DETERMINATION OF DEFLECTION OF LIGHT BY THE SUN'S GRAVITATIONAL FIELD. 329 



errors. What ground then have we apart from the agreement with the far superior 

 determination with the 4-inch lens at Sobral for thinking that the present results are 

 more trustworthy ? 



At first sight everything is in favour of the Sobral astrographic plates. There are 

 12 stars shown against 5, and the images though far from perfect are probably superior 

 to the Principe images. The multiplicity of plates is less important, since it is mainly 

 a question of systematic error. Against this must be set the fact that the five stars shown 

 on Plates W and X include all the most essential stars ; stars 3 and 5 give the extreme 

 range of deflection, and there is no great gain in including extra stars which play a 

 passive part. Further, the gain of nearly two extra magnitudes at Sobral must have 

 meant over-exposure for the brighter stars, which happen to be the really important 

 ones ; and this would tend to accentuate systematic errors, whilst rendering the defects 

 of the images less easily recognised by the measurer. Perhaps, therefore, the cloud 

 was not so unkind to us after all. 



Another important difference is made by the use of the extraneous determination of 

 scale for the Principe reductions. Granting its validity, it reduces very considerably 

 both accidental and systematic errors. The weight of the determination from the five 

 stars with known scale is more than 50 per cent, greater than the weight from the 12 

 stars with unknown scale. Its effect as regards systematic error may be seen as follows. 

 Knowing- the scale, the greatest relative deflection to be measured amounts to l"-2 on 

 EINSTEIN'S theory ; but if the scale is unknown and must be eliminated, this is reduced 

 to "67. As we wish to distinguish between the hill deflection and the half deflection. 

 we must take half these quantities. Evidently with poor images it is much more 

 hopeful to look for a difference of 0"-6 than for 0"-3. It is, of course, impossible to 

 assign any precise limit to the possible systematic error in interpretation of the images 

 by the measurer ; but we feel fairly confident that the former figure is well outside 

 possibility. 



A check against systematic error in our discussion is provided by the check plates, as 

 already shown. Its efficacy depends on the similarity of the images on the check plates 

 and eclipse plates at Principe. Both sets are fainter than the Oxford images with which 

 they are compared, the former owing to the imperfect driving of the ccelostat, which 

 made it impossible to secure longer exposures, the latter owing to cloud. Both sets have 

 a faint wing in declination, but this is separated by a slight gap from the true images, 

 and, at least on the plates measured, the wing can be distinguished and ignored. 

 The images on Plates W and X are not unduly diffused except for No. 10 on Plate W. 

 Difference in quality between the eclipse images and the Principe check images is not 

 noticeable, and is certainly far less than the difference between the latter and the Oxford 

 images ; and, seeing that the latter comparison gives no systematic error in y, it 

 seems fair to assume that the comparison of the eclipse plates is free from systematic 

 error. 



The writer must confess to a change of view with regard to the desirability of using 



