# Popular Science Monthly/Volume 12/February 1878/Correspondence

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"THE TIDES."
To the Editor of the Popular Science Monthly.
I MAKE the following comments on Prof. Schneider's second article about "The "Tides." All the objections to the statements in the first article remain in full force. The chief points of this second installment are two: 1. The disturbing action of the sun on the moon's motion; 2. The fall of the earth and the moon below their respective tangents, whereby it is sought to be proved that the moon approaches the earth at the time of opposition. If these two statements are shown to be wholly in error, the second article goes the way of the first.
On page 231, December number of this Journal, we find this: "Thus our moon moves faster, and, by a radius drawn to the earth, describes an area greater for the time, and has its orbit less curved, and therefore approaches nearer to the earth in the syzygies than in the quadratures. . . . The moon's distance from the earth in the syzygies is to its distance in the quadratures, in round numbers, as 69 to 70."
This extract, which from its form would seem to be from a single paragraph, is in reality from two widely-separated parts of Newton's works, and is besides inaccurate. The phrase "in round numbers" is neither in the original nor in Motte's translation, but instead of it there is cœteris paribus, and it is hardly necessary to say that the phrases are not exactly equivalent. But let these slips pass. I give two other extracts from the "Principia," book iii., prop, xiv., cor. i.: "The fixed stars are immovable, seeing they keep the same positions to the aphelions and the nodes of the planets."
Herein is a double error:
Again, book iii., prop, xxxvii., cor. 3: "The density of the moon is to the density of the earth. . . . as 11 to 9."
This is very far from the truth, and scores of other mistakes in the "Principia" are known to those who are familiar with that work. So "the best of authority" is sometimes at fault, and his conclusions are not always to be accepted blindly and with-out investigation. But if they are to be so accepted, as Mr. Schneider's way of parading his authority seems to imply, would it not be better to accept Newton's theory of the tides, which is the true theory, and so make an end of it. But that theory excludes Prof. Schneider's.
If Newton's statement concerning the distance of the earth and moon in the syzygies and quadratures is to be taken without qualification, then it is plainly wrong; and the mathematical proof that it is wrong can be found more or less fully developed in any of the following works on astronomy, viz., those of Woodhouse, Herschel, Lardner, Gummere, Loomis, Norton, Olmsted, Robinson, and others.
Further, there is the practical proof of the correctness of the other view in the calculated and the observed positions of the moon for every hour of every day in every year, these positions being carefully noted by a score of observers every day. There is no more possibility of universal error in these observations and calculations than there is that a person who says that two and two are four should be in error on that point.
Prof. Schneider's first statement, then, is all wrong; and, this failing, the second goes with it. But it is also easily shown by his own figures that his conclusion should be exactly the opposite to what he makes it. He says, "The distance the earth falls, in one second of time, toward the sun is about .12144+ of an inch," the moon toward the sun .12084 of an inch, and the moon toward the earth .05386 of an inch. The expression "falling toward the sun" evidently means "falling from the tangent;" any other meaning is false and absurd. With the correctness of these numbers I have nothing to do. Consider them correct; then at the end of a second the earth and moon will be farther apart than they were at the beginning. Here is the proof:
In the accompanying figure let M be the place of the moon at opposition, E, that of the earth, and S the sun; A, the place of the moon at the end of a second; B, that of the earth at the same instant. Then, since the moon at opposition moves in a second about two-thirds of a mile farther than the earth, the curve M A is longer than E B, and A is farther to the right than B, and the moon at A is below the point C by .0538 of an inch: the quantity being ascertained by supposing the earth to stand fast, while the moon moves forward with the difference of their motions. On this there can be no disagreement. The distance C A is about two-thirds of a mile. But if A is below the tangent .12084 of an inch, and B .12144 of an inch below its tangent, then B is farther from A then when the bodies were at M and E respectively. When the earth is at B it is at the same distance from the sun as it was at E—i.e., E S and B S are ​equal, and the earth must fall below the tangent .12144 in order to keep its proper distance. The same is true of the moon: in going from C to A it falls below the tangent at C.0538 of an inch, and then is at the same distance from B as it was at C—i. e., B C and B A are equal. Prof. Schneider's
way of combining these numbers is unique. It is as if the moon had dropped toward the sun first .12084 of an inch, then .05386, while the earth had dropped toward the sun only .12144 of an inch. But Nature does not proceed in that way. The .05386 is a part of .12084, as the figure plainly shows. The .05386 is the moon's distance at A below the dotted line drawn from C, and .12084 is the moon's distance at A below the tangent drawn from M. It is easy to see that the latter includes the former. In the interest of science allow me to protest against such theories and such mathematics.
It is eminently right that we all should be earnest seekers of the truth, and it may not be out of place to suggest that the search should be diligently prosecuted till the truth is found, after which there will be ample time for its publication.
* R. W. McFarland,
* Professor of Mathematics and Civil Engineering, Ohio Agricultural and Mechanical College.
* Columbus, Ohio, November 24, 1877.
We can give no more space to this controversy.—Ed.
THE QUESTION OF REST FOR WOMAN.
To the Editor of the Popular Science Monthly.
Sir: May I be permitted to point out certain passages in the kind and careful review of my essay on the "Question of Rest," just published in your valuable journal, in which it seems to me that the reviewer has misunderstood the drift of the statements he criticises? Accepting entirely the general criticism on "the defects due to hasty preparation," I am yet loath that this haste should be made to appear to have had a wider influence than is really the case.
On page 242 the reviewer observes that the "author traced this result—painful menstruation—to a want cf occupation; while we should explain the lack of occupation by the incapacity resulting from the periodical pain." I believe the essay is guiltless of such an absurdity in physiological reasoning as an attempt to trace pain directly to a negative circumstance, which could only have an influence through the medium of various physiological conditions more or less directly associated with it, and hence induced by it. The inference drawn by the reviewer from the statistics is certainly incorrect, for the "unoccupied persons" referred to were so because their fortune rendered paid labor unnecessary, and for this reason it had not been undertaken. The cases where work, once begun, had been forcibly interrupted by an acquired habit of menstrual suffering are contained in the tables of painful cases.
The reviewer, page 242, second column, says that the essay admits "that, in regard to rest, the above data do not suffice to inform us of its influence," and goes on to conclude therefore that, "so far as the main theme of the book is concerned, the author leaves the question of rest in just the condition in which she found it." The statement quoted from the essay loses its real meaning by its abbreviation. It is not asserted that the data from the tables throw no light on the "question of rest," but only that from them we can have no means of deciding how far those women who acquired the habit of menstrual pain might have escaped it, had they from the beginning "rested" during menstruation, since in no case was rest found to be taken until it had become unavoidable. But the fact that so ​large a percentage of women, even in the "upper" classes, are shown never to feel the need of rest at this period; the fact that in so large a proportion of those who suffer the suffering dates from the first menstruation, and hence precedes the habits of occupation sometimes supposed to induce it; the fact that in no case did rest alone succeed in averting pain or in curing its cause, and hence proved anything but the "panacea" the reviewer supposes it to be (page 244)—these facts appear plainly on the tables of the essay, and are certainly of importance in regard to the question at issue.
For the reason already surmised it may be that the reviewer has failed to see that the third section of the essay, which he describes as "containing a review of the various theories of menstruation," is devoted not to summarizing these, but to criticising them; and that an effort is made to replace one of the famous current doctrines of menstruation by another, substantially in agreement with those universally held prior to the writings of Bischoff and Pouchet and Raciborski, but claiming to contain some original details and suggestions for a new line of experiment. This effort is, to the intention of the author, the main subject-matter of the essay. That the reviewer has either overlooked this, or its bearing on the conclusions, or has not deemed it so worthy of notice as lesser details, is shown by his remark that the "experiments" were made "before, after, and during ovulation" (page 243), whereas the essay has ranged itself upon the side of those more modern thinkers whose researches are tending to reject the famous ovulation theory.
The reviewer further criticises the essay for a "strained meaning put upon the word rhythmic," and for confounding "reproduction with the conditions essential to reproduction" (page 243). It is true that a philosophical conception of causation compels us to regard every phenomenon as the result of a chain of sequences, and thus every intermittent phenomenon recurring at regular periods as the result of a rhythmic chain of sequences; and thus, in one sense, there can be no antagonism between "periodical" and "rhythmic." But the essay was compelled to consider not only facts in themselves, but certain popular preoccupations about those facts, and especially in regard to the intermittence of the menstrual hæmorrhage. The aim of the essay has been to show that this phenomenon is only one of a chain succeeding each other as continuously as do those involved in the processes of digestion, a detail of a rhythmic movement accomplished in the organism, and not—as much popular belief goes—a periodical accident happening to it. Again, it is true that in the essay the term "reproduction" is used as equivalent for the process by which material is accumulated in the parent organism for the function of reproduction. This restriction is justified by examples of the eminent biologists who, studying reproduction in its most general and abstract aspect, consider the whole process as a form of nutrition. (I may mention, as one example out of many, the lectures of Claude Bernard, published in the "Revue des Cours Scientifiques" for 1874.) For all those classes of animals in whom the conjugation of reproductive cells is effected externally to the parent organisms, it is evident that the influence of reproduction upon those organisms terminates with the formation of the reproductive cells and the accumulation of the material required for their nutrition. Hence, philosophically speaking, the most general view of reproduction coincides exclusively with this nutritive process—its type is discoverable in vegetable organisms, and the varying phenomena of animal life involved in the conjugation of reproductive cells may be considered apart. For its special purposes the essay was doubly justified in using the term "reproduction" in the sense thus defined.
It is because the essay was exclusively concerned with menstruation that "the derangements due to matrimony receive no attention," although the reviewer, in the preceding rather singularly-worded sentence, implies that they should.
In the same sentence the reviewer declares that the "motive of the book [is] to demonstrate woman's capacity for continuous work during certain periods." The only "motive" of the book was the desire to inquire in what way the relations of the female nutrition to the cost of reproduction might be theoretically expected to modify the capacity for exertion of the female nervo-muscular system. The reviewer is certainly in error in saying that the author "does not inform us whether ill-arrangement of work has reference to time or not;" for many pages of the essay are devoted to showing—at least in the opinion of the author—that the question of time is of great importance in regard to the nervo-muscular energies of women, but not time in regard to the period of the menstrual hæmorrhages. Morbid conditions, entailed with other diseases of civilization, may compel reference to such time; but the real necessity lies much deeper, and (theoretically) should compel more frequent intermittences in exertion, in order, roughly speaking, to allow of the accumulation in the blood of reproductive material. The essential danger of overwork in women, aside from the dangers common to both sexes, is that, if due provision be not made for "the needs of supplemental nutrition," this will be formed at the expense of the nutrition of the parent ​organism, which must, therefore, deteriorate. The question of rest has been entirely restated in the essay. And only by overlooking this can the reviewer be led to conclude that the "author is reasoning against her convictions;" because, having admitted that excessive work may become a cause of menstrual pain, it is nevertheless insisted upon that there is nothing in the nature of menstruation to imply the necessity for rest; but that the connection between overwork and menstruul suffering is more recondite than has generally been perceived.
The closing sentence of the essay, referring to the large percentage of women shown to be real sufferers at menstruation, observes that, wherever such women are engaged in industrial or other pursuits under an employer, humanity would dictate that as much rest be afforded as practicable during the period of suffering. It is difficult, therefore, to understand where the reviewer finds the recommendation for women to continue to work under the "lash of necessity or duty," if they can help it (page 244). Pain is certainly, as the reviewer says, "the ideal curse of humanity," but the world is much too far from an ideal condition to render avoidance of pain a very practicable matter in the immense majority of cases.
On page 243 the reviewer curiously misinterprets a technical statement made in the essay. It is there asserted that pain depends on an "imperfect power of resistance in the nerve-centres," an assertion which is merely the special application of a general truism in physiology. The torments suffered by dyspeptics offer a familiar illustration of the manner in which a normally painless process may become a constantly-recurring source of irritation. But no one would say, as does the reviewer, in regard to the sentence quoted from the essay, that "this presupposes an inherent tendency to pain in all human beings during this act, its expression depending on the power of repression" (page 243).
Finally, I would beg leave to say that the hope of "closing the discussion and furnishing an authoritative canon to measure the value of the question" was far beyond the ambition of the writer of the essay. The difficulty on the practical side is not "the innate delicacy of the sex in arms against the statistician" (page 241), but the difficulty common to all biological investigations upon organisms subjected to complex conditions. Every one knows that no pure experiment is possible unless all conditions are eliminated except the one whose influence is to be estimated. The difficulties in the way exactly resemble (for instance) those besetting Dr. Bowditch's recent important investigation concerning the influence of damp soils in the etiology of consumption. Although the statistics presented in the essay are, unfortunately, much smaller than is desirable, yet it is fair to add that they are the most extensive published up to this time on the subject, with the exception of those of Brierre de Boismont, and quoted in the essay. Since the addition of his results to those of the essay does not in any way conflict with the conclusions of the latter, I think it may be doubted whether more extensive general statistics would throw any further light on the subject. To be of value, further data must offer definite points of comparison in regard to the working and luxurious classes of society, since it is a matter of common observation, not yet submitted to strict analysis, that the liability to menstrual suffering increases in proportion as we recede from the former class (at least when it is composed of peasantry) and approach the latter. The conclusion (provisional to more exact investigation) is certainly that the menstrual disorder is not inherent in the process, or in habits of exertion during the menstrual period, being, on the whole, less in those who work than in those who do not work; but that this suffering is ultimately traceable to modifications of the entire female organism imposed by one or more of the influences of a complex civilization, many of which are confessedly pernicious. It has been the modest aim of the essay to trace out some of these modifications, and indicate in what way they might be counteracted.
Mary Putnam-Jacobi.
"OPEN AIR AND HEALTH."
To the Editor of the Popular Science Monthly.
I trust you will not think me too intrusive by a comment which I desire to make on the article in the December issue of The Popular Science Monthly, on "Open Air and Health." I do this because I am very solicitous that your journal will only inculcate truth, such as we are able to know by the best heads and methods. I am of opinion that the article alluded to has a private end to boost, "a movement-cure institute," perhaps, and I am fortified in this by the false points of the essay. For instance, on page 221 it is said, "The lungs, like all mucous surfaces, secrete mucus," etc. It is needless to say that the lungs proper do not consist of mucous surface. This may, however, be a translator's stumble. But the same cannot be supposed of the following, page 223: "In the city night-air is always wholesomer than day-air, being both purer and stiller." How stillness makes it wholesome I am unable to conceive; indeed, with sewers, cesspools, and the filth of a thousand points, stillness is the most favorable for poisonous concentration, slowly diffused throughout ​the ambient air by the chemical law of gaseous diffusion. Does any one suppose that, amid sources of contamination, stagnant water would be purer than running? Had Dr. Niemeyer used his nose, or attended to its monitions in his midnight ramblings among the sick, he could never have penned such an erroneous sentence. Only solicitation that your journal shall occupy the highest grounds in all its selections animates this criticism from my pen.
* J. R. Black.
* Newark, Ohio, December 22, 1877.
"THE LAW OF CONTINUITY."
To the Editor of the Popular Science Monthly.
In the interest of scientific accuracy, I would call attention to one or two statements in the article on "The Law of Continuity," in your November number, which are either greatly strained or positively erroneous.
The author of the article in question says, speaking of sulphuric acid and water, "In all possible percentages do these liquids chemically combine, and this is at variance with the generally obeyed law of definite proportions" (page 32—the italics are mine). This is a very loose use of language, as may be easily demonstrated by a comparison of this passage with the statement of the fact by any scientific authority. For example, Fownes ("Manual of Chemistry," eleventh edition, p. 203) says: "The most concentrated sulphuric acid, or oil of vitriol, as it is often called, is a definite combination of 40 parts sulphuric oxide and 9 parts water. . . . Oil of vitriol is not the only hydrate of sulphuric oxide; three others are known to exist. When the fuming oil of vitriol of Nordhausen is exposed to a low temperature, a white crystalline substance separates, which is a hydrate containing half as much water as the common liquid acid. Further, a mixture of 98 parts of strong liquid acid and 18 parts of water, 2H$_2$OSO$_3$, or H$_2$SO$_4$H$_2$O, congeals and remains solid even at 7.2° C. (45° Fahr.)," etc. There is, then, in the case of sulphuric acid and water, at least, a clear enough distinction between mechanical mixture and chemical combination, although Mr. lies quite loses sight of it.
Then, again, he says (p. 30), "Science is unable to give us any metal but gold in a translucent state." The inability does not lie with "science." It has long been known that silver may, by chemical means, be obtained in a translucent film. And likewise platinum, aluminum, bismuth, copper, lead, iron, nickel, cobalt, palladium, zinc, cadmium, magnesium, and other metals, have been procured in a layer so thin as to be transparent (Wright, American Journal of Science and Arts, No. 73, January, 1877).
* Launcelot W. Andrews.
* Springfield, Mass., November 8, 1877.