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MR. JOHN MURRAY has published the nineteenth edition of metres in length and 1-2 mm. thick. Another method which ** The Reign of Law," by the Duke of Argyll.
yielded very beautiful crystals of this modification consisted in allowThe Amateur Photographer has issued its fourth “home ing a solution of acid potassium sulphate to slowly diffuse in to a frortraiture number.” It reproduces one photograph each from solution of sodium thiosulphate. In about four weeks'time, perfect the work contributed by sixty competitors for prizes.
crystals, almost white in appearance, and exhibiting strongly the
mother-of-pearl lustre, were obtained. This third variety of In the Report of the U.S. Commissioner of Education for sulphur also crystallizes in the monoclinic system. The ratio of the year 1887-88 it is stated that 48 educational institutions in its axes is a:0:= 1'0609: 1:0*7094. The axial angle B = the United States receive the benefit of the national land grant 88° 13'. The symmetry plane, b = (oro) o Roo, is so largely of 1862. Among these institutions are the Arkansas Industrial developed as to give the crystals the appearance of plates. At l'niversity, the State Agricultural College at Colorado, the the edges of the plates the two primary pyramids (111) - Pand Slaine State College of Agriculture and the Mechanic Arts, the (111)+P, a prism (210) 60 P2, and a clinodome (012)Poo are Massachusetts Institute of Technology, the Missouri School of well developed. These crystals are totally distinct from those Mines and Metallurgy, and the Scientific School of Rutgers of the second modification ; the axial ratios of the latter are College. In 38 of the Colleges an officer of the Army or Navy a:0:c=0'9957:1;09998 and B = 84° 14'. Upon the sides of
detailed to act as professor of military science and tactics. the vessel containing the alcoholic ammonium sulphide solution If a State has more than one school endowed by the national prepared as above, Dr. Muthmann noticed carious tabular crysland grant of 1862, the school which is reported by the tals of hexagonal section, which immediately became altered Governor of the State as most nearly meeting the requirements upon contact with a disturbing body, such as a platinum wireorglass of existing law is held to have the first claim to the officer rod. They were likewise found to consist of pure sulphur, and, allotted to the State.
on optical and goniometrical examination, were found to consist M. A. Angor, of the French Meteorological Ofice, has of a distinct fourth modification, also monoclinic. They greatly published in the Annales of that office a very careful discussion resemble a rhombohedron with predominating basal plane. of the diurnal range of the barometer, based upon the best They are best obtained by allowing to slowly evaporate in a tall railable data for all parts of the globe. After having given the cylinder a saturated solution of sulphur in alcoholic ammonium meaa range for each month and for the year, he has calculated sulphide diluted with four times its volume of alcohol. The the amplitudes and phases of the first four simple harmonic temperature during this crystallization must not exceed scillations into which the complex oscillation of the barometric 14° C. Occasionally in this experiment all four forms of sulphur sliuraal range may be resolved, and which may be considered as are obtained ; the surface is covered with crystals of the third the resultant of the superposition of two waves of different origin variety, tables of the fourth modification are deposited upon the sad character. One of these, which the author terms the sides, and the base of the cylinder is spangled with rhombic thermic wave, is of a more or less complicated form in appear; form. If crystals of the third variety are suspended in their
pyramids interspersed with monoclinic needles of the second ance, and is easily explained as being produced by the diurnal variation of temperature and by the differences that this variation mother liquors and left for some days, they are converted into a presents between neighbouring stations. The other, the principal voluminous mass of minute rhombic pyramids. The conversion Semi-diurnal wave, for which he has given the numerical law, into the more stable rhombic form is almost instantaneous if a presents a much more simple form, and is not at all affected by rhombic crystal be dropped into the liquid containing suspended local conditions. It is possibly produced by the calorific action third variety crystals. The immediate alteration of crystals of of the sun upon the upper strata of the atmosphere ; but, as the
the fourth kind is even more remarkable, the mere movement of author states, this is still only an hypothesis, and the theory of the cover-glass, when examining them under the microscope, this part of the phenomenon remains to be established. His being sufficient to instantly change the optical properties to cunclasions upon the effect of the thermic wave are very interest those of the rhombic form. It is interesting that this fourth ing, and the whole discussion will well repay a careful study.
form of sulphur is isomorphous with the form of selenium
obtained by evaporation of a hot saturated solution in carbon M., T. W. BAKER writes to us that, in his note regarding bisulphide. the meteor of March 3, he omitted to state the time of its appearance, which was 7.28 p.m.
The additions to the Zoological Society's Gardens during the
past week include two Badgers (Meles taxus) from Ireland, Ax important paper upon the crystalline allotropic forms of presented by Mr. P. Bicknell ; a Grey Hypocolius (Hypocolius zalphur and selenium is contributed by Dr. Muthmann, of ampelinus 3) from Scinde, presented by Mr. W. D. Cumming ;. Munich, to the latest number of the Zeitschrift für Krystallogra a Rhesus Monkey (Macacus rhesus 8) from India, a Spotted fivce. Resides the well-known rhombic pyramids and monoclinic Ichneumon (Herpestes nepalensis) from Nepal, deposited ; an Jurisms, sulphur may, under certain conditions, be obtained in Axis Deer (Cervus axis), born in the Gardens. a third crystalline modification, which has been termed by Lernez "zvufre nacrt.” This third modification has been fully investigated by Dr. Muthmann, and, in addition, a new fourth
OUR ASTRONOMICAL COLUMN. tutally distinct variety has been discovered. The third form is best obtained by boiling about five grams of powdered sulphur
OBJECTS FOR THE SPECTROSCOPE, with 750 C.C. of absolute alcohol in a flask provided with an
Sidereal Time at Greenwich at 10 p.m. on March 13 = inverted condenser for one hour, filtering through a warmed
gh. 25m. 55s. funnel into a large flask heated to 70°C, in a water-bath, and
Colour. R.A. 1890. Decl. 18 90. allowing the alcohol to slowly evaporate. After about twelve bours a large deposit of brilliant tabular crystals is formed. Similar crystals of the third variety may be obtained by agitating (G.C. 1861
White. a saturated alcoholic solution of ammonium sulphide with excess
Reddish-yellow. of powdered sulphur, filtering, diluting with a little alcohol and (3). Hydræ
| Whitish-yellow. (4) o Leonis...
Yellowish-white. allowing to stand in a loosely covered cylinder. In a few hours
(5) 132 Schj. crystals are found deposited, often measuring a couple of centi
1 h. m. S.
9 25 47
(1) G.C. 1863
(2) 8 Leo Minoris
9 25 58 9 24 51 9 34 12 9 35 18
+ 22 0 +35 35 - O 39 + 10 24 - 12 25
ID 32 7
regions, and on the longest exposed plate it can be tracol (1) Described by Herschel as a bright extended nebula with nearly a diameter from the limb. A wide rift at the north pole two nuclei, the north following one being very faint. In 1848, extending 60° or 70° along the limb, contains several fine straigte Lord Rosse observed that the nebula was distinctly spiral, and rays similar to the polar
rays in 1878 and 1889 January 1, but not so his drawing represents it as elliptical in shape. The nebula is | distinguishable at the south pole. A remarkable fact is that it about 3' long and is situated about 2° south of the star Leonis. I am not aware that any record of the spectrum has been general mass of the corona on the eastern side is considerably published.
brcader from north to south than on the western side. This si (2) A star of Group II. Dunér states that the bands 2, 377; eastern limb, and plates taken near the end of totality show a
also the case in 1878. Numerous prominences are seen om te 8 are visible, but are rather weak and not very wide. The bands 4 and 's are very delicate. The star belongs to species feature in the plates taken with the reflector is the photographe
range of low prominences on the western limb. An interesting swarm of which the "star" is probably composed is somewhat reversal of the prominences and the brighter parts of the cores sparse. The bright carbon Autings should therefore be well In the larger exposed negatives the prominences and the car.ma developed. Bright lines may possibly also be present, if the near the limb are bright instead of dark, whilst the limb itzel swarm is not too far condensed.
is bounded by a very definite dark line indicating a decké
reversal. (3) Konkoly and Vogel both describe the spectrum of this star as a well-developed one of the solar type. The usual
THE NEBULAR HYPOTHESIS. -Mr. Herbert Spencer erndifferential observations are required.
tributed an essay on Laplace's famous theory to the Westin (4) A star of Group IV. (Vogel). The usual observations Review for July 1858. With the assistance of Mr. Thyote of the relative thicknesses of the hydrogen and other lines are Lynn, a new edition of this essay has been prepared ani required.
distributed amongst leading astronomers at home and abroad. (5) A star of Group VI., with a spectrum of extraordinary The revised calculations bring out more strongly than est beauty (Dunér). The spectrum consists of four zones, and all Mr. Spencer's views of the nebular hypothesis, and in particle the bands 1-1o are strongly developed. Band 6 is not very the portion referring to Mars. When the essay first appeared dark. The specific differences in stars of this group have not the density of this planet was taken as o'95, but recent an yet been fully investigated. The principal variations so far more exact determinations show the value to be much too high, observed are: (1) the length of continuous spectrum, as indi and taking this into account the fact comes out that to agre cated by the number of zones visible ; (2) the number and with Mr. Spencer's views Mars should have from one to for intensities of the secondary bands ; (3) the intensity of band 6 satellites as it has since 1877 been known to have. as compared with bands 9 and 10.
Olbers's theory that the asteroids are fragments of an explace! Gould believes this star to be variable, his estimates of the planet is favoured, and the genesis of the thirteen short perio magnitude varying between 4'3 and 6'1.' Birmingham's values comets is found in the same catastrophe. It is needless o vary from 4'5 to 63. The star appears to be U Hydræ, and, say that the theory is defended in a most masterly manie, if so, a maximum will be reached about March 18 (Observatory although the arguments against its acceptation are overwhelming. Companion, 1890). Espin believes the period to be about NEBULA, GENERAL, CATALOGUE No. 4795.- The Journal 195 days.
of the Liverpool Astronomical Society for December 1889 As yet, we have no information as to changes of spectrum which has just been issued, contains a note by Mr. W. L accompanying changes of magnitude in stars of this group. Jackson on this nebula, R.A. 22h. 24m., N.P.D. 1" 34
A. FOWLER. It is described in the General Catalogue as "Remarkable. THE SOLAR AND THE LUNAR SPECTRUM.-Prof. Langley's pretty faint, very large, extended or binuclear." Mr. Jackass second memoir on this subject, which was read before the bas carefully observed the nebula several times, and finds the National Academy of Science in November 1886, has been there are several stars involved, although no mention of them : received. In a previous memoir it was demonstrated that made in the Catalogue, and that there is a strong suspicion sa evidence of heat had been found in the invisible spectrum of the others beyond the reach of his 6 inch Grubb telescope Asked sunlit side of the moon, and the experiments indicated that this of the appearance accompanies the note. heat was chiefly not reflected but radiated from a surface at a A NEW ASTEROID.-Minor planet was discovered b» low temperature. The amount of heat, however, was excessively Prof. Luther (Hamburg) on February 24. minute, even when compared with the feeblest part of the solar spectrum known in 1882, yet it was easily recognizable because of the fact that, whereas in the typical solar spectrum heat is greatest in the short wave-lengths, in the typical lunar spectrum
CAMBRIDGE ANTHROPOMETRY: heat is greatest in the long wave-lengths.
In this second memoir the results of further observation of the ABOUT two years ago the results were pablished, in the infra-red solar spectrum are given, the newly investigated region of measurements taken at Cambridge. These comprised rahs
Journal of the Anthropological Society, of the first batch being close to that which contains a large part of the lunar heat. more than 1100 cases. During the last two years a nearly equal The researches considerably extend those previously made. In number have been obtained, and it therefore becomes imports passing from the visible part of the spectrum into the infra-red to compare the results yielded by these distinct batches. region, wider regions of absorption occur. To an eye which could see the whole spectrum, visible and invisible, the luminous the Cambridge Committee, were the following :-(1) A test for
The measurements proposed by Mr. Galton, and adopted by part would be, as is well known, interrupted by dark lines, the the eyesight. The extreme distance at which a man could real lower part to 5 u would appear to consist of alternate dark and "diamond type " (viz. the print employed in the little pocket bright bands, and the part below 5 m be nearly dark, but with Common Prayer-books) was noted with each eye separady. feeble “ bright” bands at intervals. This appearance is shown the figures given in our tables indicate the mean of the two lo in a plate accompanying the memoir. It is noted as a curious may be remarked that, as this instrument would only record op fact that the centres of several of the bands or lines are under some conditions found to be shifted to a recognizable extent, at this distance, it is certain that many could have seen further.
to 35 inches, and as about ten per cent. of the men could real and hence their wave-lengths are, within certain limits, variable. The aritbmetical mean, therefore, though good enough for all This apparent shift is found to be because the absorption does present purposes, is here less scientifically appropriate that the not increase symmetrically with the centre of the band, but more median." (2) A test of the muscular strength of the arme on one side than another, so as to considerably modify the when employed in an action similar to that of pulling a bon. position of greatest absorption.
Two handles, connected at a convenient distance apart, at THE CORONA OF 1889 DECEMBER 22.—The March number palled away from each other against the pressure of a spring of the Observatory contains a Woodburytype reproduction of 13) A test of the power of “squeeze" of each hand separately this corona taken by the late Father Perry with a short focus | In this case two handles stand a short distance apart, and se reflector of Mr. Common's, and a note by Mr. W. H. Wesley, then pressed towards each other against the action of a spring assistant secretary of the Royal Astronomical Society, upon its The figures here given denote the mean of the two results. u prominent features. Mr. Wesley finds that, as in the eclipse of Measurement of the size of the head. This is taken in the January 1, 1889, the extension is greatest towards the equatorial different directions, viz. from front to back, between the #
825 837 8407 81'5
sides, and upwards from a line between the eye and the ear.
Class B (913). The product of these three measurements is what is given in the annexed tables as "head-volumes." It need hardly be said 38
821 236-7 | 2350 68.92 | 148.5 that these numbers do not assign the actual magnitudes of the
19 25 4 787 80'3 238 0 249.8 68-78 149*7 heads; but they do all that is wanted for our purpose, viz, they 280 20 24'0
84'2 237'3 | 255'1 69'08 1535 are proportional to these magnitudes, on the assumption, of 21 235
837 2355 257-268-84 153'0 course, that the average shape of the head is the same through. 136 22 246
85'3' 239*2 | 257'2 .69.17 1533 out. (5) A test of the breathing capacity. The volume of air, 54 23 227
83'5 234'4 259'0 69-31 154'0 at ordinary pressure, that can be expired is measured by the
906 8714 245*5 261.5 68.93 157-7 amount of water displaced from a vessel. The result is given 36 | 25 226 85.8
86'1 237'1 | 264.5 68.83 157-2 in cubic inches. (6) The height ; deducting, of course, the thickness of the shoes. (7) The weight, in ordinary indoor clothing. Average.. 24•I 83-2 844 237'3 2549 69'00! 152.8 This is assigned, in our tables, in pounds.
As regards the persons measured, they are exclusively students --that is, undergraduates, with a small sprinkling of bachelors
Class C (734). and masters of arts. Nine-tenths of them were between the ages of 19 and 24 inclusive. Statisticians will understand the
837 | 234'2 | 238.0 | 6868 . 1560 importance of this fact in its bearing upon the homogeneity of
83*6.2314 our results; since a comparatively small number of measure
250*0 69'10 ! 1529 185
20 248 83.5 828 2350 2527 69'03 | 1536 ments, in such cases, will out balance in their trustworthiness a 163
86'1 84'5 2396 258'1 69'23' 156'o very much larger number which deal with miscellaneous crowds.
123 22 244
866 2368 255'5 6879155-4 But it is not so much to the above characteristics that I wish
57 23 238 881 87'2 '238.5 256-4 68 97 1562 la direct attention here as to one in respect of which our Uni. 26 24 254
239*3 244'0 68.35 156'o versity offers an almost unique opportunity. No previous at: ! 50 25 24'0
82-5 842, 243-2 247.5 68.24' 154*2 tempt, it is believed, has ever been made to determine by actual statistics the correlation between intellectual and physical capa- | Average.. [24-4 85'2 84'5 236-8 2529 6893 1548 cities What, however, with the multiplicity of modern examinations, and the intimate knowledge possessed by many tutors about the character and attainments of their pupils, this could These tables may be looked at from two points of view, which here be effected to a degree which could not easily be attempted would commonly be called the practical and the theoretical. By soywhere else. By appeal to these sources of information, the the former, to speak in the more accurate language of statistics, tadients were divided into three classes (here marked as A, B, I understand any conclusions to be involved which do not reand C), embracing respectively (1) scholars of their College, and cognize distinctions of less than about 4 or 5 per cent. of the those who have taken, or doubtless will take, a first class in any totals in question. Looked at with this degree of nicety, the tripos ; (2) those who go in for honours, but fall short of a first main fact that the tables yield is, that there is no difference class; and (3) those who go in for in for an ordinary degree, to whatever (with a single exception, to be presently noticed) be. which class also are assigned those who fail to pass. It is not tween the physical characteristics of the different intellectual for a moment pretended that such a classification is perfect, even grades. Whether in respect of height, weight, power of squeeze, within the modest limits which it hopes to attain. Very able eyesight, breathing capacity, or head-dimensions, there is no men may fail from indolence or ill-health, and very inferior ones perceptible distinction. There are differences, of course, but may succeed through luck or drudgery. But it must be remem to say whether or not these are of any significance requires an Lered that we only profess to deal with averages, and not with appeal to the theory of statistics and to tests beyond the reach individuals, and on average results such influences have little
of the practical" standard. power. There are probably few cricket or football clubs in
The one exception is in the power of “pull.” I called attenwhich one or more men in the second eleven or fifteen are not
tion to this two years ago ; but, with the bulk of statistics at really better than some in the first, but no one supposes that the that time at our command, I felt somewhat doubtful as to its second team would have much chance of beating the first. All
real significance. But there can scarcely be any doubt as to the that is maintained here is that our A, B, C classes, as classes, non-casual nature of a difference of power between the A and stand out indisputably distanced from each other in their intel- C classes amounting to 4:6 per cent., when this difference dislectual capacities. The average superiority of one over the plays itself between the averages of such large numbers as 487 next is patent to all who know them, and would be disputed and 734 respectively. At least, if there were any doubt, it by very few even of the men themselves.
would be removed by another mode of displaying the results, to The plan adopted has been to classify the A, B, C men separ explain which a brief digression must be made. In the precedately, arranging each of these in sub-classes according to their age. ing tables the primary division into three classes was based on On the last occasion about 1100 were thus treated, and it is very intellectual differences. Let us make, instead, one based on important to observe that the new batch (of about 1000) inde- physical differences. Let the first class, in respect of each kind pendently confirms the conclusions based on the previous set.
of measurement, embrace “the best in ten”; in other words, Space can scarcely be afforded for these tables separately, so I select the top 200, or thereabouts, in each separate list. Such a only give here the results of grouping the entire two sets toge table will show, for one thing, the extent to which one kind of ther. But as a matter of evidence, it must be insisted upon that physical superiority is correlated with another ; and also, by the two separate tables tell the same tale.
reference to the triposes and tutors' information, it will show The following. then, are the results of thus tabulating the how these classes are composed in respect of their A, B, C con measurements of 2134 of our students :
stituents. The following is such a table, arranged to show how TABLE I.
such "first classes ” in one physical department stand in relation. Class A (487).
to the principal other such departments.
Comparative Excellence in Different Physical Capacities. 753 2358 2440 68'13 1426 42,19 226 753 80'92429 25595 69'04 1480
Eyes. Pull Squeeze. Breath. | Height. Weight. 99 20 237
812 83.5 242-8 252 7 69'00 152'1 104 21 236
152-3 Ist Class, Eyes 346 866 83'5 263-269-40 157-1 94 22 24 -6 839 87*1 244*3 2572 68 71 1540
Pull 254 1130 939 280*2 69.82 1673 48 23 219 820 84'2 242'9
2628 69-11 1497
Squeeze 24'2 96.5 1037 2787 70-45 170'1 24 236 84'9 84'0 2459 2615 68'90 | 1548
249 943 92'4 320-5 | 7119 167*3 57 25 230 80 9 827 247*2 2510 68.59 1546
88'0 90'4 286'7 | 73-25 17145 Average.. 234 815 835 2436 255*6 68 85 152'5 Average student.. 24'1 8345 84-2 254'5 68.94 | 1534
I shall call attention hereafter to certain conclusions furnished of candidates who had failed to pass, and whose names therefore by this table as to the correlation of these various physical were not mentioned. characteristics. At present they are only appealed to in con Now, this being so, it follows that the differences between firmation of the fact alluded to above. It is rather curious say, the last 20 per cent. who succeeded, and the first 20 € that, when we sort out these first classes into their A, B, C con cent. who failed, are extremely slight, in respect of the quan stituents, we find that, with the same single exception, the thus tested. Might it not then be wise to take account of me distribution is about what it would be on a chance arrangement. other quality, and what better could be found than the ptysicz That is, the men of exceptional height or breathing capacity are If by sacrificing little or nothing of mental superiority ** just as likely to be found amongst the A's as amongst the B's or can gain a good deal of physical superiority, there is muna C's. This is the case even with the eyesight. The first class to be said in favour of such a final appeal. If, for instance, here was confined to men who could read distinctly the small we accepted, in the first instance, 20 per cent. more tint az print (diamond) employed, at a distance of at least 35 inches ; wanted to retain, and then subjected the whole number to some with the additional restriction that the weaker eye of the two physical test, for which a moderate amount of marks were could read the same at 33 inches. Of such men there were 196 assigned, the men finally excluded would at worst necessarily to out of 2134. Now had these been taken indiscriminately from those who were only just admitted on the customary plan, xa} the three classes A, B, C, the most likely proportions would have those finally admitted would at worst necessarily be those who been respectively 44, 84, and 68. The actual numbers were 46, otherwise would only just have been rejected. 88, and 62. But when we select in the same way a first class There is not space here to discuss fully any such proposal, bet consisting of 182) of the strongest "pullers,” we find that if any scheme of this kind is ever introduced its justification muwhereas A, B, C, should contribute respectively 41, 78, and 63, rest on considerations such as those displayed in our second they actually contribute 28, 78, and 83. Taken in connection table. One or two results may be pointed out. In the fira with our previous results, the conclusion seems inevitable that place, it must be insisted that the whole merit of any such scheme this particular kind of physical superiority is, to a certain extent, rests upon the assumption that mental superiority may be co for some reason or other, hostile to intellectual superiority. sidered as perfectly "independent" (in the mathematical senk
The question why this is so is one which it is not easy to of physical This we find is not quite the case as regards the answer with confidence, but the following suggestion may be pulling" power, but is the case as regards every one of the offered. The action of "pulling" is the only one in the above other qualities here displayed. If we set much store upon tri list of physical tests which is much practised in any popular men, or upon men with good eyes, we may rest assurer les games : it obviously is so in rowing, whilst in cricket a similar little or nothing will be sacrificed in the way of mental results, set of muscles appear to be exerted. But no known game ap giving reasonably good marks for such excellence. Again, pears much to practise our “squeezing" power; and, as regards may be remarked to what extent these different kinds of physuz the height, weight, breathing, and seeing powers, probably any superiority are correlated. It appears that great superioriy :: form of exercise which keeps a man in good health offers any one kind of physical power is accompanied by considerable sufficient scope for development. It would therefore seem to superiority in every other. It is a striking fact that in only cc meet all the observed facts if we suppose that our hard-reading of the thirty subdivisions there indicated, do we fail to find the men take amply sufficient exercise to develop their general | “first class” man, in any one department, standing abore the physical powers fully up to the same relatively high standard average man in every department. sound amongst the others; but that the non-reading men, or a This being so, it is rather for the physiologist, or for the an certain proportion of them, are rather apt to devote themselves of affairs, to select the particular physical test which is likely to certain kinds of exercise which develop a proportional best to serve the public interest. So far as mere statistics : superiority in one special muscular development.
concerned, I should give the preference to the breatking MI I should not have directed so much attention to this second For one thing, this appears, in my judgment, to be correlate's table if it were not that such considerations have a very direct on the whole, with a higher general physical superiority than bearing upon a question of importance at the present day. As the case with the other qualities. I apprehend also that god some readers of this journal probably know, it has been seriously breathing power could not readily be “ crammed," so to sys discussed, in influential quarters, whether it is not advisable to attendance at a gymnasium, and by aid of professional adni take some account of physical qualifications in our Civil Service and direction, as can be done to some considerable
extent in the or other State examinations. By this, we may presume, is not case of muscular power. to be understood any mere pass examination. The necessity of It has been already remarked that high excellence in co some test of that kind may be taken for granted, and would physical capacity seems correlated with decided superiority a naturally be secured by a medical certificate. Something much the others. This is evident from a glance at the tables Bor, more serious than this may plausibly be defended, and on the deserves notice that equally high excellence is not by any following grounds.
implied. The chance of a man who is in one of these placa In most of the examinations of any magnitude with which the first classes being also in another such class is not very next State is concerned, it may be taken as a fact of experience that more than what it would be if the two capacities were discribe! the number of selected candidates bears some moderate ratio to at random. As a matter of fact, four men only out of the enter that of those who compete. If two hundred men are found to number are in every one of these first classes. As between ik go in and try, it will seldom be the case that there were very exertions of muscular strength apparently so closely similar as many more or less than fifty vacancies. Supply and demand, those of pulling and squeezing, it is found that only 14. mrt in a country in the present social and economic condition of the total of 195 in the latter, also secured a place in the former. England at any rate, will generally obviate any extreme dispro- whereas a purely chance distribution might have been expecte! portion between the two quantities. Now it is well known that to secure as many as about 20. As between the correspondir where many aims of any kind are made at an object the so-called selections, of about
equal numbers, from the best in respect "law of large numbers," or "law of error," comes into play. eyesight and breathing, it appears that not more than jo obtura At the two ends of our list of competitors the discrepancies in a place in both classes. their performances will be very great. But, for a wide range on Turn now to some of the less obviously certain conclusion both sides of the middle, the differences will be comparatively Comparing the "head-volumes" of the students, two ta' small
. A glance at any one of the lists, which are published claim notice, viz. first, that the heads of the high-honour men in the papers from time to time, of the selected candidates for are distinctly larger than those of the pass men; and, secum.' the army, with the number of marks gained by each, will that the heads of all alike continue to grow for sume years aft: : illustrate this. Near the top the difference between one can
the age of 19. didate and the next may be measured by hundreds of marks,
The actual amount of difference as between the A and whilst towards the botiom of the selected candidates (i.e. to students is, of course, small. On our scale it is just about : wards the middle of the competitors) the difference will be given inches--that is 3 per cent. on the real size of the head. ? in tens only, or even in units. So marked is this tendency that this small difference to be regarded as significant? The answer any well-informed statistician could often give a very shrewd can only be given by an appeal to the theory of statistics, which guess, from the mere inspection of such a list, as to the number yields the following conclusions.
I must premise that the figures given here as average heel See Mr. Galton's paper on this subject at the last meeting of the British volumes were thus obtained. The average was taken at tath.
the three separate head-measurements in the three directions
already explained) of each sub-class of students-e.g. of those of selected from the whole number, we do not find any appreciable the A class who were 19 years of age ; these three were then intellectual selection to be thereby entailed. multipliesi together, and the product resulting (in the case in An equally trustworthy basis of comparison is found by obquestion, 2429) was entered in the table. What we have, serving the distribution of the short-sighted men. Let us take berefore, is not strictly the mean of the products, but the pro- as the limit of what shall be termed " short sight” the inaduct of the means. Theoretically, I apprehend, the former bility to read the diamond print with both eyes at a distance -hould have been preferred ;- but as the extra labour entailed greater than ten inches. Adopting this test, we find that the would have been very great, and as the difference, when dealing A, B, C classes furnish respectively 14, 11, and 11 per cent., with large numbers of cases and small amounts of divergence, is | indicating a very small difference between them. extremely small, I have been content with the latter. It may be added that the actual computation was made in both of these ways for a sample number of cases, and the insignificance of the difference for our purposes of comparison was statistically verified.
What theory directs us to do is of course to begin with deter- : mining the probable error of the individual head volumes of the men generally. This is found to be, on the scale in question, abont 17 inches. The usual formula for the difference between the means of 734 and of 487 would then assign to this difference a pratable error of 17 *
viz. nearly one inch.
734 The actual observed difference, of nearly 7 inches, thus lies enormously outside the bounds of probability of production from mere statistical chance arrangement. But in this calculation there is a source of error omitted to which attention was directed not long ago by a correspondent in NATURE, viz. the actual errors (in the literal sense of that rather unfortunate technical term) committed by the observer, or involved in the mechanism of the instrument. Two years ago I had taken it for granted trat these were insignificant ; and, had it been otherwise, the materials at our disposal would hardly have enabled us to make this. With the single exception of eyesight-and this to a very
The general conclusion to be drawn here seems, then, to be the due allowance. Bat, as the correspondent pointed out, the slight extent-it does not appear that intellectual superiority is error is by no means to be neglected, and we have now the in the slightest significant degree either correlated with any kind means of fairly estimating it. A considerable number of men of natural physical superiority or inferiority, or that it tends whilst one man, who seems to have had a morbid love of this incidentally to produce any general superiority or inferiority. I -bysical inspection, has actually had his various dimensions and emphasize the word "general” in the last clause in order to capacities tested no less than eighteen times during the course of allow for the difference shown in respect of pulling power. It sume three years. These cases have furnished a fair basis of seems probable, as has been already suggested, that the superidetermination. They show that these personal errors are ority of the non-honour men does not point to the slightest certainly greater than they should be (they seem to arise in part indicated perhaps if it displayed itself in respect of their height,
superiority of their general bodily development—as would be from a certain looseness in the machine, which will be remedied weight, or breathing capacity—but is solely brought about by 10 future), amounting in certain extreme cases to as much as esen half an inch on the single measurement, and therefore to greater muscular exercise in the pursuit of certain athletic
games. much more in what appears here as a "head-volume." The resultant "probable error” from this fresh source of disturbance' the third—which is arranged in order to show the development
So much as regards the first and second tables. As regards amounts to about five (cubic) inches. Those unfamiliar with probability may perhaps be staggered by such an admission, but
TABLE III. they may be assured that the healing tendency of the averages of large numbers is very great, and that the results remain sub
Physical Development of Students from 18 to 25. stantially unaffected. The problem appears to be simply one of
A, B, C combined (2134). the superposition of two independent sources of error, and may be stated thus: Given a large number (over 2000) of magni No., Age. Eyes. Pull. Squeeze. Head. Breath. Height. Weight. ludes, with a mean of 239, and a "probable error," about this mean, of 17; and assume that these magnitudes are inaccurately 80
79'2 819 2356 237'3 68-72 150-8 measured with a further probable error of 5 inches (as seems to 276 19 24'
79'3 816 2364 250:8 68.93 150-5 be the fact), what is the probable error of the divergence be- 1 564 20 24'2
826 836 237-52539 69'05 153-3 tween the two averages obtained respectively from 734 and 487 479 21 236 84'0 838 2383' 257'0'68.96 154'I of these results? The answer is still a little less than one inch. 353 22 246 86'2 862 239 7 2566 68 91 1542 T: is, that is to say, an even chance that the two averages will 159 23 228 84'0 85'0 238'4 . 259-4 69'12 1535 not differ by more than this; and it is, consequently, thousands 80 24 248
85-6 2436 2558 6873 1560 to one that they will not differ by so much as seven inches. 143 25 23-3 827 84'1 243*3 : 2532 68.53 1551 The conclusions, therefore, previously drawn, lose little of their force.
It seems to me almost as certain that the size of the head of the physical powers between 18 and 25—there is very little continues to increase up to at any rate the age of 24. This will to be said, as statistics of this character offer no particular be made clear by looking at the following diagram, which is novelty. Such merit, therefore, as this may possess must depend drawn to show the sum of the figures of the head-measurements mainly on the homogeneity of the class of men concerned." As. 25 contained in Table III.
indicated at the commencement of this paper, this homogeneity As regards the comparative physical endowments, in the other is equivalent to a considerable increase in the total numbers respects, of the different classes of students, there does not seem where more heterogeneous materials are dealt with. They to be much to say. The differences-sometimes one way and appear to indicate that the physical powers, as a whole, culSometimes the other—between them in respect of height, weight, minate at the age of 22 or 23, and thence begin to steadily breathing, and squeezing power, are so small as to be statistically decline. Too much stress, however, must not be laid upon the insignificant, averaging only about i per cent. That the first rate of decline here, since the last subdivision is of a somewhat class honour men, however, have slightly inferior eyesight less homogeneous character than the others. For one thing, seems established, especially when we bear in mind that each the men of twenty-five really include those also who are over barch of about 1000 cases tells the same tale; the only evidence that age, though these are relatively but few. Again, whilst the telling the other way is the fact, already adverted to, that when men up to 24 remain (for all statistical purposes) identically the a class comprising the best in ten," as regards eyesight, is same individuals, with a year or two more added on to their