68o 



NA TURE 



[May 27, 1922 



of the bisection of a space, I may refer to the results 

 of the recent ecUpse expedition which were supposed 

 to confirm Einstein's theory regarding tlie effect of 

 gravity on Hght. 



According to the account given in the Report 

 (Phil. Trans. A, vol. 220) only one of the sets of eclipse 

 photographs was quite satisfactory, and this was 

 taken by a 4-inch object glass having a focal length 

 of 19 ft. At this distance one-thousandth of an inch 

 would subtend one second of arc nearly, and a 4-inch 

 lens would be just sufficient to separate objects this 

 distance apart. Thus if the lens and photographic 

 plate were perfect, the image of a star would be 

 represented by a circular spot o-ooi in diameter 

 surrounded by one or perhaps two faint rings. In 

 the actual negatives, from irradiation and other 

 causes, the star images were easily visible to the naked 

 eye, and were (speaking from inspection only) about 

 a hundredth of an inch across. 



The object of the photograph was to determine 

 the position of the stars to within a small fraction 

 of i", so that 10 per cent, in the estimate of the 

 bisection of the o-oi inch image would represent an 

 angular error several times as great as the whole 

 deviation of the ray suggested by the theory. 



The image of a star on a gelatine plate is not a 

 sharply defined disc, but a group of dots crowded 

 together towards the centre but more sparsely 

 scattered round the circumference. This is illustrated 

 by Fig. 3, which is the enlargement ( x 300) of the 



direct contact print on a slow " Imperial " plate of 

 a hole 0-0015 in diameter pierced through thin 

 copper foil, and is therefore probably rather more 

 sharply defined than an image formed by a lens. 



Thus the evidence for Einstein's theory (so far as 

 the echpse results are concerned) turns on the question 

 of how much closer than ten per cent, can the bi- 

 section of such an area as the figure shows be esti- 

 mated by the eye. 



What magnification was used in the measuring 

 apparatus is not stated in the Report, but assuming 

 that it was between 20 and 40, Fig. 3 would have 

 to be held between 25 and 50 inches from the eye 

 in order that it should appear of the same size as 



the star image would in the 



measurmg microscope. 



Another matter of some interest is the acuteness 

 with which the senses perceive vertical or horizontal 

 acceleration, or in other words the variation of the 

 intensity and direction of the forces acting on the 

 body. 



In the inquiry into the vibrations caused by trains 

 in the London Tube Railways, it was found that 

 residents in the neighbourhood began to complain 

 .when the vertical movements at the rate of 15 per 

 second amounted to so little as one-thousandth of 



NO. 2743, VOL. 109] 



an inch (amplitude 0-0005), corresponding to a 

 maximum acceleration of ^/i2, but that much 

 smaller accelerations could be felt. Up to a frequency 

 of 40 per sec. or thereabouts, the quicker the vibration 

 the smaller was the amplitude which was perceptible. 

 With frequencies sufficient to give rise to an audible 

 note, the character of the sensation gradually changed. 



Church towers rock when the bells are rung, and 

 on one tower rather celebrated in this respect I 

 measured the maximum horizontal amplitude of 

 t't of an inch, the frequency being rather less than 

 3 per second. The maximum acceleration in this 

 case also was about gliz and produced feelings of 

 sea-sickness in many people. Accelerations of less 

 than a tenth of this amount, however, were quite 

 noticeable. 



I have no notes on the effects of vibrations of long 

 period, but I should expect that any periodic motion 

 which involved an acceleration of ^/20o would not 

 pass unnoticed, if the conditions were favourable 

 and the attention directed to the subject. 



The following are a few examples of the accuracy 

 with which the senses can direct muscular action. 

 In match-rifle shooting sequences of 100 bulls'-eyes 

 (24 inches) at 1000 yards are not unknown. In this 

 case the symmetry of the sight and the target are 

 an assistance in aiming, and since part at any rate 

 of the deviations of the shots are due to wind, etc., 

 the actual ahgnment of the sights cannot be much 

 greater than i in 4000. 



By the assistance of a champion billiard player I 

 found that, in playing at a ball under the cushion 

 from balk, he seldom missed the centre aimed at by 

 more than \ inch. This is equivalent to an accuracy 

 of I in 1000. The trials were made by using a paper 

 disc, backed with carbon-tissue and a hard wood 

 support, as the target, the disc being of the same 

 diameter as a billiard ball. The point of impact was 

 shown by the black dot left by the carbon on the 

 reverse side. 



A good bowler can generally hit a single stump 

 at 22 yards. A cricket ball has, I believe, a diameter 

 of 2f inches, so that taking the thickness of the 

 stump into account the accuracy in this case is about 

 I in 380. 



As regards archery, the best of modern archers ^ 

 will scarcely keep his arrows within a 3-ft. circle 

 at 100 yards. If he did the accuracy would be 

 I in 200. 



For a game-shot who can bring down 75 per cent, 

 of his birds at 40 yards, the implied accuracy of aim 

 is about I in 70. 



In all these cases the attention is concentrated on 

 a field of only a few degrees, and the effect of the 

 restriction of the field on the accuracy of the estima- 

 tion of the position of objects within it is worthy of 

 more investigation than it has yet received. 



In judging the qualities of the instrument with 

 which measures are made, a distinction should be 

 drawn between accuracy or resolving power and 

 definition. The accuracy with which a weight can 

 be determined by a balance, or a resistance by a 

 W^heatstone bridge, is greater than one part in a 

 million, but the definition is, for the balance, the 

 length of the arc in which it can swing compared to 

 the least angular motion which gives a trustworthy 

 indication, and, for the bridge, the length of the 

 resistance wire on which contact is made compared 

 with the least variation of the position of contact 



^ How old is the legend of the pole, string, and bird, as a test of an archer's 

 skill ? Tom Sawyer, it may be remembered, improved on this, saying that 

 Robin Hood " would take his yew bow and plug a ten cent piece every 

 time — mile and a half." In Joshua .xx. i6 there is a reference to seven 

 hundred left-handed men of Benjamin. "Every man could sling stones 

 at a hair's-breadth and not miss." This, I think, is the only Biblicil refer- 

 ence to accuracy of marksmanship. 



