The sloping line AB passes through all possible mid-parental heights. The sloping line CD passes through all the corresponding mean heights of their children. It gives the "smoothed" results of the actual observations. The ratio of CM to AM is as 2 to 3, and this same ratio connects the deviate of every mid-parental value with the mean deviate of its offspring. The point of convergence is at the level of mediocrity, which is 684 inches. The above data are derived from the 928 adult children of 205 mid-parents, female statures having in every case been converted to their male equivalents by multiplying each of them by 1.08. Fig. b. Forecasts of stature. This is a diagram of the mechanism by which the most probable heights of the sons and daughters can be foretold, from the data of the heights of each of their parents. The weights M and F have to be set opposite to the heights of the mother and father on their respective scales; then the weight sd will show the most probable heights of a son and daughter on the corresponding scales. In every one of these cases it is the fiducial mark in the middle of each weight by which the reading is to be made. But, in addition to this, the length of the weight sd is so arranged that it is an equal chance (an even bet) that the height of each son or each daughter will lie within the range defined by the upper and lower edge of the weight, on their respective scales. The length of sd is 3 inches 2f; that is, 2 x 1.50 inch. = A, B, and C are three thin wheels with grooves round their edges. They are screwed together so as to form a single piece that turns easily on its axis. The weights M and F are attached to either end of a thread that passes over the movable pulley D. The pulley itself hangs from a thread which is wrapped two or three times round the groove of B and is then secured to the wheel. The weight sd hangs from a thread that is wrapped in the same direction two or three times round the groove of A, and is then secured to the wheel. The diameter of A is to that of B as 2 to 3. Lastly, a thread wrapped in the opposite direction round the wheel C, which may have any convenient diameter, is attached to a counterpoise. It is obvious that raising M will cause F to fall, and vice versâ, without affecting the wheels AB, and therefore without affecting sd; that is to say, the parental differences may be varied indefinitely without affecting the stature of the children, so long as the midparental height is unchanged. But if the mid-parental height is changed, then that of sd will be changed to of the amount. The scale of female heights differs from that of the males, each female height being laid down in the position which would be occupied by its male equivalent. Thus 56 is written in the position of 60.48 inches, which is equal to 56 × 1:08. Similarly, 60 is written in the position of 64-80, which is equal to 60 × 1·08. In the actual machine the weights run in grooves. It is also taller and has a longer scale than is shown in the figure, which is somewhat shortened for want of space. Plate X. This is a diagram based on Table I. The figures in it were first "smoothed" as described in the memoir, then lines were drawn through points corresponding to the same values, just as isobars or isotherms are drawn. These lines, as already stated, formed ellipses. I have also explained how calculation showed that they were true ellipses, and verified the values I had obtained of the relation of their major to their minor axes, of the inclination of these to the coordinates passing through their common centre, and so forth. The ellipse in the figure is one of these. The numerals are not directly derived from the smoothed results just spoken of, but are rough interpolations so as to suit their present positions. It will be noticed that each horizontal line grows to a maximum and then symmetrically diminishes, and that the same is true of each vertical line. It will also be seen that the loci of maxima in these follow the lines ON and OM, which are respectively inclined to their adjacent coordinates at the gradients of 2 to 3, and of 1 to 3. If there had been no regression, but if like bred like, then OM and ON would both have coincided with the diagonal OL, in fig. a, as shown by the dotted lines. I annex a comparison between calculated and observed results. The latter are inclosed in brackets. Given "Probable error of each system of mid-parentages = 1.22. Ratio of mean filial regression = 3. "Probable error "of each system of regressed values = 1.50. Sections of surface of frequency parallel to XY are true ellipses. [Obs. Apparently true ellipses.] MX YO 6: 175, or nearly 1: 3. = [Obs.-1: 3.] Major axes to minor axes = √7: √ 2 = 10 : 5·35. [Obs.-25°.] Section of surface parallel to XY is a true curve of frequency. [Obs. Apparently so.] "Probable error " of that curve = 1.07. [Obs.-10 or a little more.] The DOLMENS of BRITTANY. THE following remarks by Mr. A. L. LEWIS on Admiral Tremlett's paper on "The Sculptured Dolmens of Brittany" should have appeared at page 113 of the last number of the "Journal":— Mr. LEWIS said the Institute was fortunate in receiving papers on this subject from Admiral Tremlett, since he had not only spent much time in each of a number of years on the spot, but had inherited the "unexhausted improvements" of his brother-in-law, the late James Miln. It was very remarkable that the inscribed dolmens should be contained in so small an area while there were so very many uninscribed ones outside that area. The suggestion that they had been built or had been ornamented by people landing casually was not tenable, for the ornaments had, in some cases at least, been cut on the stones before they were placed in position, and, except the ornamentation, there was no difference between those and the other dolmens; the suggestion that this area was inhabited by a special tribe did not commend itself to his mind, and he thought it more likely that these dolmens were the tombs of persons of a special rank or class. While it was possible that the custom of erecting dolmens and menhirs might very occasionally have been continued into and even beyond Roman times, the things found in them were almost without exception Celtic, and included very large quantities of stone implements. The country appeared to be full of Roman remains, but these were on the top of the mounds, and Mr. Miln had found Roman walls built over fallen menhirs in the middle of an alignment, proving the pre-Roman date of the alignments beyond the possibility of doubt. Mr. Miln's sumptuous book, containing the details of this discovery, had been placed by Admiral Tremlett in the library of the Institute, so that it could be consulted by any member. FRANCIS GALTON, Esq., M.A., F.R.S., President, in the Chair. The Minutes of the last meeting were read and signed. The following presents were announced, and thanks voted to the respective donors : FOR THE LIBRARY. From LORD ARTHUR RUSSELL, M.P.-Correspondence relating to the Native Population of Fiji. From the UNITED STATES GEOLOGICAL SURVEY.-The_Copper- Les Récents Voyages des Néerlandais à la Nouvelle-Guinée. Remarks upon Chipped Stone Implements. By F. W. Putnam. Les Primitifs. By Elie Reclus. The Iroquois Book of Rites. By Horatio Hale, M.A. From the ACADEMY.-Atti della Reale Accademia dei Lincei. Serie Boletin de la Accademia Nacional de Ciencias en Cordoba. From the INSTITUTION. Journal of the Royal United Service Institution. No. 129. VOL. XV. T From the SOCIETY.-Transactions of the Geological Society of Glasgow. Vol. VII, Part 2. Journal of the Society of Arts. Nos 1699, 1700. VI-VII. Jahresbericht des Vereins für Erdkunde zu Metz für 1883-1884. From the EDITOR.-The American Antiquarian. Vol. VII, No. 3. Matériaux pour l'Histoire de l'Homme. June, 1885. The election of the following new Members was announced:- CADELL, V.C.; C. HEAPE, Esq.; H. H. JOHNSTON, Esq.; LADY BRASSEY exhibited a large collection of objects of ethnological interest from Polynesia. MISS NORTH exhibited several ethnological specimens from New Ireland. Mr. CARL LUMHOLTZ exhibited a series of Australian imple ments. The following paper was read by the author, and illustrated by an exhibition of objects made by the Solomon Islanders : On the PHYSICAL CHARACTERS of the SOLOMON ISLANDERS. By H. B. GUPPY, M.B., F.G.S., late Surgeon of H.M.S. “Lark.” THESE observations, which were made between 1881 and 1884, were confined for the most part to the natives of the opposite extremities of the group, at the eastern extremity to the natives of St. Christoval and of the adjoining small islands of Ugi, Santa Anna, and Santa Catalina, and towards the opposite extremity to the natives of the islands of Bougainville Straits, which include Treasury Island, the Shortland Islands, Faro Island, together with Choiseul Bay. Observations, although fewer in number, were also made on the natives of the following intermediate islands, viz., Malayta, the Florida Islands, and Simbo or Eddystone Island. All the measurements, unless otherwise stated, refer to male adults and with these preliminary remarks, I will at once proceed to describe the physical characters in their order. |