is rather curious. Why "must" a tetrad be equal to ? Why "must" b four be equal to two in order to satisfy the conditions of the case?

somes.

In my first paper on the subject ('95, p. 9-13) it is stated that in the spermatogonia there are 12 univalent chromosomes which divide longitudinally or by the equation division of WEISMANN. In the growth-stage, during which the spermatogonia become the spermatocytes, the chromatic granules group themselves into 24 chromoThese 24 chromosomes become arranged in pairs, the individual chromosomes of each pair being connected with each other by a considerable number of linin threads. Later the pairs become associated together in tetrads by a process of conjugation. From this conjugation we get as a result the quadrivalent chromatic rings of VOM RATH. In the first maturation division these tetrads are separated, each into two bivalent chromatic bodies which consist of two chromosomes held together by linin threads. During the next division, these pairs of chromosomes are separated into single chromosomes. The number of chromosomes in the spermatogonia as well as in the somatic cells is 12. During the prophases of the first division of the spermatocytes 24 chromosomes appear in the form of 6 tetrads. The spermatocytes of the second order receive each 12 chromosomes in the form of 6 pairs of chromosomes. Finally the spermatids receive 6 chromosomes. Or, to state the matter in still another way, the normal number of chromosomes is at first doubled, and afterwards, by the two maturation divisions, reduced first to 12 and then to 6.

Now, if in the prophases of the first maturation division it were true that, as WILSON attempts to explain my account, "the 12 dumbbell-shaped primary segments must therefore represent single chromosomes, not bivalent ones", it would manifestly be quite impossible for the spermatids to receive each 6 chromosomes, without the assumption of a splitting of the chromosomes. But I was unable to find any evidence of a splitting of the chromosomes during the two maturation divisions, and stated my belief that in my material it did not occur. The original statement is therefore not self contradictory, but it evidently would be contradictory, if the substitution of values proposed by WILSON should be made.

WILSON'S arithmetical difficulties in understanding my account are created by his own method of interpretation. In my first paper ('95) I took some pains to make clear the assertion that in the spireme stage of the spermatocytes of the first order 24 chromosomes arise. WILSON's statement that "Each of these dumbbell-shaped bodies

is assumed to be a bivalent chromosome, and the tetrad formation is therefore interpreted as follows: - abcd-l (spireme) ab-cd-kl (segmented spireme)" etc. is incorrect in so far as the formules are concerned. The number of letters from a to l inclusive is 12. I distinctly maintained that the number of chromosomes in the spireme stage is 24. ab When I proposed the formula. for a tetrad in Caloptenus, my only cd purpose was to use a formula which would indicate that all the four chromosomes of a tetrad are unlike, and hat I thought it necessary, to avoid misunderstanding, to give letters for all the chromosomes, the complete formula would plainly have been not abcd-l but abcd-x, which latter series amounts to 24 in number. As a matter of fact I have nowhere used the formula abcd-l. This formula is, therefore, not my interpretation of the spireme-stage in the formation of tetrads and I can scarcely be held accountable for the difficulties which this interpretation entails.

So much für the arithmetical side of the matter.

a b

A much more interesting question is raised by WILSON'S assumption that a tetrad must not be made up of four unlike chromosomes. To quote again from WILSON, "his primary tetrad must therefore be ab not as he assumes, but either or (if we assume that the cd normal number of chromosomes undergoes a preliminary doubling) aa" Underlying this statement there is manifestly the assumption bb that a doubling of the chromosomes involves a division of the chromosomes which is qualitatively and also quantitatively an exact halving. This assumption simply begs the whole question under discussion. As far as I can discover, the only essential point on which we differ is just the point which WILSON settles by an assumption. Is there in all cases a preliminary longitudinal splitting of the chromatic thread in the spireme stage? WILSON believes that there always is such a longitudinal splitting, relying upon the work of VOM RATH, HÄCKER, RÜCKERT and others. I have maintained that in Caloptenus there is no longitudinal splitting. To assume that even in Caloptenus there must be a longitudinal splitting is certainly no argument against my position, nor is it at all apparent how this assumption shows my account to be self-contradictory. But if in the place of my formula ab for the tetrad we should substitute WILSON's proposed formula c d'

the account would then be plainly self-contradictory.

It

aa

would, in my opinion, be sheer nonsense for me to use the formula bb

for a tetrad whose four component chromosomes according to my account are all unlike one another.

Thus we have seen that either of WILSON's proposed substitutes for my formula would, if adopted, render the account self-contra

a

dictory. If we should adopt the formula each spermatid could

aa bb

receive but 3 chromosomes, whereas each spermatid actually receives 6. If we adopt the formula this implies a longitudinal splitting which I claim does not take place in Caloptenus. The proposed formulas, therefore, instead of obviating difficulties and self-contradictions, as WILSON asserts, only serve to introduce such contradictions and to create glaring inconsistencies, which do not exist in the original account.

The account which I gave of the spermatogenesis of Caloptenus differs in some respects from most other accounts of the spermatogenesis of animals. In accordance with nearly all spermatologists I found a doubling of the normal number of chromosomes in the prophases of the first maturation division. But this doubling, I maintained, was, in Caloptenus, not due to a longitudinal splitting of the chromosomes. In the spireme of spermatocytes of the first order the chromosomes were described as arising separately and independently of one another. The chromosomes then became associated in pairs the individuals of which are held together by linin threads.

Later the pairs by conjugation form tetrads. The four components

of a tetrad are therefore all unlike one another and the formula could certainly not be used for such a tetrad.

aa

b|b

We have, moreover, no right to assume that a doubling of the chromosomes necessarily implies a longitudinal splitting. WAGNER ('92) indicates that such a splitting is not necessary to a doubling of the chromosomes. GODLEWSKI ('97) saw no longitudinal splitting in Helix. If, as I maintained in the case of Caloptenus, no splitting is to be observed, and the chromosomes arise by an aggregation of the minute chromatic granules into a definite and constant number of chromatic bodies or chromosomes, no two of these bodies can be assumed to be qualitatively identical, and the formula for a tetrad bb

composed of four such chromosomes is out of the dumbbell-shaped bodies of which I have spoken are

aa

question. The not, as WILSON

seems to suppose, continuous masses of chromatic substance but each one consists of two distinct chromosomes connected by linin threads, and should therefore be designated by ab or any other two letters, and not, as WILSON's formula would require, by aa or bb.

We have abundant reason to believe from the divergent published accounts of the two maturation divisions that the processes are not so remarkably uniform in all animals as to admit only one formula for all. It is quite probable that the observed and recorded instances are but the various manifestations of a more fundamental law which is as yet not even formulated. The progress of biology has exhibited a frequent mistaking of special instances for the general law, and that may be the case in this particular field.

Believing that he had discovered inherent inconsistencies in my published account, WILSON apparently did not deem it necessary to offer any real criticism of my position. But since I have shown that WILSON'S remarks are based on an erroneous interpretation, the case simply stands as it was.

Bozeman, Mont., Oct. 29, 1897.

Literature cited.

'92 WAGNER, J., A Review of the present Condition of the Question as to the Existence and Meaning of Fertilization. (Russian.) Rev. des sci. nat., St. Pétersbourg.

'95 WILCOX, E. V., Spermatogenesis of Caloptenus femur-rubrum and Cicada tibicen. Bull. Mus. Comp. Zoöl. Harvard College, Vol. XXVII, No. 1, p. 1-32, Pl. I—V.

'96 WILSON, E. B., The Cell in Development and Inheritance. New York, The Macmillan Co.

'97 GODLEWSKI, E. jun., Ueber mehrfache bipolare Mitose bei der Spermatogenese von Helix pomatia L. Anz. der Akad. der Wiss. in Krakau, p. 68–81.

[Reprinted from the Proceedings of the National Educational Association, 1897.]

ZOOLOGY IN THE HIGH-SCHOOL CURRICULUM.

BY HENRY BALDWIN WARD, UNIVERSITY OF NEBRASKA.

A long time has elapsed since Bacon gave to the world the sound advice that "we should accustom ourselves to things themselves." Little by little this idea has gained ground, until now it is recognized as a general principle in every grade of educational work and in widely separated departments of study that contact with concrete objects is far more inspiring and thought-producing than the mere scanning of black marks on a white page. So far as natural science is concerned, the varied training which it affords has been abundantly discussed before this association and elsewhere. To be sure, its practical value was for many years, unfortunately, the chief, or even the only, reason advanced for its importance from the educational standpoint. But of late attention has been directed to more fundamental considerations, prominent among which. may be mentioned the interest always aroused and, consequently, developed by it along a "line of least resistance." It was reserved for the work of this Natural Science Department last year to furnish through the papers of two able educators specific demonstration of what many of us have felt for years, that natural science possesses a culture value in education as well as practical worth, and that, furthermore, its culture value is not a whit less important or less necessary than that of certain educational shibboleths. In fact, the educational world is just coming to believe what Louis Agassiz maintained more than twenty-five years ago: "A few weeks' training in natural science is the best preparation a man can have for work in any department of life."

The right of natural science to a place in the curriculum of our schools is still less open to question, since its introduction in various places has been productive of such favorable results. These have been

attained in spite of many adverse circumstances: lack of knowledge on the part of the teachers of both the subject-matter and of the method of teaching it; lack of facilities in schools, and not only lack of sympathy, but even active and violent opposition in many cases, from the public. All this is rapidly passing away; natural science has won its place. But there still exist differences of opinion with reference to the time and, especially, with regard to the manner in which it shall be studied. It is my purpose to discuss these questions briefly, as far as they concern the