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THE

THURSDAY, OCTOBER 12, 1871

RECENT UTTERANCES

HE Oracle has spoken. In fact several Oracles have spoken. Let us take them seriatim. From the lips of two of the most enlightened members of the Cabinet we have had at last an authoritative expression of the desirability - nay more, of the absolute necessity of scientific education for the country at large. Addressing his constituents at Bradford on Monday the 2nd inst. in a speech to which we have already alluded, on the occasion of the opening of the new Mechanics' Institute for that town, Mr. W. E. Forster, the Minister for Education, as he ought to be styled, made use of the following emphatic language :-"The old grammar-school teaching was almost framed upon the advantage that Latin and Greek well taught gave to the boys; now, we find that the boys cannot do without the use of more general knowledge than is given by Latin and Greek, that there must be a knowledge of modern languages. But there may be also a feeling that we ought to know something of the daily facts of life, and the rudiments of Science. There, again, I speak from a sense of my own want, and I have often thought how much more useful I might have been at any rate, how much stronger I might have been-if I had had given to me a scientific education, such as I think we may now hope that our children will attain." And again: "We now believe that we have taken measures by which we may secure elementary education to all children of all classes in our borough, and throughout the country, and, consequently, those who attend this institution will have the foundation of a training that will enable them to fulfil the original idea of its promoters," that is, " to give mechanics scientific knowledge."

On the following day Lord Granville, the Secretary of State for Foreign Affairs, when presiding at the opening of the Dover College (intended to provide, at a very moderate cost, a first-class English and classical education), took the opportunity to make the following pertinent remarks:-" Then there is the study of Science in its different departments. I believe this to be eminently wise, and a matter to which parents in the present day attach very great importance. I believe the results of this branch of education are of considerable consequence; for after all, a mere smattering of education is of very little use in any department, but a really scientific mode of studying different branches of Science is one of the best and most useful instruments of education you can use, I remember reading a very remarkable speech, with most of which I agree, delivered by Mr. John Stuart Mill, on the difficulties of a comprehensive education. He said the study of Science taught young men to think, while the study of Classics gave them the power of expressing their thoughts. I own I have thought there is some little fallacy in the distinction drawn between the education taught in these two departments. I believe it is almost impossible for a man to study the ancient languages without himself acquiring great habits of thought, and I daresay you have all had opportunities of hearing some of the most distinguished professors, some now dead and others living, who have conveyed their thoughts to their audiences in such singularly clear and perfectly eloquent language, that

VOL. IV.

I feel there is something in the study of Science which makes a man feel that in what he is talking about, he must eschew all redundant and irrelevant verbiage."

The significance of these outcomes is not to be mistaken, and Lord Granville's remarks are of none the less authority because he does not happen to be our Home Secretary. His knowledge of the state of education in some other European countries has doubtless made him all the more sensible to the lamentable defects of our own. Of the other leading members of the Cabinet, Mr. Gladstone is too far-seeing a man to oppose the manifest tendencies of the age, Mr. Lowe has shown himself ready to respond to every legitimate demand made on the public purse by the proper representatives of the wants of Science, and the Duke of Argyll is himself a writer on Science. While we cannot but congratulate ourselves that our rulers are at length alive to the importance of making Science the base of all true education, a necessity we have so constantly and earnestly insisted on, we still cannot but inquire how it is that all this has been so long in making itself self-evident to our public men. In the same address from which we have already quoted, Mr. Forster pointed out that the original design of the founders of Mechanics' Institutes was to give a scientific education to the working classes; but that they soon found that there was an almost universally spread absolute ignorance of even the most elementary facts on which a scientific education could be based. And yet all these years have been allowed to pass, and it is only yesterday, as it were, that any serious attempt has been made to provide a scientific education for the working classes. We are even surprised to find that the first advances made by teachers of science in this direction are met by an eagerness and enthusiasm which will soon outstrip the limited means at command to satisfy its cravings. In the higher strata of society it is the same; wherever the elements of science, natural or physical, are taught by a competent teacher, they are absorbed by boys and girls, and grown-up men and women too, with a zeal seldom bestowed on their Latin or Mathematics; there is something in these studies which the human mind finds really to respond to its own instincts. If the next generation of Englishmen does not grow up with more than a smattering of the rudiments of science, it will be the fault of the present teachers of science themselves.

From men of high position but out of the Cabinet, who are clear-sighted enough to discern the wants of the age, we hear the same demands on every side. Sir J. Lubbock the other day, in addressing a meeting of working men at Liverpool, after delivering the prizes in connection with science classes, said that scientific men throughout the country unanimously regretted the manner in which the grants to elementary schools are distributed. Reading, writing, and arithmetic, although the foundations of education, are not education itself, and the schools will never be placed on a sound and satisfactory basis until they take a wider ground. And at the meeting of the Social Science Congress, held during the present week at Leeds, Mr. Joseph Payne, than whom no more practical authority could be found, read a paper on scientific teaching and the advantages of mental discipline for children, approving of the cultivation of the faculties of observation and experiment and direct training from nature. Science teach

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ing, and not literary teaching, he said, ought to be the basis of all other knowledge.

One of the best recent utterances on the relation of the State towards Science is contained in the address of Prof. Huxley, delivered at Birmingham on Monday last, as president of the Birmingham and Midland Institute. In this admirable discourse he spoke of the principles of governing, and the relation of the State to its members, in a manner which enables us to congratulate ourselves

that Prof. Huxley is no longer among the advocates of the limitation of State functions. He repudiated the idea of the functions of a Government being confined to those of a protective constabulary. Adopting the definition that the end of Government would be the good of mankind, he said he took it that the good of mankind meant the attainment by everyone of all the happiness which he could enjoy without diminishing the happiness of his fellow-men. The pursuits in which pleasure and happiness could be enjoyed by all, with detriment to none, were those which ought to be smiled upon by the State. If it were beyond the province of the State to interfere directly in commerce and the individual relations of men, it might safely foster these indirectly. He urged that it was the duty of Government to take the initiative in promoting the teaching of Science, leaving local energy, as soon as it could be evoked, to develop the work. The State should understand that local scientific institutions such as those at Birmingham, Manchester, and Newcastle-on-Tyne do not benefit the locality alone, but the nation at large. With regard to the effects of Government subsidies on private enterprise, Prof. Huxley clearly showed how baseless are the grounds of alarm on this head. There are those who maintain that the State has no right to do anything but protect its subjects from oppression, but even "accepting the proposition that the functions of the State might all be summed up in one great negative commandment, 'Thou shalt not allow any man to interfere with the liberty of any other man,' Prof. Huxley said he was unable to see that the consequence was any such restriction as its supporters implied. If his next door neighbour chose to have his drains in such a state as to create a poisonous atmosphere which he breathed at the risk of typhus and diphtheria, it was just as much a restriction on his just freedom to live as if his life was threatened with a pistol. If his neighbour were allowed to let his children go unvaccinated, he might just as well be allowed to leave strychnine lozenges about in the way of his (Prof. Huxley's) children. And if his neighbour brought up his children untaught and untrained to earn their living, he was doing his best to restrict his (the lecturer's) freedom by increasing the burden of taxation for the support of gaols and workhouses for which he had to pay."

There is nothing new in these utterances, nothing that was not obvious to thinking men years and years ago; but they are of the highest importance nevertheless, for we may now hope that their lead will be followed in our English fashion throughout the length and breadth of the land. It was wisely said not long ago, that one of the most certain ways to make the study of Science national would be to make Science itself fashionable. This is true, and we may now hope that this task will for the future fall on Cabinet Ministers and the like, for scientific men who attempt it are apt to become martyrs to the good cause.

THE LAWS OF POPULATION

1. Population: its Laws of Increase. By Nathan Allen M.D. (Lowell, Mass., 1870.)

2. Physical Degeneracy. By the same. (New York: Appleton and Co., 1870.)

3.

The Law of Human Increase. By the same. DR. NATHAN ALLEN, in three pamphlets, of which

the titles are given above, discusses different aspects of a question of grave importance to American society, and indirectly to other societies also-namely, the comparative infecundity of that part of the population of the United States described as "native Americans." This fact, which seems pretty generally recognised, first came before Dr. Allen as a matter of personal observation, and he gives us more precise information from census returns. It appears that in the State of Vermont, for instance, the birth-rate even of the whole population, including the foreign element, is but three-fifths of what it is in England, while that of the strictly American population taken alone is estimated at only one-half of the English standard. This fact is the more remarkable, since, as Dr. Allen points out, "the comparison is between a people Occupying the healthiest part of New England, engaged principally in agricultural pursuits, scattered in settlement, and a population situated as that of England is, living mostly in cities and thickly settled places, as well as composed largely of the extremes in society." Nor was it always so with the same race; for a hundred years ago the number of children under fifteen years of age was, relatively to the adult population, double what it is now. As regards the causes of this difference, Dr. Allen does not assign more than a secondary place either to emigration westward or to prudential considerations. He himself regards the physical weakness of American women, their inattention to the rules of health, and the over-straining of their nervous system, as the chief determining causes of the small number of children in a family. We have the usual complaints of tight-lacing, low dresses, in sufficient exercise, and so on, which have been urged by physical moralists in all countries; but more special evils are pointed out in "the excessive use of fine flour bread," and the overstrained intellectual education of girls. To the latter cause Mr. Herbert Spencer has already ascribed the same consequences. At all events the fact of general physical weakness in American women seems to be made out, and is curiously illustrated from one point of view by the estimate of a manufacturer, that more than seven million feeding bottles are annually sold in the United States. So many mothers are unable to nourish their offspring!

Dr. Allen further ventures on a general theory of population, which may be stated broadly thus :-That fecundity depends upon the perfect development or harmony of all the organs of the body. The principle thus stated is very vague, and the author cannot be called successful in his attempt to give it precision; but the subject is too large for discussion here. The practical counsels which he addresses to his countrywomen are valuable and judicious, but so long as large families are regarded with disfavour, advice in this direction seems little likely to meet with acceptance. More promising are his suggestions as to the origin of this sentiment. If it be chiefly due, as he implies, to

nobler sentiment.

weakness of physical constitution, which causes women to dread the dangers of a large family, while "their delicate organisation breaks down in bringing into the world one, two, or three children," then undoubtedly greater physical vigour might remove some of the moral obstacles to increase of population. We cannot regard moral causes, or, in the words of an American writer, the "feeling that has grown up of late years with respect to offspring," as without importance. Is it possible, for instance, that certain circles of American society have come to resemble the Hungarians, in actually priding themselves on their small families? If any such feeling as this should exist, it is not likely to be expelled but by the supremacy of some stronger and Such might be found, one would have thought, in the sentiment of posterity, that pride in the destiny of their race, which occupies the popular imagination among Americans to a greater extent than in any other nation. Are the "native Americans" prepared to surrender the future of their country to foreign immigrants? This must be the case unless the tide should turn. At present, indeed, we hear only of a stationary not a diminishing population, and were such a community standing alone, it might do no more than realise the ideal "stationary state" of the Malthusian philosophers. But, unfortunately, the other elements of population are not stationary, and to stand still in the midst of growth is to be choked. Such a prospect can hardly be a matter of indifference to the race which is thus threatened with extinction; nor is it on several grounds without importance to the world at large. In the first place the New England Puritan stock is one possessed of many noble qualities which the world can ill afford to lose, and, secondly, it is hard to see where this process is to stop. If the influence of the milieu has reduced the descendants of a people so mentally and physically vigorous as the English colonists of the seventeenth century, to a state of infecundity and "physical degeneracy" (to use Dr. Allen's words), what are the prospects for later colonists, whether of English, Irish, or German descent? They will soon be "native Americans," and subject, as we must suppose, to the same laws of change. Is transplantation of a race, as Knox and others thought, impossible? This question is neither raised nor answered by Dr. Allen, but it is inevitably suggested by the gloomy pictures which he draws. His pamphlets, in spite of much repetition, and an occasional superficiality of treatment, are worth reading by those who are interested in the important problems

which he discusses.

OUR BOOK SHELF

National Health. By Henry W. Acland, F.R.S., &c. (Oxford and London: James Parker and Co., 1871.) DR. ACLAND'S pamphlet should be read in connection with the report of the Royal Sanitary Commission, of which he was a member, and some of whose recommendations have already been embodied in a Government measure. Not that it is intended as an exposition or defence of that report, but rather as an exposition of the general principles of sanitary legislation and reform. It would be impertinent to say that in knowledge and enlightenment Dr. Acland is on the level of his important theme, but we may point out as his special

qualification for treating a subject of such complex relations, a certain comprehensiveness of mind, which does not allow him to leave untouched either the moral or the health. We think it the more important to draw attention material, the scientific or the political, aspects of national to this valuable quality because it is so often wanting in professional, perhaps especially in medical writers, and the want is so often a source of weakness. Dr. Acland does not forget, in treating of national health, the dependence of disease on poverty or of poverty on over-population; and insists strongly on the often-forgotten principles of Malthus. It is instructive to contrast the dangers he points out with the apprehensions of an entirely opposite kind entertained by Dr. Nathan Allen. On this side of the Atlantic we dread the results of too rapid multiplication; on the other side their fear is lest, among a certain class, this danger should have been too completely averted. But both would agree that the property of fertility does not always belong to those whom we should think best fitted to be the progenitors of the race to come. Dr. Allen laments the decay of the highly cultivated and intellectual New Englanders; while Dr. Acland, quoting Mr. Galton, points out the possibility of "the races best fitted to play their part on the stage of life being crowded out by the incompetent, the ailing, and the desponding," merely in consequence of a reckless system of early marriages. This very fact, we may remark, of the rapid multiplication of the "incompetent and ailing" is of itself fatal to the theory of population advanced by the American physician. In his remarks on the regulation of public health, Dr. Acland shows the same breadth of view as in treating the more scientific aspect of the subject, and his wise, we might say, statesmanlike advice contrasts with the too absolute and inconsiderate claims put forward by some medical and sanitary reformers. It should never be forgotten that the power of seeing even the plainest evils cannot go beyond the general standard of public enlightenment, and that the power of removing them must be limited by the social and political conditions of the country in which we live. The following quotation appears to us to contain very sound advice :

"Two things and two only remain to be done. "First. To continue to interest intelligently the mass of the people in sanitary progress, and to interest them more systematically.

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England must rule herself in these as in all other matters. The time is gone when people can be dragooned into cleanliness and virtue. We hear that the middle class of England is inefficient, the guardians of the poor bad, and the working classes ignorant. If so they are still the people; they and their children pay the penalty of disease and of vice. Show them, truly and without exaggeration, the source of avoidable disease and of destructive vice; they will abate it. Bring the knowledge to their doors, they have heart and will; give the power by enactment, and the work is done.

"Second. To establish such a health department in the metropolis as shall with certainty appreciate the growing wants of the people, as shall bring in bills to meet their wants, and shall disseminate information and advice without stint to every part of the country."

LETTERS TO THE EDITOR

[The Editor does not hold himself responsible for opinions expressed by his Correspondents. No notice is taken of anonymous communications.]

Local Scientific Societies

THE following statement appeared a short time ago in an article in NATURE. Throughout the country we find societies, field clubs, local museums, &c., all of which are more or less actively engaged in the pursuit of knowledge, local inquiries, or

explorations, &c., I fear this flattering description must have arisen from the writer not having a practical acquaintance with local societies.

In a society in the West of England, consisting of nearly 400 members, I know of but one who does anything for the local museum, or for the advancement of geological science. The society's principal results are archæological; geology and natural history are in the background. Another west country society is divided into innumerable sections, which have their excursions, and an occasional general excursion; but their results in the cause of science are as valuable as those of an ordinary picnic party. This description will, I fear, answer also very well for one with which I am acquainted in Sussex. In all these instances the local museums are such as might be expected from such apathy.

In too many instances the science of the scientific societies begins and ends with the name. There may, perhaps, be one or two members who are active, but feel little encouragement to do much for the public good, or in the way of contributing to the local museum. Of course these societies are composed in a great measure of members who take no interest whatever in science, and who join them without any definite object; but it is a pity that the public should be subjected to such a delusion. There are, of course, some few societies which are fortunately more active, and produce valuable results, but as yet I have seen no good local museum in connection with them, and that is a bad test of the practical nature of a society. I know of but one museum which at all answers the description of a local museum, and that is at Bath, which is due to the genius and energy of Mr. Charles Moore. But as long as members of local societies collect for themselves and, not for the public good, their museums must remain at a stand still. Few have any idea of the valuable collections which are made, or the labour spent on their formation, by individuals who are indifferent as to what eventually becomes of them.

It is want of public spirit and self-complacency, which are the great hindrances to all progress. It is to be regretted that the Geological Society of London does not set more of an example to the provincial societies; it ought to exert an influence throughout the country, and take some interest in their progress. The state of the collections at Somerset House is certainly not an honour to any society.

The co-operation of local societies, and having their results published for the benefit of all, might have a great effect on the advancement of science. A general contribution for the purpose of a weekly issue of British Journals of Science (in various departments), which should be common to all, would be a step of great importance. I know of no remedy for this state of ignorance and apathy as to the valuable results of which they might be capable, but such a co-operation, combined with a certain amount of union with the scientific societies of London, which might have the effect of keeping the provincial societies up to the mark. This must also be accompanied by a unity of object, as well as of system in the management and arrangement of their museums. F. G. S.

Newspaper Science

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IN reply to the letter of "Medicus" in last week's NATURE, allow me again to state that the curious details as to Krupp's gun manufactory, with which the public were enlightened in the Globe of September 11, appeared in that paper as a leading article, and not as a mere note-paragraph," as "Medicus," who "never writes articles," evidently desires to be understood. Had they been in the form of the ordinary newspaper paragraph, containing accounts of some wonderful discovery in zoology, chemistry, or mineralogy, such as, for example, some late ones on "the appearance of a gigantic lizard in North Wales," "the extraction of the fixed air from the pea sausage for use in the army," or the "abundance of platinum at Bathgate, in Scotland,' which I find copied into the Times of to-day, I should not have troubled the readers of NATURE with my letter of September 13. When, however, we find such "blunders," to use "Medicus's" own word, whilst he admits at the same time that they "had passed the editorial eye," palmed on the public on the authority which should be due to the leading article of a highly respectable and largely circulated newspaper, I think it is high time to protest against technical science being popularised in this style; and à propos to style, the peculiarly pleasant and what would vulgarly but expressively be called the "chaffing" style of "Medicus's" communication to NATURE conveys to the reader the impression

that its author is more at home in writing for penny newspapers than for scientific periodicals.

In conclusion, the perusal of the letter of "Medicus" will certainly remind metallurgists of the man who, when he felt his feet slipping under him in the water, brought himself altogether out of his depth by imprudent and convulsive struggles to extri cate himself. The use of the French word "creuset" instead of the plain English "crucible," suggests a French source of information, and not the original German "Schmelztiegel" of Krupp's manufactory at Essen; and when "Medicus" corrects his text, and tells us it should read "the iron is alloyed in crucibles formed with certain clays and a preparation of plumbago "(!) metallurgists will still believe that it was steel not iron which is introduced into these crucibles, and doubt its being alloyed at all, but only melted in them; and will, moreover, be of opinion that if "Medicus was at home in the subject on which he has been writing, he would have at once explained that when he unfortunately described the steam-hammer as "of the force of 25,000 kilometres" (in plain English, 15,532 miles), that the last word was simply a misprint for kilogrammes (so that the hammer was nearly 24 English tons), and not grasped at a straw in the shape of the far-fetched and in this instance equally misapplied term kilogrammetre ! DAVID FORBES

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II, York Place, Portman Square, London, Oct. 9 P.S. If "Medicus" desires correct information as to the steam-hammers, &c., at Krupp's manufactory at Essen, he will find it in the recently-published official report of the Chamber of Commerce there, a short abstract of which is embodied in my fourth quarterly report (for 1871) to the Iron and Steel Institute, on the "Iron and Steel Industries in Foreign Countries."

The Cyclone in the West Indies

I THINK others besides me would be glad of an article in your paper on the Cyclone of the 21st of August in the West Indies. The narrow limits of the hurricane are noteworthy. I hear from the West Indies that Nevis, between Antigua and St. Kitts, has escaped, being a little to leeward. Has Saba escaped likewise? To windward Barbuda and Anguilla seem to have been also beyond the storm, as was also Virgin Gorda; the centre of the cyclone passing over St. Thomas (and, I presume, Tortola also) on its way to Porto Rico.

I have exact details only from St. Thomas, which I could, I think, put at the service of any one writing on the matter; but the principal fact in them is, that the main rush of wind, which did the damage, fell on the harbour from N. E. to N., destroying horribly all houses in the N. E. gully which slopes down to the harbour; but so turned right and left by the high hills above the town, that it was impossible for one in the harbour to discern the actual direction of the main current. This blast fell just before the central calm.

I trust that we shall have from some of your contributors somewhat which will throw more light on all hurricanes, from

the lessons of this last.

Excuse the interest which one who knows those seas and islands-when he passed through them, blazing in beauty and repose-must needs take in the details of such a tragedy. Eversley, Winchfield C. KINGSLEY

On the Solution of a certain Geometrical Problem I REGRET that the work I referred to should have been so readily identifiable; still more, that Mr. Todhunter should think I intended to imply "signal geometrical weakness" on his part. I should imagine, on the contrary, that few living men surpass Mr. Todhunter in geometrical strength; though I may have inferred from some passages in his works that that special part of his mathematical strength had not been so fully developed by practice as his power in mathematical analysis.

It must be quite obvious to anyone who reads the whole of the appendix to Mr. Todhunter's Euclid, that sooner or later the series of problems on circle-contact (ie. to Prop. 16) would require the introduction of the sixth-book method. This method is also very conveniently introduced in Prop. 7. But the omission of all mention of the third-book method* would certainly lead the student to infer that the sixth book must be employed. If it led me to infer that Mr. Todhunter happened not to know *Especially as but three lines would be needed to indicate the method. Thus: From the given point A draw a perpendicular AD to the bisector of the angle between the given lines; produce A D to E so that D E is equal to A D; a circle described (by the preceding proposition) through D and E to touch either of the given lines will obviously touch the other also.

of the third-book method, I can readily show that such an inference was by no means so absurd as might be inferred from his remarks about the oldness of the problem. For I remember distinctly an occasion on which the solution of this problem was required during a lecture at King's College, London, at which my friends Baily (second wrangler in 1860) and Hudson (third wrangler in 1861) were present. Three of the students at once submitted to the lecturer the solution by the sixth-book method (which no one can well miss), and the lecturer (a second wrangler), while admitting that the solution was not very pleasing, was unable at the moment to suggest a better; he added, jokingly, that the best way to solve the problem would be to describe a parabola having the given point as focus and either of the given lines as directrix. Now, he had not been long engaged in teaching, and it may be perfectly true that one who had been so engaged would certainly have in his memory one or more solutions of this problem;" but this would depend on the subjects he had been engaged upon. If he chanced to be one of the most eminent mathematical professors at Cambridge, it is probable that no problem in the higher analysis would be unknown to him, but the odds would be rather against than in favour of his being familiar with the best solutions of geometrical problems, just as the odds would be against his being proficient in the rules for "Barter," "Tare and Trett," and "Alligation Partial."

From letters which have reached me I find that the general purport of my letter has been misapprehended, since some appear to infer that I question the geometrical power of our University mathematicians. I meant nothing so unreasonable. We have geometricians who rival (and I believe more than rival) in power the best Continental geometricians. But their geometrical strength has not been attained during their University career; and no one who considers carefully the mathematical course at either University, can believe that it tends either to form geometricians or to foster geometrical taste.

I candidly admit that I do not speak of either course from personal experience. All I know of geometry was learned before my Cambridge time, and very nearly all I know of analytical mathematics was learned after that time. But I know quite well the nature of each course, and can sustain my statement that our universities do not encourage the study of geometry. Whether they should do so is a matter on which I have expressed no opinion. RICHD. A. PROCTOR

Brighton, Oct. 7

P.S.-Mr. Todhunter refers to the actual solution of the problem as a "matter of some interest, though of course unconnected with the theoretical solution." As I have had some experience in constructive geometry (having always made it a practice to solve astronomical problems constructively before proceeding to numerical calculation), I may be permitted to make some remarks on this point. First I would add to the compasses and parallel ruler (the only instruments mentioned by Mr. Todhunter) that most useful instrument the square. With this instrument (which would be needed in any case) the following construction would be as convenient as the one founded on the sixth-book solution. The problem, be it remembered, requires that a circle should be described through a given point to touch two given straight lines. Let P be the point, AB and AFCG the lines, AHDK the bisector of BAC (this bisector must be drawn in both methods, so that I leave its construction untouched); with the square draw CPD square to AK, and PE square to CD; with centre D draw circular arc PE; with centre С and distance PE draw half circle FLG; then FH and GK drawn square to AG (with the square) are radii of the two circles fulfilling the conditions.

Prof. Newcomb and Mr. Stone

IN Mr. Proctor's letter to NATURE of the 23rd ult., he remarks that Prof. Newcomb had stated to him that he was bewildered at having a discussion of the transits of Venus and the parallax of the Sun, deducible from them, prior to that of Mr. Stone, attributed to himself; and Mr. Proctor goes on to state that he was justified in his belief that such a discussion had been made because a writer, signing himself "P. S." had asserted that it had in a letter appearing in the Astronomical Register for December 1868. He further gives two reasons for the unhesitating credit which he had given to the assertion of "P. S." The first of them is that there is strong internal evidence that the writer was a distinguished astronomer having those as his initials (or a part of his initials, it would be more

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correct to say); of this it seems scarcely needful to say more, as the writer in question may prefer not to be unearthed. But of Mr. Proctor's other reason, may I be permitted to say a word? It is that the assertion of "P. S." was "permitted to remain uncorrected."

Had Mr. Proctor turned to the very next number of the Astronomical Register (that for January 1869) he would have found a letter signed also with initials "W. T. L." in which "P. S.'s" assertion that Prof. Newcomb had published any discussion of the transit of Venus in 1769, is most emphatically contradicted. "P. S.," it is true, made a rejoinder in the March number of the Register (page 65) but in it he neither denies "W. T. L.'s" contradiction, nor refers (as of course he could not) to any original investigation of the transit-of-Venus problem by Prof. Newcomb. He contented himself with the rather unintelligible remark that "W. T. L.'s" answer was not in "the spirit of the age we live in." The latter writer in the following number of the Register (page 88) pointed how, in all probability, the mistake of "P. S." had arisen from misunderstanding part of the title of a paper by Prof. Newcomb on the Distance of the Sun, and the matter dropped.

Now, as Prof. Newcomb was as likely to have seen "W. T. L.'s" contradiction as "P. S.'s" assertion, there would certainly seem no necessity for his further disowning himself what P. S." had claimed for him. W. T. LYNN Blackheath, Oct. 2

Note on the Cycloid

I Do not know whether it has been noticed that the cycloid is a projection of the common helix (thread-inclined 45°). I suppose the property must have long since been recognised, but have not seen it mentioned.

The proof is very simple, and may be thus presented :Suppose a vertical circle to have its plane east and west (a luminous point, for the nonce), the sun in the meridian and 45° high. Then the shadow of the circle on a horizontal plane will clearly be a circle; and further, if a point move uniformly round the vertical circle, the shadow of the point will move uniformly round the shadow-circle. Now, let the centre of the vertical circle advance horizontally towards the south, while a point moves round its circumference at the same uniform rate. The moving point will describe a right helix with a thread-inclination of 45°. Its shadow will move uniformly round the shadow-circle while in a straight line. It will therefore describe a cycloid. the centre of this circle advances uniform'y and at the same rate

It is obvious that all the varieties of curtate and prolate-cycloids may be obtained as projections of helices, by changing the threadinclination.

Also it is obvious that if the sun (or the point of projection) were in the zenith, the shadow (or projection) of the helix first dealt with would be the curve called "the companion to the cycloid." RICHARD A. PROCTOR

Is Blue a Primary Colour?

IN recent works on colour blue is called a primary colour. If blue is a primary colour a mixture of yellow and blue transparent pigments could not produce green, but would form an opaque combination. The colour produced by a mixture of yellow and blue pigments-if blue is an elementary colourwill depend on the colour reflected by the coloured layer itself, and not on the light passed through it from the white surface underneath The brilliancy of the green produced by mixing yellow and blue pigment, is a measure of the transparency, to the green rays, of the blue pigment employed. Or in other words, there is as much green in the blue pigment employed, as there is green in the green produced by mixing that pigment with yellow. Blue must, therefore, be a compound colour, since the blue pigment passes the green rays.

Further. When the light reflected from blue substances is examined with a prism, it is found to be composed of green and violet. Again, when green and violet are combined by means of a rotating disc, blue is produced. By varying the proportions of green and violet any colour from green through blue green or sea-green, blue, blue violet or indigo to violet, may be obtained. Again, when the solar spectrum is thrown on a blue surface, the green and the violet rays are reflected in the same way as a yellow surface reflects the red and the green rays.

The following is a simple way of showing that blue is not an elementary colour, and that violet is an elementary colour :Take a piece of red, a piece of green, and a piece of violet

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