174 Prof. Eddingten : Significance of Einstein s Gravitational 



effects are due to contaminations, chiefly by oxidation, of the 

 surfaces of the tungsten filament and the copper anode. 

 The extreme variations which have been observed for the 

 position of the voltage at which the current attained half 

 the saturation value are — 211 and +0"17 ; the corre- 

 sponding curves are shown in fig. 7. This corresponds to a 

 total change in the contact potential difference of 2'28 

 volts. tine extreme displacements in the positive direction 

 along the voltage axis, such as that with the half saturation 

 value at +'17 in fig. 7, were obtained when the tube had 

 been well baked out and the tungsten filament had been 

 intentionally oxidized by glowing in air at a low pressure 

 with the tube cold before testing. The evidence seems clear 

 that an oxidized filament is electropositive by about 0*6 volt 

 as compared with a clean filament at these temperatures. 



When the filaments were oxidized the currents were found 

 to be difficult to saturate. This is shown by the upward 

 slope of the relatively flat part of the curve on the right in 

 fig. 7. There see jus to be no doubt that this upward slope 

 is due to the oxidized conditions of the tungsten surface. 

 On glowing out the tungsten at a high temperature so as to 

 cause the layer of oxide to evaporate, curves such as B fig. 7 

 were obtained. These are displaced about 0*6 volt to the 

 left, corresponding to the more electronegative character of 

 the clean tungsten, and at the same time the upward slope of 

 the saturation part is found gradually to disappear. 



XV. On the significance of Einstein 7 s Gravitational Equations 

 in terms of the Curvature of the World. By A. S. 

 Eddington, M.A.) FM.S., Plumian Professor of Astro- 

 nomy in the University of Cambridge *. 



IN the Appendix to the paper on " The Relativity of Field 

 and Matter " t, I gave a proof of the theorem that 

 Einstein's equations G fLV = \g lJLV express the condition that the 

 radius of curvature of sections of the world is the same at all 

 points and for all directions. I have since found that this 

 proof is not sufficiently general. I took too limited a view 

 of the vagaries of which a four-dimensional surface is 

 capable when it has six extra dimensions to twist about in. 

 I assumed that, although ten dimensions of Euclidean space 

 are necessary for the representation of a four-dimensional 

 Biemannian space, a small portion of the latter near the 



* Communicated by the Author. 

 t Phil'. Mag. November 1921, p. 800. 



