amount in the male than in the female. Now if the only difference between the two sexes lies in one chromosome, it is conceivable that one X might be dropped from each sex, without disturbing the sex balance. Besides the paired chromosomes which were alike in both sexes, the female would now contain one X, the male none. It is possible that this hypothetical simpler condition actually preceded the other, that the X chromosome really was at first a structure developed in the egg and handed on by this route from mother to daughter as an exclusively female structure, very much as extra-nuclear structures or plastids (chromatophores) are handed on in certain plants, or in the egg of the green hydra, being never found in the male gamete. It may be also that this condition is realized in birds and moths, but of this more later. Now Wilson has shown, by comparative studies of the sex-determining mechanism of insects, that the single unpaired X of the male is apt to acquire a mate which he calls Y, of unknown origin and function but certainly of different nature from X. This is frequently much smaller than its synaptic mate, X, but in other cases is almost or quite as large as X, so that the chromosome count shows the same number of pairs in both sexes. Only comparative studies, coupled with experiments in sexlinked inheritance, show that throughout the series there is an odd or single X in the male, while in the female there is a pair of X's. The Y chromosome, which makes its appearance as a mate of the odd X, is now a purely male structure, counterpart of the hypothetical original single X of the female, and Schmidt's observations show that such a structure may perfectly well be a vehicle of transmission in heredity of characters which are the exclusive possession of males. For males would now form (as in Drosophila) two kinds of sperm, differing only in one respect. One type containing X would be female determining, the other type containing Y would be male determining when respectively they fertilized the single type of mature egg, which contained one X. If, however, by non-disjunction in

maturation an egg retained two X's and was fertilized by a Y sperm, it would of necessity develop into a female (2X) (as is the case in Drosophila, Bridges) which nevertheless would possess inherited characters previously possessed only by males, because of the presence of the Y. Eggs of this character might (as in Drosophila) produce four types of gametes, viz., XX and Y, or X and XY. Sperm also (as in Drosophila) might be produced of the classes X, Y, and XY. A great variety of possible combinations would result, as Bridges has shown in cases of nondisjunction in Drosophila. Of these various combinations, two sets might give rise to stable self-perpetuating systems of the Abraxas type, viz., (1) female XX-Y, in which the two X's are permanently united into a single body which acts as the synaptic mate of Y, while the male is Y-Y in formula; or (2) female X-Y with an increased potency of X sufficient to determine femaleness in single dose, male Y-Y. It is true that in Drosophila Bridges finds Y-Y zygotes non-viable but this is no evidence that Y-Y zygotes would be non-viable in all organisms. It is also true that he finds that the non-disjoining X's may later separate, but this would not preclude permanent union of two X's in other organisms.

On the other hand, it is conceivable that the poultry type of sex-linked inheritance may not have been derived from the Drosophila type at all but from a simpler primitive condition in which the female bore one X, the male no X. If in a species of this type, a Y chromosome appeared in the egg as the synaptic mate of X, it would necessarily go exclusively into those eggs which were to become males and would thus seem to be an exclusive male possession even though it had originated in a female. But the male which had received Y from his mother would now produce two types of sperm, Y and no- -Y. An egg transmitting Y, if fertilized by sperm also Y would produce a Y-Y male, which might prove to have greater survival value than the male which contained no Y or only a single Y. If this happened, the race would become permanently, female X-Y, male Y-Y, which in

so far as Y is concerned is exactly the condition demanded in the poultry type of sexlinked inheritance for a carrier of sex-linked characters. This line of thought leads to the following hypothetical outline of the evolution of sex-linked inheritance.

1. Sex-linked inheritance begins with the inclusion in the nucleus of the egg of a structure, X, perhaps originally found in the cytoplasm and handed on there from egg to egg in the female line, never in the male line. This structure is itself (or is attached to) the specific determiner of femaleness; it is an element which keeps the organism at the metabolic level of femaleness, its absence allowing the organism to drop down to the metabolic level of maleness. Characters (genes) located in X would pass only from mother to daughter. 2. From the foregoing state two divergent lines of evolution may have arisen.

(a) In one the X chromosome becomes duplicated in the female (perhaps by splitting at the reduction division) and is in consequence found in all eggs after maturation. It thus passes into male zygotes as well as female zygotes. The female will now be XX in formula, the male XO. Whatever inherited characters have their genes located in the X chromosome will now be transmitted as in Drosophila and man.

(b) A chromosome, Y, not concerned primarily in sex-determination, may develop as the synaptic mate of X in the egg; it would at once pass into male offspring and being transmitted in sperm cells would speedily produce the male type Y-Y. But in the female, Y would be kept from becoming duplex by the presence of X, the synaptic mate of Y. If Y contained genes, these would be transmitted as are the genes of sexlinked characters in poultry and other birds and in moths.

3. If in the Drosophila type of inheritance, Y should come to contain genes, these would be handed on from father to son, without ever entering a female zygote (Lebistes type). In the poultry type of sex-linked inheritance, Y would not afford a suitable mechanism for this one-sided type of inheritance, since Y

there passes into females. Hence the Lebistes type must be a further evolution of the Drosophila and human type, not of the poultry type. W. E. CASTLE

BUSSEY INSTITUTION, March 1, 1921

THE AMERICAN ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE SECTION A AND ASSOCIATED MATHEMATICAL ORGANIZATIONS

Section A of the American Association for the Advancement of Science met in Chicago on Wednesday morning, December 29, in joint session with the American Mathematical Society (Chicago Section), the Mathematical Association of America, and a group of persons interested in the History of Science.1 Professor D. R. Curtiss, chairman of the Section, presided. Professor O. D. Kellogg, of Harvard University, the retiring chairman, gave an address entitled "A decade of American mathematics." Professor Florian Cajori gave an illustrated address on "The evolution of algebraic notations.'' This meeting was attended by more than 200 persons, including 80 members of the American Mathematical Society and 150 members of the Mathematical Association of America.

At the business meeting following the program, the nominations made by the sectional committee (on December 27) were approved. These nominations, which were acted upon by the council of the association at its meeting of December 31st, were as follows:

I. For Chairman of the Section, who will preside at Toronto and give his retiring address at Boston, Oswald Veblen, Princeton University.

II. For Secretary of the Section, who will hold office until the meeting of 1924-25, William H. Roever, Washington University. According to the new constitution four instead of five members, in addition to the chairman and secretary, constitute the Sectional Committee. Therefore it was unnecessary to elect a member to succeed Professor H. L. Rietz, whose term expired with the Chicago meeting. The four members are: Dunham Jackson (January, 1920, to December, 1924), Minneapolis, Minn.; A. D. Pitcher (January, 1920, to December, 1923), Cleveland, Ohio; Gilbert A. Bliss (January, 1920, to December, 1922), Chicago, Illinois; James M. Page (January, 1 SCIENCE, February 18, 1921 (p. 164).

APRIL 8, 1921]

1920, to December, 1921), Charlotteville, Virginia. Professor D. R. Curtiss, Northwestern University, will give the retiring address at Toronto (19211922).

A joint dinner for mathematicians and astronomers was given at the Quadrangle Club of Chicago University on Wednesday evening, Decem

ber 29.

The following announcements concerning members of Section A are of special interest: (1) Professor E. H. Moore, head of the department of mathematics of the University of Chicago, was elected president of the American Association for the Advancement of Science.

(2) Professor G. A. Bliss, of the University of Chicago, was elected president of the American Mathematical Society.

was

(3) Professor G. A. Miller, of the University of Illinois, elected president of the Mathematical Association of America, and member of the executive committee of the council of the American Association for the Advancement of Science.

(4) The American Mathematical Society and the Mathematical Association of America were invited by the American Association for the Advancement of Science to become affiliated societies. As soon as these organizations officially accept the offer to affiliate, they will be represented on the council of the association by their respective secretaries, Professor R. G. D. Richardson, of Brown University, and Professor W. D. Cairns, of Oberlin College.

At the sessions of the American Mathematical Society on Wednesday afternoon and on Thursday, the following papers were read:

Construction of doubly periodic functions with singular points in the period parallelogram: PROFESSOR W. PAUL WEBBER.

(Sec

Boundary value problems with regular singular points: PROFESSOR H. J. ETTLINGER. ond paper.)

Note on the permutability of functions which have the same Schmidt fundamental functions: PROFESSOR E. W. CHITTENDEN.

On kernels which have no Fredholm fundamental functions: PROFESSOR CHITTENDEN.

Note on convergence in mean: PROFESSOR CHIT

Transformation of conjugate nets into conjugate
nets: PROFESSOR WILCZYNSKI.
Conditions under which one of two given closed
linear point sets may be thrown into the other
one by a continuous transformation of a plane
into itself: PROFESSOR R. L. MOORE.

A closed connected set of points which contains no
simple continuous arc: PROFESSOR MOORE.
On the history of symbols for n-factorial: PRO-
FESSOR FLORIAN CAJORI.

Homogeneous polynomials_with a multiplication theorem: PROFESSOR L. E. DICKSON. Applications of algebraic and hypercomplex numbers to the complete solution in integers of quadratic diophantine equations in several variables: PROFESSOR DICKSON.

Arithmetic of quaternions: PROFESSOR DICKSON. Determination of all general homogeneous poly

nomials expressible as determinants with linear elements: PROFESSOR DICKSON.

I-conjugate operators of an abelian group: PROFESSOR G. A. MILLER.

The integrals and associated divergent series: PROFESSOR W. D. MACMILLAN.

Elementary geometry in n-dimensions: PROFESSOR R. P. BAKER.

Note on an ambiguous case of approximation: PROFESSOR DUNHAM JACKSON.

On the method of least m-th powers for a set of simultaneous equations: PROFESSOR JACKSON. Note on the convergence of weighted trigonometric series: PROFESSOR JACKSON.

On polynomials and their residue systems: PROFESSOR AUBREY J. KEMPNER. (Second paper.) Expansion of the double frequency function into a series of Hermite's polynomials: PROFESSOR E. R. SMITH.

On amicable numbers and their generalizations: PROFESSOR T. E. MASON.

On the complete characterization of the set of points of "approximate" continuity: PROFESSOR HENRY BLUMBERG. Comparison of different line-geometric representations for functions of a complex variable: DR. GLADYS E. C. GIBBENS.

On the trigonometric representation of an ill-defined function: PROFESSOR DUNHAM JACKSON. An adaptation of Bing's paradox, involving an arbitrary a priori probability: PROFESSOR EDWARD L. DODD.

A convergence theorem of Osgood's with an application: PROFESSOR O. D. KELLOGG. Invariant points under transformations in function space: PROFESSORS G. D. BIRKHOFF and O. D. KELLOGG.

Fundamental points of potential theory: PROFESSOR G. C. EVANS.

Functionals of summable functions: PROFESSOR W. L. HART.

The papers of Professors Moore, Dodd and Evans, and the paper of Dr. Gibbens were read by title.

The New York meeting of the society was reported in SCIENCE of February 25.

At the sessions of the Mathematical Association of America on Tuesday and Wednesday afternoon the following papers were read:

Geometrical development of analytical ideas: PROFESSOR L. C. KARPINSKI, University of Michigan. The anharmonic ratio in projective geometry: PROFESSOR E. B. STOUFFER, University of Kansas. The association's ideal for expository papers: PROFESSOR E. J. WILCZYNSKI. (Introductory Note.) The first work on mathematics printed in the new world: PROFESSOR DAVID EUGENE SMITH, Columbia University.

Rolle's theorem and its generalizations: PROFESSOR A. J. KEMPNER, University of Illinois. Some geometrical aspects of the theory of relativity: PROFESSOR L. W. DOWLING, University of Wisconsin.

Note on the metric question from the historical standpoint": PROFESSOR L. C. KARPINSKI, University of Michigan.

General aspects of the problem of interpolation:
PROFESSOR DUNHAM JACKSON, University of
Minnesota.

Construction of double entry tables: PROFESSOR
A. A. BENNETT, in charge of the U. S. Ordnance
Ballistic Station, Baltimore, Md.
Certain general properties of functions: PROFESSOR
HENRY BLUMBERG, University of Illinois.

In addition to the election of Professor G. A. Miller as president of the Mathematical Association of America, the following elections were made:

For Vice-president: R. C. Archibald, Brown University; R. D. Carmichael, University of Illinois.

For Members of the Board of Trustees: A. A. Bennett, U. S. Ordnance Ballistic Station; Florian Cajori, University of California; H. L. Rietz, University of Iowa; D. E. Smith, Columbia University; C. F. Gummer, Queen's University.

Seventy-two individuals and three institutions were elected to membership and a Texas Section of the association was approved.

SYMPOSIUM

Our Present Knowledge of Methods of Corn
Breeding

Leader: H. K. HAYES, University of Minnesota, St. Paul, Minn.

The experimental basis for the present status of corn breeding: F. D. RICHEY. A review of experimental efforts to increase corn yields by breeding points to the following conelusions: (1) Mass selection on the basis of production of mature, sound grain per plant, under conditions of uniform stand and fertility, may be recommended as a means of at least maintaining yields. (2) There is no evidence that ear-to-row breeding can be relied upon to obtain increased yields commensurate with the cost. (3) First generation varietal crosses, and crosses or double crosses between pure lines, offer possibilities for obtaining larger yields; but the value of each combination must be determined experimentally. (4) The evidence as a whole shows clearly the value of selection in obtaining better adaptation to a specific environment and the value of hybrid vigor in obtaining larger yields. These principles, in connection with the Mendelian interpretation of heterosis as due to linked dominant growth factors, point to selection, hybridization, and further selection, all based on pure lines and controlled pollination, as the only sound basis for real corn improvement.

The bearing of modern genetic studies on corn breeding: R. A. EMERSON.

Corn breeding as a hobby: H. A. WALLACE. Eight rather late corn varieties were combined as pollinating parents with each of twenty rather early mother parents. Of these 160 combinations, 50 were tried out in comparison with the Iowa Station strain of Reids at Ames and the others were tried out at Des Moines. At both places a strain of Reids known as Iowa 10 proved to be the best of the eight as a pollinating parent and a Kentucky strain of Johnson Co. White proved to be poorest. During 1916, 1917, 1918 and 1919, the Iowa Station has tried out 287 hybrids and of these only 50 have outyielded the station strain of Reids. There is probably about one chance in one hundred of finding a cross of two distinct varieties which will prove to be an improvement on the best of the varieties now in use. The most promising cross so far discovered in Iowa is a cross of the Iowa Station strain of Reids with Argentine corn.

The author believes that there must eventually be special purpose corns such as 90-day corns, silage corns, etc., as well as standard grain vari

eties. He advocates as an aid to specialized corn breeding the formation of a Corn Record Association for the registration of promising selfed strains. By proper encouragement, he believes

that retired farmers could be interested in the development of selfed strains of corn as a hobby.

Progress report on the method of selection in self-fertilized lines: D. F. JONES. Selection in self-fertilized lines makes possible a control of the heredity from both the pollen parent and seed parent. Some seventy-five lines selected in this way and started from four different varieties chosen from among the best as grown in Connecticut have shown the usual segregation of type and reduction in vigor. Many clear-cut undesirable characters have appeared and are being eliminated. For example: fifteen lines have contained various forms of chlorophyll-deficient seedlings; ten, the "defective seed" factor; three, different forms of dwarf plants; two, golden plants; three, variegated plants; and five, various forms of sterility. Along with these outstanding weaknesses other marked variations in height, size of stalk, type of tassel and ear, and color of foliage have appeared. Such differences as these form the material for effective selection for productiveness.

,

Overcoming "root rot" by breeding: W. D. VALLEAU. In breeding for resistance to corn root rot, the fact should be kept in mind that diseasefree seed probably does not exist, under average field conditions. All plants examined in the field as well as those grown in the sand box have been found to be infected. Differences in time of death of plants of a given variety under field conditions are dependent on differences in resistance of the plants to root rot, and are not the result of planting diseased or disease-free seed. Various seed treatments, including all of those commonly recommended for small grains, have failed as a means of control. Attempts to obtain disease-free seed by harvesting before ripening and protecting ears from further infection has failed as infection occurs before the milk stage. Ears may be graded according to resistance by growing seedlings in a sand box and noting the time required for the individual seedlings to rot to the surface of the sand. By this method premature death of plants has been reduced from an average of 36.1 in the checks to 8.4 per cent. in the plants from the most resistant ears, An attempt is being made to obtain pure lines of the most resistant strains by self-pollination. Self-pollination, even for many years, does not materially reduce the number of days between

the death of the first and last plant from a given ear, over open-pollinated ears, in the sand box. Preliminary experiments indicate that field selection of seed from the longest-lived plants may prove a means of obtaining seed of a high degree of resistance.

Ear type selection and yield in corn: T. A. KIESSELBACH. From the seed standpoint, ear characteristics of dent corn fall into two classes, utilitarian and non-utilitarian. The utilitarian characters comprise those which indicate soundness and hereditary adaptation to certain environmental conditions. This adaptation can not be reliably forecasted by a mere ear examination. However, associated with marked differences in the plant growth habits resultant from corresponding regional differences in the environment (and especially climatic differences), are found rather distinct adaptive ear type characteristics. The more adverse plant growth conditions are for corn, the more nearly do the adapted types approach the small stalk, low leaf area, slender ear and smooth shallow kernel of flint corn. Approach of a balance or equilibrium between adverse environment and the plant and its ear type, is frequently spoken of as "running out" of the corn, whereas such a reaction is an actual betterment for

the prevailing conditions. The corn grower is coming to recognize the advantage of modifying his conception of ear type to harmonize with the environment of his locality. There is no such thing as a universal best type,

Progress report on corn disease investigations: JAMES R. HOLBERT. Cooperative investigations by the Bureau of Plant Industry and certain agricultural experiment stations during the past three years have shown that the root, stalk and ear rot diseases of corn are widely distributed in this country wherever corn is grown. These diseases have been found to be a limiting factor in corn production. They may be largely controlled by careful field selection of healthy, productive plants, physical selection of seed ears, and the proper use of the germination test, as described in Farmer's Bulletin 1176. The continued selection of seed according to these recommendations has been effective in improving a number of varieties of corn. Other means for control, such as the breeding of resistant varieties, soil sanitation, and the use of certain soil correctives, are being investigated.

The present status of continuous selection experiments with corn: L. H. SMITH. Several lines