DETERMINATION OF DEFLECTION OF LIC4HT BY THE SUN’S GRAVITATIONAL FIELD. 329 
errors. ^VTiat ground then have we—apart from the agreement with the far superior 
determination ^vith the 4-inch lens at Sobral—for thinldng 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, wliich 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 1"*2 on 
Einstein’s theory ; but if the scale is unknown and must be eliminated, this is reduced 
to 0 • 67. As we wish to distinguish between the full 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 ovdng to the imperfect driving of the coelostat, 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 
