Oct. 31, 1889] 



NATURE 



649 



in the testing of the chromatic aberration of objectives, 

 by those whose eye experiences cannot be a sufficiently 

 accurate guide, to allow the image of a star, as found by 

 the objective, to fall on the slit of a spectroscope, and to 

 judge of the focus of each particular ray by the breadth 

 of the spectrum at that ray. Wherever the light is brought 

 to a focus the spectrum is of insensible breadth. When 

 it is out of focus, a more or less sensible breadth, by 

 moving the spectroscope in and out of the position of 

 maximum and minimum foci, can be obtained. 



I tried this plan, but found it very unsatisfactory, as it 

 was very difficult to determine the exact place where the 

 spectrum was narrowest, the curves being so very shallow. 

 After much thought I arrived at the following very 

 simple and efficient plan, which I described in full, as it 

 may be useful to some for other purposes. It should be 

 remembered that the object is to get the focus of the 

 objective for various parts of the spectrum. 



If, therefore, we could obtain various objects when 

 light was derived for such portions, and such portions 

 only, of the spectrum as we required, our object would be 

 accomplished. 



I take a spectroscope with a fairly large dispersion 

 ■equal to about 2 prisms of 60° and with a pencil of light 

 of about 2° diameter. I remove the observing telescope, 

 and substitute one of very long focus, so that the linear 

 dimensions of the spectrum shall be as large as possible. 

 I observe with this the solar spectrum, and note the 

 position of such lines as I intend to work on. I then re- 

 move the eye-piece and insert in its place a tube carrying 

 a small convex mirror. The apparatus is left till dark, 

 and a small electric glass lamp attached outside the slit. 

 The observing telescope is then placed at such a reading 

 as I know will bring any certain line into the centre of the 

 field, and on looking at the small mirror through a long slit 

 which is purposely made on the top of the tube to allow 

 it to be viewed from the front, you see a small bright star 

 whose light is due to that particular line in the spectrum, 

 and to no other part. The apparatus is placed at a suffi- 

 cient distance in front of the photographic telescope, and 

 these stars are the objects examined. In this way I can 

 produce a small bright star of a colour corresponding to 

 any of the lines in the spectrum, and the foci of these, as 

 observed in the photographic telescope, can be measured 

 with great exactitude. 



There are, of course, small matters of detail which I 

 have been unable to touch upon in the present commu- 

 nication, many of which are very important for the effec- 

 tive working of these instruments, and which require 

 special treatment. I have, however, confined myself to 

 the principal and more important parts, but I trust that I 

 have been able to show that we have at least made a sub- 

 stantial advance ; and it remains for us to hope that when 

 these instruments are placed in the hands of astronomers 

 they may yield a rich harvest of work, and leave their 

 mark on the history of astronomical science. 



Howard Grubb. 



ON THE PRINCIPLE AND METHODS OF 



ASSIGNING MARKS FOR BODIL V 



EFFICIENCY.^ 



'X'HE question to be solved is of this kind. Suppose 

 -*■ that one man can just distinguish a minute test 

 object at the distance of 25 inches, another at that of 35, 

 and again another at 45 inches, how should we mark 

 them ? We should be very rash if we marked them in 

 the proportion of 25, 35, and 45, or even if, for some good 

 reason, we had selected 25 as the lowest limit from which 

 marks should begin to count, we should mark them as o, 

 10, and 20. 



' Read at the British Association, by Francis Gallon, F.R.S. ; but slightly 

 revised, in order to introduce the diagrams herewith printed. Followed by 

 remarks on experiments made at Eton College, by A. A. Somerville. 



Two separate considerations are concerned in the just 

 determination of a scale of marks — namely, absolute per- 

 formance and relative rank, which are apt to be confused 

 in unknown and varying proportions. 



Absolute performance is such as is expressed by the 25, 

 35, and 45 inches just spoken of. It is perfectly correct 

 in some cases to mark, or let us say to pay, for this, and 

 this alone, upon the principle of piece-work — namely, 

 that the pay ought to be proportionate to the work 

 accomplished, or to the expected output in after life. 



Relative rank is, however, on the whole, a more im- 

 portant consideration than the absolute amount of per- 

 formance by which that rank is obtained. It has an im- 

 portance of its own, because the conditions of Hfe are 

 those of continual competition, in which the man who is 

 relatively strong will always achieve success, while the 

 relatively weak will fail. The absolute difference between 

 their powers matters little. The strongest even by a trifle 

 will win the prize as completely as if he had been 

 strongest by a large excess. Undertakings where many 

 have failed, are accomplished at last by one who usually 

 is very little superior to his predecessors, but it is to just 

 that small increment of absolute superiority that his suc- 

 cess is due. Therefore it is clear that relative rank has at 

 least as strong a claim for recognition as absolute per- 

 formance, if not a much stronger one. They have each 

 to be taken into separate consideration, and each to be 

 separately marked. The precise meaning intended to be 

 conveyed by the phrase " relative rank " will be better 

 understood further on. 



Recurring to the example of keenness of eyesight, let 

 the test object be words printed in diamond type, and the 

 persons tested be Englishmen of the middle classes, be- 

 tween the ages of 23 and 26, then the performance of read- 

 tng diamond type at 25 inches happens to be strictly 

 mediocre. Fifty per cent, of the many persons who were 

 tested performed better than this, and 50 per cent, per- 

 formed worse. The 35-inch performance was exceeded 

 by only 2j per cent, of the persons tested ; and as to the 

 45-inch performance, it has not in my experience been 

 reached at all. I have had altogether 12,000 persons 

 tested in this way, of both sexes and of various ages, but 

 not one of them has succeeded in reading diamond type 

 at the distance of 45 inches. It is very rare to find one 

 who can do so at 40 inches. Wherever superiority in 

 eyesight is eminently desirable, it would be absurd to 

 make the marks for the three supposed cases to run pro- 

 portionately either to 25, 35, and 45, or to o, 10, and 20. 

 The achievement of 45 inches would deserve much higher 

 recognition. Relative rank and absolute performance 

 should not be confused together. 



I use the term relative rank in a large sense, with refer- 

 ence to all persons who have been, or are likely to be- 

 come, candidates, and not to the small number of them 

 who may happen to be present at a particular examina- 

 tion. Statistical tables concerning the class of persons in 

 question have to be compiled from past examinations, 

 and the rank of the individual has to be determined 

 amidst these. I have often described how this is to be 

 done (" Natural Inheritance," p. 38, Macmillan and Co., 

 1889), but the diagram (Fig. i) is, I think, the simplest of 

 all forms for the use of an examiner. It tells at a glance 

 the rank held by a man among his fellows in respect to 

 any single and separate faculty. The class from which 

 it is constructed might consist of any large number of 

 persons subject only to the condition that the distance 

 between the limits within which it extends shall be 

 always divided into centesimal grades ; that is to say, 

 running from 0° to 100°. The grades are printed along 

 both the top and the bottom of the diagram, and refer 

 alike to every line. As a specimen of the way to read it, 

 let us take the line of keenness of eyesight among the 

 males. Here we see that the performance of reading 

 diamond type at the distance of 25 inches is . appropriate 



