The HOME SECRETARY and the FOREIGN SECRETARY of the ACADEMY The CHAIRMAN and the PERMANENT SECRETARY of the NATIONAL RESEARCH COUNCIL WILLIAM DUANE, '23 A. L. DAY, '22 R. G. HARRISON, '23 GANO DUNN, '22 J. M. CLARKE, '21 INFORMATION TO SUBSCRIBERS SUBSCRIPTIONS TO THE PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES at the rate of $5.00 per annum should be made payable to the National Academy of Sciences, and sent either to Easton, Pa., or to C. G. ABBOT, Home Secretary, National Academy of Sciences, Smithsonian Institution, Washington, D. C. Single numbers, $0.50. PAST publications of the NATIONAL ACADEMY OF SCIENCES are listed in these PROCEEDINGS, Volume III, pp. 743-753, December, 1917. In good part these publications are no longer available for distribution. Inquiries with regard to them should be addressed to the Home Secretary, National Academy of Sciences, Smithsonian Institution, Washington, D. Č. PAST volumes of the PROCEEDINGS may be obtained at five dollars per volume unless the sale of the volume would break a complete set of Volumes I to V. Single numbers may be obtained for fifty cents except where the sale of such numbers would break up a complete volume. Only two hundred complete sets of the Proceedings are available for sale-Volumes I to VI, price $30.00. Orders should be sent to the Home Secretary, National Academy of Sciences, Smithsonian Institution, Washington, D. C. The following publications are issued by the NATIONAL RESEARCH COUNCIL. Orders and inquiries should be addressed: Publication Office, National Research Council, 1701 Massachusetts, Ave., Washington, D. C. (A) THE BULLETIN OF THE NATIONAL RESEARCH COUNCIL published at irregular intervals; Price $5.00 per volume of about 500 pages; individual numbers priced variously. (B) THE REPRINT AND CIRCULAR SERIES OF the National Research COUNCIL, individual numbers, variously priced. OF THE NATIONAL ACADEMY OF SCIENCES Volume 7 MAY 15, 1921 Number 5 THE DIFFUSION OF AIR THROUGH WATER IN THE LAPSE OF YEARS1 BY CARL BARUS DEPARTMENT OF PHYSICS, BROWN UNIVERSITY Communicated January 10, 1921 In 1912 I put up a U-tube of the form annexed, containing a charge of water, ww', below the air chambers, aa', both at nearly atmospheric pressure. The tubes were sealed by fusion cautiously, to avoid the presence of flame faces in aa'. They were then put away in a dark vault of nearly constant temperature, for short time ranges, to be examined from time to time as to the displacement of the thread of water within: for it will be seen that the meniscus under a' is at a pressure excess of hpg as compared with the meniscus under a. If L is the total length of the thread of liquid in the tube, we may define the coefficient (k) of diffusion (by volume) by the equation v = Kat(hpg)/L where v is the volume diffusing at nearly constant mean pressure in the time t through an area a, the density of liquid being p = 1. Hence, where dh/dt is the loss of head per second. The factor 1⁄2 appears since the volume lost at a' appears at a, and their sum is equivalent to the loss of head. The amount of diffusion is so small that corrections may be disregarded. The observations made before the spring of 1914 were not satisfactory because of deficiencies. of method. They were, therefore, discarded. Measurement was thereafter made with the cath etometer. The following table gives the essential data for the interval of 6 years, 9 months and 6 days with the increment from leap years: K K The two values of x found are of the same order, but the one for tube II is definitely larger than the one for tube I. This may be due to infinitesimal difference in the separated gases (a,a') of the tubes. But since the tube II has a shorter (L) and wider column, and a meniscus nearer the bend, it is more probable that thermal correction is the cause of the difference; for the inside sectional area of II is about 2.2 times larger than that of I. The data obtained for x with a cylindrical cartesian diver (Carnegie Publications, No. 186, Washington, 1913, p. 21) about 3 cm. in diameter of 7.05 cm2. in area, are enormously larger than the above, reading a = 90 X 10-12. The result is in keeping with the enormously larger area and consequent effectiveness of the solution-temperature mechanism which I have described in the preceding paper. Whether in case of tube I, a condition of true diffusion has been reached will have to be ascertained in the lapse of further years. Meanwhile the question whether a long slender cartesian diver may not obviate the discrepancies hitherto encountered is worth consideration. 1 Advance note from a Report to the Carnegie Institution, Washington, D. C. 2 These PROCEEDINGS, 6, 1920 (495-8). THE INFLUENCE OF AGE ON FERTILITY IN SWINE 1 BY TAGE ELLINGER Communicated by R. Pearl, March 10, 1921 In the breeding of domestic animals the problem of fertility is of prime importance. The neglect of this essential factor has again and again caused breeders disappointments and often heavy economic losses. Thus it is desirable to study this chapter of the physiology of reproduction thoroughly and to examine the factors, internal and external, that affect the ability to produce offspring. During an investigation on these subjects, in this laboratory the results of which are soon to be published, the writer has been confronted with the question of the influence of age of the sow on the size of her litters. Although a number of records on this and similar subjects have been published from time to time, the writer is of the opinion that the special qualities of his material, and the mathematical treatment of it that it is possible to employ, justify this further publication. In going over the literature on the influence of age on fertility in mammals, a number of records bearing on the question can be collected. Sarah V. Johes and James E. Rouse1o have in a recent paper give an extensive summary of the literature, to which paper I only need to refer for further information. The records published are of two different kinds. First: results of experiments chiefly with rats (King"), rabbits (Hammond3), and guineapigs (Minot14). The experiments on swine by Mumford15 (1917) are of further interest in this connection. The second group consists of statistical investigations generally using as material the numerous records given in the herd books of the different breeds of domestic animals. Carlyle and Mc Connell, Pearl, 16 Bell,3,4 Humphrey and Kleinheinz, Jones and Rouse 10 give records showing that the percentage of multiple births in sheep increases with age up to five years and then again declines. Pearl16 and Jones and Rouse10 give similar data for cattle showing a steady increase in the percentage of twin births with age. Swine have often been subject to investigations of this kind. One of two sources of error have always been present in these. 1. The number of individuals involved have been so limited as to make dependable results unobtainable, or 2. The method of computing has been so rough as to give room for the effect of selection. The usual way of approaching the problem has been to take from herd book records of all available litters and to refer them to the age of their mothers at their birth. In this way it is possible to get a great number of litters from young sows but rather few from older ones as the less desirable animals are disposed of early. The older sows represent only a selected group of the best of those recorded at an early age, and the average size of litters at different ages of the sows are for that reason not directly comparable. Owing to these difficulties the results are very contradictory and uncertain. Rommel18 found a steady increase in size of litter from one to five years. Frölich and Georgs report a maximum in the second litter and then a decrease in size of the the litters. Machens12 claims a maximum at the fourth litter. Carmichael and Rice' give a table showing an increase in fertility to the third year followed by a decrease. 2. The material used in this investigation consists of 134 sows of native Danish breed2 which all have records from all of their first ten litters. The records are taken from the Danish herd book Vols. V and VII. All these sows have been kept in state-supervised breeding centres under uniform conditions and care. They have all farrowed the first time at about one year of age and from then on been bred regularly producing ca. 214 litter per year, practically without regard to season. The successive litters will for that reason be highly correlated with age, but it seems most convenient to use the litter-number as unit. The average of all litters, being 11.5 pigs, is far above the average shown by swine of the American type, and although these 134 sows undoubtedly are selected group, the great fertility is one of the outstanding and valuable qualities of the breed. The dots indicate the actual found averages for litter-size in the first ten litters. The curve is fitted to these valves. In the second column of table 1 the average sizes of the successive ten litters are given. Plotting the series of average values over a base indicating the successive generations (fig. 1) we see that they show an increase in fertility |