 18 lines 

 + •0014 A.U., with a mean of zero for the 43 lines in the 

 band spectrum of nitrogen (cyanogen) ; again, the mean 

 displacement at the limb is 0*000 for 17 lines, and -f- 0'0063 

 for 18 lines, with a mean of +'0018 for the 35 lines. The 

 final conclusion is that " within the limits of error there is 

 no evidence of a displacement to longer wave-length, either 

 at the centre or at the limb of the sun, of the order *008 A." 

 (loc. cit. p. 265). This negative result certainly outweighs 

 the much more dubious and less numerous figures quoted in 

 1914 by E. Freundlich (Phys. Ztschr. xv. p. 370) in favour 

 of Einstein's prediction. As a matter of fact, Einstein him- 

 self, while mentioning Freundlich's star-spectra testimony, 

 is of the opinion that "a final verification is still [1916] 

 outstanding" [Ann. d. Physik, xlix. p. 820). Notice al<o 

 that the masses of Freundlich's stars can only be guessed in a 

 rough manner while our sun's mass is sufficiently well known 

 (M/c 2 =l*5 km.) to be substituted into Einstein's shift for- 

 mula. Whence the obvious superiority of St. John's results. 

 It is well-known that the predicted shift was one of the most 

 immediate consequences of the equivalence hypothesis, even 

 in its original form of 1911 ; in Einstein's recent theory 



* Charles E. St. John, "The Principle of general Relativity and the 

 Displacement of Fraimhofer Lines, etc.," Astrophys. Journ. xlvi., Nov. 

 1917, p. 249. 



