3i8 



NA TURE 



\Augtist I, 1889 



inches, each measurement is open to an error of from i"3 to 2"o 

 per cent. 



The product of these three is found, and is supposed propor- 

 tional to the cranial capacity. That this is most imperfectly so 

 in individuals is manifest ; but the author hopes that in the 

 average of a large number of cases the effect of the extreme 

 variability of shape of the head may be obliterated. He there- 

 fore tabulates the products, using the first decimal place, i.e. up 

 to four significant figures. Since the original measurements only 

 included two figures, the last two of the four must be inaccurate. 

 The product is open to an error of 3 or 4 or even up to 6 per 

 cent. Since the probable error is from 3 to 6 per cent., which 

 is nearly the same size as the difference between the " honour" 

 qian's and "poll" man's heads, and also the difference supposed 

 to be due to growth, I therefore hold that there is no evidence 

 for any of the author's conclusions. 



I have recently had a better opportunity of judging the value 

 of the statistics, for two of my friends, who have been several 

 times measured, have kindly shown me the results. 



From the above table it will be seen that (i) in the measure- 

 ments of the same individual taken at different times the width 

 may vary o-i inch ; (2) the Itngth may vary 0-2 inch ; (3) the 

 height may vary 0-4 inch ; (4) the above variations are not due 

 to head growth, for they are as often negative as positive. 



As anyone would expect who had seen the instrument used, 

 the height measurement is most unsatisfactory. The error of 

 o"4 inch is not an isolated case. Yesterday another friend of 

 mine, who was measured for the second time, found that his 

 height of head had apparently decreased 0-5 inch. 



The products are seen to vary in the first case from 236-7 to 

 250-1, nearly 6 per cent. So far are the figures capable of 

 affording good evidence of head growth of either individual, they 

 are so inaccurate as not to make certain whether X. or Y. had the 

 bigger head. It is quite evident that numbers, each open to an 

 error of 5 or 6 per cent., cannot, when combined into averages, 

 teach us anything about differences as minute as 3 per cent. 



Trinity College, Cambridge, July 16, F. M. T. 



The errors made m measuring the height of the head are cer- 

 tainly much larger in the instance given by " F. M. T." than 

 they should be ; still they do not seem to me large enough to 

 throw doubt on the truth of the general conclusions to which 

 he refers. (i) As regards the difference between the means of 

 the " products " in the high honour and the poll men. Those 

 means are 224 and 237, and they depend on 258 and 361 ob- 

 servations respectively, which numbers are much the same as 

 l6'^ and 19-. Therefore the probable error in the determination 

 of each of thesernieans will be equal to the probable error of a 

 single "product" divided by 16 in the one case and by 19 in 

 the other. I have as yet no data to determine the probable error 

 of a single "product," due to faults of measurement alone, 

 other than those given by " F. M. T.," which suggest, though in 

 the rudest way, lliat it is about 4 units. Accepting this for the 

 moment as a basis, the probable error of the means of the two 

 sets of "products" would be 4 divided by 16 and by 19, equal, 

 say, to \ and \ respectively. Now, the chance of an error ex- 

 ceeding 4 or 5 times the probable error is not worth regarding ; 

 therefore safety, so far as regards the effects of inaccuracy of 

 measurement, is practically to be found in each mean value 

 beyond a range of about i unit. In the differences between the 

 mean measures, safety will be found beyond the range ^2, say 



\\ units. But the two means 224 and 237 differ by as much as 

 7 uiiits. It should, however, be remarked that the seven obser- 

 vations fall into two well-marked groups, each of which is very 

 consistent within itstlf, but which differ from one another by 10 

 units. This raises strong suspicion of some peculiarity in the 

 shape of the head, which caused doubt as to the exact line oF 

 maximum height, and that one line was followed in three of the 

 measurements and another line in the remaining four. (2) As re- 

 gards the differences between the high honour and the poll men at 

 different ages, the observations at each stage are, of course, much 

 less numerous than in the sum of all of them, still they range in 

 all cases but two between 25 (or 5-) and 102 (or say lo'-). Each 

 person must judge for himself, frcm the diagram that accom- 

 panied my little paper, how far the run of those differences con- 

 firms my conclusions. 1 think they do well enough to give " an 

 approxima'ely true " idea of what we should find if we had the 

 opportunity of discussing a much larger number of observations, 

 and this was all that I claimed. 



The remarks of " F. M. T. " lead to two useful deductions. 

 One is the desirability of checking, as. soon as may be, the 

 conclusions already reached, by discussing the observations that 

 have since accumulated. The other is to improve, if possible, 

 the method of measuring the height of head. The existing plan 

 was adopted, after consultation with many competent persons, 

 and many trials, as the best then available for making this very 

 difficult measurement. I have, however, never ventured to 

 introduce its use in my laboratory at South Kensington. 



Francis Galton. 



Intermittent Sensations. 



In a short notice in Nature ofMay23(p. 86), calling attention 

 to theintermittence of the intensity of some sensations, and more 

 particularly to the experience of M. Couetoux as reported in the 

 Kcznie Scunlijiqtie, the writer very properly remarks, that these 

 sensorial fluctuations deserve more thorough study. It may 

 interest him, therefore, to learn that the interrupted sensibility 

 of the retina can be easily demonstrated, to anyone possessed 

 of binocular vision. 



Some years ago, on converging the eyes, so as to fuse the 

 images of two squares, each square being composed of parallel 

 lines I mm. broad with an equal interval between them, and the 

 lines in one squaie being perpendicular to those of the others, I 

 was astonished to find that instead of squares, which ought to 

 have resulted from the perfect fusion of the two images, the field 

 was occupied by a series of zig-zags, composed of portions of 

 straight lines of each square, passing across the field sometimes 

 from right to left, sometimes the contrary way, and too com- 

 plex and transitory to admit of analysis. 



Since your notice, while experimenting with my students with 

 a stereoscope, we have obtained the same result in every case. 

 But, in order to determine the rateof intermiltence, the attention 

 was fixed on a small mark made in the centre of one of the 

 squares. 



This mark was found, on an average of a number of experi- 

 ments by different individuals, to be visible, with its accom- 

 1 anying lines, for from 6 to 8 seconds, and then completely 

 extinguished ; and the lines of the other square, appearing for 

 an equal interval of time, thus completed the cycle of activity 

 and rest in from 12 to 16 seconds. 



On covering the eye not directed to the mark, this point was 

 never entirely lost sight of, but went through a series of changes 

 of brightness and degradation of the sensorial imiiression, corre- 

 sponding in time with those of the previous experiment. 



These experiments seem to show that the impression is not 

 equally intense, at the same instant, over the surface of each 

 retina, but occupies successive areas, in somewhat irregular 

 patches, which appear to be supplemented by the other retina 

 in binocular vision It is probably due to this that the imper- 

 fect images of objects formed on the retina are corrected, and 

 our perceptions made more accurate than they would be if our 

 sensaticn.s were not intermittent. THOMAS Riill». 



II Flmbank Street, Glasgow. 



The Aurora. 



The aurora in the Unites States is rarely seen at a single 

 station for two nights in succession, but is usually reported from 

 different stations fcr about four days at each manifestation. 

 Recurrence at intervals of nearly twenty-six days is common. 



