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MR. JOHN MURRAY has published the nineteenth edition of "The Reign of Law," by the Duke of Argyll.

THE Amateur Photographer has issued its fourth "home portraiture number." It reproduces one photograph each from the work contributed by sixty competitors for prizes.

IN the Report of the U.S. Commissioner of Education for the year 1887-88 it is stated that 48 educational institutions in the United States receive the benefit of the national land grant of 1862. Among these institutions are the Arkansas Industrial University, the State Agricultural College at Colorado, the Maine State College of Agriculture and the Mechanic Arts, the Massachusetts Institute of Technology, the Missouri School of Mines and Metallurgy, and the Scientific School of Rutgers College. In 38 of the Colleges an officer of the Army or Navy is detailed to act as professor of military science and tactics. If a State has more than one school endowed by the national land grant of 1862, the school which is reported by the Governor of the State as most nearly meeting the requirements of existing law is held to have the first claim to the officer allotted to the State.

M. A. ANGOT, of the French Meteorological Office, has plished in the Annales of that office a very careful discussion of the diurnal range of the barometer, based upon the best vailable data for all parts of the globe. After having given the can range for each month and for the year, he has calculated the amplitudes and phases of the first four simple harmonic scillations into which the complex oscillation of the barometric diurnal range may be resolved, and which may be considered as the resultant of the superposition of two waves of different origin

1ad character. One of these, which the author terms the thermic wave, is of a more or less complicated form in appearance, and is easily explained as being produced by the diurnal variation of temperature and by the differences that this variation presents between neighbouring stations. The other, the principal semi-diurnal wave, for which he has given the numerical law, -esents a much more simple form, and is not at all affected by Ical conditions. It is possibly produced by the calorific action of the sun upon the upper strata of the atmosphere; but, as the athor states, this is still only an hypothesis, and the theory of this part of the phenomenon remains to be established. His conclusions upon the effect of the thermic wave are very interesting, and the whole discussion will well repay a careful study.

ME. T. W. BAKER writes to us that, in his note regarding Le meteor of March 3, he omitted to state the time of its appearance, which was 7.28 p. m.

As important paper upon the crystalline allotropic forms of sulphur and selenium is contributed by Dr. Muthmann, of Munich, to the latest number of the Zeitschrift für Krystallogra7. Besides the well-known rhombic pyramids and monoclinic risms, sulphur may, under certain conditions, be obtained in a third crystalline modification, which has been termed by Gernez "ufre nacre." This third modification has been fully investigated by Dr. Muthmann, and, in addition, a new fourth totally distinct variety has been discovered. The third form is best obtained by boiling about five grams of powdered sulphur with 750 c.c. of absolute alcohol in a flask provided with an inverted condenser for one hour, filtering through a warmed funnel into a large flask heated to 70° C. in a water-bath, and allowing the alcohol to slowly evaporate. After about twelve hours a large deposit of brilliant tabular crystals is formed. Similar crystals of the third variety may be obtained by agitating a saturated alcoholic solution of ammonium sulphide with excess of powdered sulphur, filtering, diluting with a little alcohol and allowing to stand in a loosely covered cylinder. In a few hours crystals are found deposited, often measuring a couple of centi

metres in length and 1-2 mm. thick. Another method which yielded very beautiful crystals of this modification consisted in allowing a solution of acid potassium sulphate to slowly diffuse into a solution of sodium thiosulphate. In about four weeks' time, perfect crystals, almost white in appearance, and exhibiting strongly the mother-of-pearl lustre, were obtained. This third variety of sulphur also crystallizes in the monoclinic system. The ratio of its axes is a : b: c = 10609: 1:07094. The axial angle ẞ = 88° 13'. The symmetry plane, b = (010) ∞ R∞, is so largely developed as to give the crystals the appearance of plates. At the edges of the plates the two primary pyramids (111) – P and (11)+P, a prism (210) ∞ ₹ 2, and a clinodome (012)1⁄2 R∞ are well developed. These crystals are totally distinct from those of the second modification; the axial ratios of the latter are a:b: c = o'9957: I: 0.9998 and B = 84° 14'. Upon the sides of the vessel containing the alcoholic ammonium sulphide solution prepared as above, Dr. Muthmann noticed curious tabular crystals of hexagonal section, which immediately became altered upon contact with a disturbing body, such as a platinum wire or glass rod. They were likewise found to consist of pure sulphur, and, on optical and goniometrical examination, were found to consist of a distinct fourth modification, also monoclinic. They greatly resemble a rhombohedron with predominating basal plane. They are best obtained by allowing to slowly evaporate in a tall cylinder a saturated solution of sulphur in alcoholic ammonium sulphide diluted with four times its volume of alcohol. The temperature during this crystallization must 14° C. Occasionally in this experiment all four forms of sulphur are obtained; the surface is covered with crystals of the third variety, tables of the fourth modification are deposited upon the sides, and the base of the cylinder is spangled with rhombic pyramids interspersed with monoclinic needles of the second form. If crystals of the third variety are suspended in their mother liquors and left for some days, they are converted into a into the more stable rhombic form is almost instantaneous if a voluminous mass of minute rhombic pyramids. The conversion rhombic crystal be dropped into the liquid containing suspended third variety crystals. The immediate alteration of crystals of the fourth kind is even more remarkable, the mere movement of

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the cover-glass, when examining them under the microscope, being sufficient to instantly change the optical properties to those of the rhombic form. It is interesting that this fourth form of sulphur is isomorphous with the form of selenium obtained by evaporation of a hot saturated solution in carbon bisulphide.

THE additions to the Zoological Society's Gardens during the past week include two Badgers (Meles taxus) from Ireland, presented by Mr. P. Bicknell; a Grey Hypocolius (Hypocolius ampelinus 8) from Scinde, presented by Mr. W. D. Cumming; a Rhesus Monkey (Macacus rhesus 8) from India, a Spotted Ichneumon (Herpestes nepalensis) from Nepal, deposited; an Axis Deer (Cervus axis), born in the Gardens.

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(1) Described by Herschel as a bright extended nebula with two nuclei, the north following one being very faint. In 1848, Lord Rosse observed that the nebula was distinctly spiral, and his drawing represents it as elliptical in shape. The nebula is about 3' long and is situated about 2° south of the star A Leonis. I am not aware that any record of the spectrum has been published.

(2) A star of Group II. Dunér states that the bands 2, 3, 7, 8 are visible, but are rather weak and not very wide. The bands 4 and 5 are very delicate. The star belongs to species 5 of the subdivision of the group, which means that the meteorswarm of which the "star" is probably composed is somewhat sparse. The bright carbon flutings should therefore be well developed. Bright lines may possibly also be present, if the

swarm is not too far condensed.

(3) Konkoly and Vogel both describe the spectrum of this star as a well-developed one of the solar type. The usual differential observations are required. (4) A star of Group IV. (Vogel). The usual observations of the relative thicknesses of the hydrogen and other lines are required.

(5) A star of Group VI., with a spectrum of extraordinary beauty (Duner). The spectrum consists of four zones, and all the bands 1-10 are strongly developed. Band 6 is not very dark. The specific differences in stars of this group have not yet been fully investigated. The principal variations so far observed are: (1) the length of continuous spectrum, as indicated by the number of zones visible; (2) the number and intensities of the secondary bands; (3) the intensity of band 6 as compared with bands 9 and 10.

Gould believes this star to be variable, his estimates of the magnitude varying between 4'3 and 6'1. Birmingham's values vary from 4.5 to 6.3. The star appears to be U Hydræ, and, if so, a maximum will be reached about March 18 (Observatory Companion, 1890). Espin believes the period to be about 195 days.

As yet, we have no information as to changes of spectrum accompanying changes of magnitude in stars of this group. A. FOWLER.

THE SOLAR AND THE LUNAR SPECTRUM.-Prof. Langley's second memoir on this subject, which was read before the National Academy of Science in November 1886, has been received. In a previous memoir it was demonstrated that evidence of heat had been found in the invisible spectrum of the sunlit side of the moon, and the experiments indicated that this heat was chiefly not reflected but radiated from a surface at a low temperature. The amount of heat, however, was excessively 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 heat is greatest in the long wave-lengths.

In this second memoir the results of further observation of the infra-red solar spectrum are given, the newly investigated region being close to that which contains a large part of the lunar heat. The researches considerably extend those previously made. In passing from the visible part of the spectrum into the infra-red region, wider regions of absorption occur. To an eye which could see the whole spectrum, visible and invisible, the luminous part would be, as is well known, interrupted by dark lines, the lower part to 5 μ would appear to consist of alternate dark and bright bands, and the part below 5 μ be nearly dark, but with feeble "bright" bands at intervals. This appearance is shown in a plate accompanying the memoir. It is noted as a curious fact that the centres of several of the bands or lines are under some conditions found to be shifted to a recognizable extent, and hence their wave-lengths are, within certain limits, variable. This apparent shift is found to be because the absorption does not increase symmetrically with the centre of the band, but more on one side than another, so as to considerably modify the position of greatest absorption.

THE CORONA OF 1889 DECEMBER 22.-The March number of the Observatory contains a Woodburytype reproduction of this corona taken by the late Father Perry with a short focus reflector of Mr. Common's, and a note by Mr. W. H. Wesley, assistant secretary of the Royal Astronomical Society, upon its prominent features. Mr. Wesley finds that, as in the eclipse of January 1, 1889, the extension is greatest towards the equatorial

regions, and on the longest exposed plate it can be tracnity nearly a diameter from the limb. A wide rift at the north puis, extending 60° or 70° along the limb, contains several fine atraigh rays similar to the polar rays in 1878 and 1889 January 1, but naka numerous, regular, or distinct. The usual polar rays are sorry distinguishable at the south pole. A remarkable fact is that general mass of the corona on the eastern side is considerably broader from north to south than on the western side. This also the case in 1878. Numerous prominences are seen on t eastern limb, and plates taken near the end of totality show range of low prominences on the western limb. An interesting feature in the plates taken with the reflector is the photograp. reversal of the prominences and the brighter parts of the coman In the larger exposed negatives the prominences and the cor is bounded by a very definite dark line indicating a docie near the limb are bright instead of dark, whilst the limb itat


THE NEBULAR HYPOTHESIS.-Mr. Herbert Spencer er tributed an essay on Laplace's famous theory to the Westmin Review for July 1858. With the assistance of Mr. Thyun Lynn, a new edition of this essay has been prepared i distributed amongst leading astronomers at home and abroad.

The revised calculations bring out more strongly than eve Mr. Spencer's views of the nebular hypothesis, and in partisi the portion referring to Mars. When the essay first appea the density of this planet was taken as o'95, but recent an more exact determinations show the value to be much too high, and taking this into account the fact comes out that to a with Mr. Spencer's views Mars should have from one to f satellites as it has since 1877 been known to have.

Olbers's theory that the asteroids are fragments of an explor! planet is favoured, and the genesis of the thirteen short-per comets is found in the same catastrophe. It is needless fi say that the theory is defended in a most masterly manner. although the arguments against its acceptation are overwhelming

NEBULA, GENERAL CATALOGUE No. 4795.-The Journal of the Liverpool Astronomical Society for December 18%, which has just been issued, contains a note by Mr. W. Jackson on this nebula, R. A. 22h. 24m., N.P.D. 111" 24 It is described in the General Catalogue as "Remarkable.

pretty faint, very large, extended or binuclear." Mr. Jackso has carefully observed the nebula several times, and finds there are several stars involved, although no mention of them made in the Catalogue, and that there is a strong suspicion ( others beyond the reach of his 6 inch Grubb telescope. A skect of the appearance accompanies the note.

A NEW ASTEROID.-Minor planet Prof. Luther (Hamburg) on February 24.

was discovered


ABOUT two years ago the results were published, in the Journal of the Anthropological Society, of the first batch of measurements taken at Cambridge. These comprised rathe more than 1100 cases. During the last two years a nearly el number have been obtained, and it therefore becomes importa to compare the results yielded by these distinct batches.

The measurements proposed by Mr. Galton, and adopted by the Cambridge Committee, were the following:-(1) A test f the eyesight. The extreme distance at which a man could real 'diamond type" (viz. the print employed in the little pocket Common Prayer-books) was noted with each eye separately the figures given in our tables indicate the mean of the two. I may be remarked that, as this instrument would only record ay to 35 inches, and as about ten per cent. of the men could rest The arithmetical mean, therefore, though good enough for " at this distance, it is certain that many could have seen farther present purposes, is here less scientifically appropriate than the "median.' (2) A test of the muscular strength of the m when employed in an action similar to that of pulling a bow Two handles, connected at a convenient distance apart, are pulled away from each other against the pressure of a spr (3) A test of the power of "squeeze" of each hand separately In this case two handles stand a short distance apart, and ur then pressed towards each other against the action of a spre The figures here given denote the mean of the two results. 4, Measurement of the size of the head. This is taken in thre different directions, viz. from front to back, between the tw

sides, and upwards from a line between the eye and the ear. The product of these three measurements is what is given in the annexed tables as "head-volumes." It need hardly be said that these numbers do not assign the actual magnitudes of the heads; but they do all that is wanted for our purpose, viz. they are proportional to these magnitudes, on the assumption, of course, that the average shape of the head is the same throughout. (5) A test of the breathing capacity. The volume of air, at ordinary pressure, that can be expired is measured by the amount of water displaced from a vessel. The result is given in cubic inches. (6) The height; deducting, of course, the thickness of the shoes. (7) The weight, in ordinary indoor clothing. 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 and masters of arts. Nine-tenths of them were between the ages of 19 and 24 inclusive. Statisticians will understand the importance of this fact in its bearing upon the homogeneity of our results; since a comparatively small number of measurements, in such cases, will outbalance in their trustworthiness a very much larger number which deal with miscellaneous crowds.

But it is not so much to the above characteristics that I wish to direct attention here as to one in respect of which our University offers an almost unique opportunity. No previous attempt, it is believed, has ever been made to determine by actual statistics the correlation between intellectual and physical capacities. 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 here be effected to a degree which could not easily be attempted anywhere else. By appeal to these sources of information, the tudents were divided into three classes (here marked as A, B, and C), embracing respectively (1) scholars of their College, and those who have taken, or doubtless will take, a first class in any tripos; (2) those who go in for honours, but fall short of a first class; and (3) those who go in for in for an ordinary degree, to which class also are assigned those who fail to pass. It is not for a moment pretended that such a classification is perfect, even within the modest limits which it hopes to attain. Very able men may fail from indolence or ill-health, and very inferior ones may succeed through luck or drudgery. But it must be rememtered that we only profess to deal with averages, and not with individuals, and on average results such influences have little power. There are probably few cricket or football clubs in which one or more men in the second eleven or fifteen are not really better than some in the first, but no one supposes that the second team would have much chance of beating the first. All that is maintained here is that our A, B, C classes, as classes, stand out indisputably distanced from each other in their intellectual capacities. The average superiority of one over the next is patent to all who know them, and would be disputed by very few even of the men themselves.

The plan adopted has been to classify the A, B, C men separately, arranging each of these in sub-classes according to their age. On the last occasion about 1100 were thus treated, and it is very important to observe that the new batch (of about 1000) independently confirms the conclusions based on the previous set. Space can scarcely be afforded for these tables separately, so I only give here the results of grouping the entire two sets together. But as a matter of evidence, it must be insisted upon that the two separate tables tell the same tale.

The following. then, are the results of thus tabulating the nieasurements of 2134 of our students :

TABLE I. Class A (487).

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These tables may be looked at from two points of view, which would commonly be called the practical and the theoretical. By the former, to speak in the more accurate language of statistics, I understand any conclusions to be involved which do not recognize distinctions of less than about 4 or 5 per cent. of the totals in question. Looked at with this degree of nicety, the main fact that the tables yield is, that there is no difference whatever (with a single exception, to be presently noticed) be. tween the physical characteristics of the different intellectual grades. Whether in respect of height, weight, power of squeeze, eyesight, breathing capacity, or head-dimensions, there is no perceptible distinction." There are differences, of course, but to say whether or not these are of any significance requires an appeal to the theory of statistics and to tests beyond the reach of the "practical" standard.

The one exception is in the power of "pull." I called attention to this two years ago; but, with the bulk of statistics at that time at our command, I felt somewhat doubtful as to its real significance. But there can scarcely be any doubt as to the non-casual nature of a difference of power between the A and C classes amounting to 4'6 per cent., when this difference displays itself between the averages of such large numbers as 487 and 734 respectively. At least, if there were any doubt, it would be removed by another mode of displaying the results, to explain which a brief digression must be made. In the preceding tables the primary division into three classes was based on intellectual differences. Let us make, instead, one based on physical differences. Let the first class, in respect of each kind of measurement, embrace "the best in ten "; in other words, select the top 200, or thereabouts, in each separate list. Such a table will show, for one thing, the extent to which one kind of physical superiority is correlated with another; and also, by reference to the triposes and tutors' information, it will show how these classes are composed in respect of their A, B, C con stituents. The following is such a table, arranged to show how such "first classes" in one physical department stand in relation to the principal other such departments.

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I shall call attention hereafter to certain conclusions furnished by this table as to the correlation of these various physical characteristics. At present they are only appealed to in confirmation of the fact alluded to above. It is rather curious that, when we sort out these first classes into their A, B, C constituents, we find that, with the same single exception, the distribution is about what it would be on a chance arrangement. That is, the men of exceptional height or breathing capacity are just as likely to be found amongst the A's as amongst the B's or C's. This is the case even with the eyesight. The first class here was confined to men who could read distinctly the small print (diamond) employed, at a distance of at least 35 inches; with the additional restriction that the weaker eye of the two could read the same at 33 inches. Of such men there were 196 out of 2134. Now had these been taken indiscriminately from the three classes A, B, C, the most likely proportions would have been respectively 44, 84, and 68. The actual numbers were 46, 88, and 62. But when we select in the same way a first class consisting of 182) of the strongest "pullers," we find that whereas A, B, C, should contribute respectively 41, 78, and 63, they actually contribute 28, 78, and 83. Taken in connection with our previous results, the conclusion seems inevitable that this particular kind of physical superiority is, to a certain extent, for some reason or other, hostile to intellectual superiority.

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The question why this is so is one which it is not easy to answer with confidence, but the following suggestion may be offered. The action of "pulling " is the only one in the above list of physical tests which is much practised in any popular games: it obviously is so in rowing, whilst in cricket a similar set of muscles appear to be exerted. But no known game appears much to practise our squeezing" power; and, as regards the height, weight, breathing, and seeing powers, probably any form of exercise which keeps a man in good health offers sufficient scope for development. It would therefore seem to meet all the observed facts if we suppose that our hard-reading men take amply sufficient exercise to develop their general physical powers fully up to the same relatively high standard found amongst the others; but that the non-reading men, or a certain proportion of them, are rather apt to devote themselves to certain kinds of exercise which develop a proportional superiority in one special muscular development.

I should not have directed so much attention to this second table if it were not that such considerations have a very direct bearing upon a question of importance at the present day. As some readers of this journal probably know, it has been seriously discussed, in influential quarters, whether it is not advisable to take some account of physical qualifications in our Civil Service or other State examinations. By this, we may presume, is not to be understood any mere pass examination. The necessity of some test of that kind may be taken for granted, and would naturally be secured by a medical certificate. Something much more serious than this may plausibly be defended, and on the following grounds.

In most of the examinations of any magnitude with which the State is concerned, it may be taken as a fact of experience that the number of selected candidates bears some moderate ratio to that of those who compete. If two hundred men are found to go in and try, it will seldom be the case that there were very many more or less than fifty vacancies. Supply and demand, in a country in the present social and economic condition of England at any rate, will generally obviate any extreme disproportion between the two quantities. Now it is well known that where many aims of any kind are made at an object the so-called "law of large numbers," or "law of error,' comes into play. At the two ends of our list of competitors the discrepancies in their performances will be very great. But, for a wide range on both sides of the middle, the differences will be comparatively small. A glance at any one of the lists, which are published in the papers from time to time, of the selected candidates for the army, with the number of marks gained by each, will illustrate this. Near the top the difference between one candidate and the next may be measured by hundreds of marks, whilst towards the bottom of the selected candidates (i.e. towards the middle of the competitors) the difference will be given in tens only, or even in units. So marked is this tendency that any well-informed statistician could often give a very shrewd guess, from the mere inspection of such a list, as to the number

See Mr. Galton's paper on this subject at the last meeting of the British Association.

of candidates who had failed to pass, and whose names therefore were not mentioned.

Now, this being so, it follows that the differences betwee say, the last 20 per cent. who succeeded, and the first 201 cent. who failed, are extremely slight, in respect of the quali. thus tested. Might it not then be wise to take account of som other quality, and what better could be found than the physica If by sacrificing little or nothing of mental superiority can gain a good deal of physical superiority, there is mac to be said in favour of such a final appeal. If, for instance, we accepted, in the first instance, 20 per cent. more than we wanted to retain, and then subjected the whole number to some physical test, for which a moderate amount of marks wer assigned, the men finally excluded would at worst necessarily those who were only just admitted on the customary plan, ani those finally admitted would at worst necessarily be those who otherwise would only just have been rejected.

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There is not space here to discuss fully any such proposal, if any scheme of this kind is ever introduced its justification mu rest on considerations such as those displayed in our secon table. One or two results may be pointed out. In the fir place, it must be insisted that the whole merit of any such scheme rests upon the assumption that mental superiority may be sidered as perfectly "independent" in the mathematical sens of physical. This we find is not quite the case as regards the "pulling" power, but is the case as regards every one of th other qualities here displayed. If we set much store upon t men, or upon men with good eyes, we may rest assured tha little or nothing will be sacrificed in the way of mental results: giving reasonably good marks for such excellence. Again.. may be remarked to what extent these different kinds of physa superiority are correlated. It appears that great superiority any one kind of physical power is accompanied by considerable superiority in every other. It is a striking fact that in only one of the thirty subdivisions there indicated, do we fail to find the "first class" man, in any one department, standing above 1average man in every department.

This being so, it is rather for the physiologist, or for the man of affairs, to select the particular physical test which is like) best to serve the public interest. So far as mere statistics : concerned, I should give the preference to the breathing po. For one thing, this appears, in my judgment, to be correlate! on the whole, with a higher general physical superiority than the case with the other qualities. I apprehend also that go ! breathing power could not readily be "crammed, so to say. attendance at a gymnasium, and by aid of professional adn z and direction, as can be done to some considerable extent case of muscular power.


It has been already remarked that high excellence in one physical capacity seems correlated with decided superiority i the others. This is evident from a glance at the tables Burl deserves notice that equally high excellence is not by any implied. The chance of a man who is in one of these phys first classes being also in another such class is not very a more than what it would be if the two capacities were distribu at random. As a matter of fact, four men only out of the entire number are in every one of these first classes. As between the exertions of muscular strength apparently so closely similar s those of pulling and squeezing, it is found that only 44, mt of the total of 195 in the latter, also secured a place in the former. whereas a purely chance distribution might have been expect? to secure as many as about 20. As between the corresponding selections, of about equal numbers, from the best in respect of eyesight and breathing, it appears that not more than jo obta a place in both classes.

Turn now to some of the less obviously certain conclusion Comparing the "head-volumes of the students, two tact claim notice, viz. first, that the heads of the high-honour men are distinctly larger than those of the pass men; and, secon that the heads of all alike continue to grow for some years aft the age of 19.

The actual amount of difference as between the A and C students is, of course, small. On our scale it is just alwat inches-that is 3 per cent. on the real size of the bead. I this small difference to be regarded as significant? The answe can only be given by an appeal to the theory of statistics, which yields the following conclusions.

I must premise that the figures given here as average heal volumes were thus obtained. The average was taken of each 4 the three separate head-measurements (in the three directions

already explained) of each sub-class of students-e.g. of those of the A class who were 19 years of age; these three were then multiplied together, and the product resulting (in the case in question, 242'9) was entered in the table. What we have, therefore, is not strictly the mean of the products, but the product of the means. Theoretically, I apprehend, the former should have been preferred; but as the extra labour entailed would have been very great, and as the difference, when dealing with large numbers of cases and small amounts of divergence, is 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 determining the probable error of the individual head-volumes of the men generally. This is found to be, on the scale in question, about 17 inches. The usual formula for the difference between the means of 734 and of 487 would then assign to this difference a probable error of 17 x


734 487'

viz. nearly one inch. 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 that these were insignificant; and, had it been otherwise, the materials at our disposal would hardly have enabled us to make the due allowance. But, as the correspondent pointed out, the error is by no means to be neglected, and we have now the means of fairly estimating it. A considerable number of men have been measured five or six times, and some even oftener, whilst one man, who seems to have had a morbid love of this physical inspection, has actually had his various dimensions and capacities tested no less than eighteen times during the course of some three years. These cases have furnished a fair basis of determination. They show that these personal errors are certainly greater than they should be (they seem to arise in part from a certain looseness in the machine, which will be remedied In future), amounting in certain extreme cases to as much as even half an inch on the single measurement, and therefore to much more in what appears here as a "head-volume." The resultant probable error" from this fresh source of disturbance amounts to about five (cubic) inches. Those unfamiliar with probability may perhaps be staggered by such an admission, but they may be assured that the healing tendency of the averages. of large numbers is very great, and that the results remain substantially unaffected. The problem appears to be simply one of the superposition of two independent sources of error, and may be stated thus: Given a large number (over 2000) of magnitudes, with a mean of 239, and a "probable error," about this mean, of 17; and assume that these magnitudes are inaccurately measured with a further probable error of 5 inches (as seems to be the fact), what is the probable error of the divergence between the two averages obtained respectively from 734 and 487 of these results? The answer is still a little less than one inch. It, that is to say, an even chance that the two averages will not differ by more than this; and it is, consequently, thousands to one that they will not differ by so much as seven inches. The conclusions, therefore, previously drawn, lose little of their force.

It seems to me almost as certain that the size of the head continues to increase up to at any rate the age of 24. This will be made clear by looking at the following diagram, which is drawn to show the sum of the figures of the head-measurements as contained in Table III.

As regards the comparative physical endowments, in the other respects, of the different classes of students, there does not seem to be much to say. The differences-sometimes one way and sometimes the other-between them in respect of height, weight, breathing, and squeezing power, are so small as to be statistically insignificant, averaging only about I per cent. That the firstclass honour men, however, have slightly inferior eyesight seems established, especially when we bear in mind that each batch of about 1000 cases tells the same tale; the only evidence telling the other way is the fact, already adverted to, that when a class comprising "the best in ten," as regards eyesight, is

selected from the whole number, we do not find any appreciableintellectual selection to be thereby entailed.

An equally trustworthy basis of comparison is found by observing the distribution of the short-sighted men. Let us take as the limit of what shall be termed "short sight" the inability to read the diamond print with both eyes at a distance greater than ten inches. Adopting this test, we find that the A, B, C classes furnish respectively 14, 11, and II per cent., indicating a very small difference between them.


The general conclusion to be drawn here seems, then, to be this. With the single exception of eyesight-and this to a very slight extent it does not appear that intellectual superiority is in the slightest significant degree either correlated with any kind incidentally to produce any general superiority or inferiority. I of natural physical superiority or inferiority, or that it tends emphasize the word "general" in the last clause in order to allow for the difference shown in respect of pulling power. It seems probable, as has been already suggested, that the superiority of the non-honour men does not point to the slightest superiority of their general bodily development—as would be weight, or breathing capacity-but is solely brought about by indicated perhaps if it displayed itself in respect of their height, greater muscular exercise in the pursuit of certain athletic games.

So much as regards the first and second tables. As regards the third-which is arranged in order to show the development

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of the physical powers between 18 and 25-there is very little to be said, as statistics of this character offer no particular novelty. Such merit, therefore, as this may possess must depend mainly on the homogeneity of the class of men concerned. As indicated at the commencement of this paper, this homogeneity is equivalent to a considerable increase in the total numbers where more heterogeneous materials are dealt with. They appear to indicate that the physical powers, as a whole, culminate at the age of 22 or 23, and thence begin to steadily decline. Too much stress, however, must not be laid upon the rate of decline here, since the last subdivision is of a somewhat less homogeneous character than the others. For one thing, the men of twenty-five really include those also who are over that age, though these are relatively but few. Again, whilst the men up to 24 remain (for all statistical purposes) identically the same individuals, with a year or two more added on to their

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