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NOTES AND REFERENCES-a. from aller; L. S. 25, R. 1.— b. moissonnée, cut off; literally, harvested.-c. reculer, start back. -d. L. part ii., § 65.-e. qu'un, let a.-f. from pouvoir; L. part ii., p. 100.-g. the word étendars is here used partitively; L. part Composed from the French Dictionaries of the French Academy, Bescherelle, ii., § 78.

ANSWERS TO CORRESPONDENTS.

W. STEPHENSON is wrong in his solution of his first quadratic equation, though he is right in his answer. After extracting the square root of both sides of his final equation he ought to have ended thus:

2 x 61+ 32
.. 2 x = 61 +32

... * 48 or 16

But as the first value would not answer the conditions of the problem, the
second must be adopted.
W. C. (Colchester) may easily obtain a cheap Latin author at any book-
seller's. Hann's Trigonometry, published by Weale, for a shilling, is the
cheapest and best for a beginner. Haddon's Algebra is very good and
cheap.

ARTHUR H. WOOD has, we fear, mistaken his vocation. He had better abandon all thoughts of Parnassus.

A. LAIDLAW has solved all the second portion of the Second Centenary of Algebraical Problems, except two. The following have solved the numbers respectively attached to their names:

W. STEPHENSON (Lancaster), 29.

J. PROCTER (Snowdon), 67.

W. C. (Colchester), 32.

GEORGE WRIGHT (Hull), 5.

JOHN A. CARSE (Launceston), 32.

ROBERT PARKINSON (Everton), 32.

GEORGE WRIGHT is wrong in his solution of Problem 32. His writing is good.

ANNI SEPT. (Leeds): It is not necessary to be acquainted with the Eton Latio Grammar in order to pass examinations at Oxford or Cambridge.

GEORGE WILLIAMS wishes us to announce that, if any persons are disposed to join him in the formation of a class for the study of geology, and will leave their names at the library of the Bristol Young Men's Christian Association, he will be happy to call upon them and make the necessary arrangements.

AMICUS may obtain a very good work on drawing and perspective from

the Messrs. Chambers.

ANTODIDAKTOs: There is no rule for determining what Greek verbs have second tenses, except the usage of good writers, nor are any reasons to be given.

S. W.: The Lessons on German Pronunciation in the POPULAR EDUCATOR are the same as the separate work on the subject, but the latter contains many additional lessons.

GEORGE WILSON: The cheapest work on Land Surveying is published by Weale, in Holborn, price one shilling.

bookseller.

W. ROSSITEN, (43, Swinton-street, Gray's Inn-road), will be happy to meet any of our Latin students occasionally for the purpose of mutual assistance. JAMES LEWIS: The study of mathematics will best answer the purposes mentioned. A cheap edition of the French Bible may be obtained of any G. M. Y.: The object of geometry is to investigate the relations between parts of space, whether linear, superficial, or solid. It is explained at length in vol. i. p. 23. A circle may be conceived to be generated on a plane surface by the revolution of a finite line about a fixed point. Euclid gives no definition of equality beyond the axiom that "magnitudes which exactly coincide with one another are equal;" but we have given a full explanation of the term in vol. ii. p. 205, to which our correspondent refers. GEORGE SAMURL: There is no key to "Cassell's Algebra." The follow. ing are the solutions desired, The fractions in No. 11 may be put in the (x + 2) (x − 2) X ;; whence, striking out the x2-1 tors common to numerator and denominator, we get the answer 2)2

form

X

1 7

T-2
x + 2

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ON PHYSICS, OR NATURAL PHILOSOPHY.

No. LI.

(Continued from page 365.)

OPTICS.

OPTICAL INSTRUMENTS.-Continued. Photography on Paper.-In the process of Daguerre, which has just been described, the images are produced immediately on the metallic plates. It is not so with photography on paper, which comprises two distinct processes. In the first we obtain an image whose colours are reversed; that is, the parts which are lightest become the darkest on the paper. and vice versa. This is the negative image. In the second process, we avail ourselves of the first image in order to form an ther, whose colours are reversed again, and are found, consequently, in their natural order: this is the positive image.

To obtain the negative image, we use paper imbued with iodide of silver, which we press, while still slightly moist, between two plates of glass, in order to render its surface very smooth. Then we put it, thus pressed, in the focus of the dark chamber of Daguerre, fig. 329, in the place of the metallic plate. There, under the influence of the light, the iodide of silver begins to undergo decomposition, but without the image becoming apparent, the action not having been sufficiently prolonged. "In order to render the image visible, Fig. 332.

and they do not require so much manipulation; but they do not exhibit the same clearness in the lines, nor the same delicacy in the tints.

Photography on Glass.-Photography on glass, which we owe to M. Niepce de Sant Victor, nephew to the fellow-labourer of Daguerre, bears much analogy to photography on paper, but it gives the images more distinctly and renders the details better. Here also two proofs are taken, the one negative, and the other positive; but the first instead of being formed on Paper, is on glass, covered first with a coat of albumen, or white of an egg, then with a solution of nitrate of silver, and of acetic, crystallizable acid. The positive image is obtained by means of the negative image, on paper impregnated with chloride of sodium and nitrate of silver. The proofs which are thus obtained upon paper, almost equal the beauty of those which are produced on the plate.

The Magic Lantern.-The magic lantern is a small apparatus which serves to obtain greatly magnified images of small objects upon a white screen in a dark chamber. It consists of a white iron box, in which a lamp is placed at the focus of a concave reflector A, fig. 331. The rays reflected by this are received by a convergent lens B, fig. 332, which concentrates them towards the different figures painted on a plate of glass v. These figures, thus strongly illumined, are placed before the second convergent lens c, at a distance a little greater than the principal focal distance. In this position this lens produces on a screen at a convenient distance a real image, inverted and greatly enlarged, of the objects painted on the glass. In order Fig. 831.

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the paper is plunged into a solution of gallic acid and slightly heated. Wherever the iodide begins to be decomposed, gallate of silver is formed, which is black, and the image suddenly appears. Its shaded parts, which have not been subject to the action of the light, remain white, the iodide of silver not having been decomposed. But as this salt would quickly become black under the action of the light, and would thus cause the image to vanish, the paper is then washed in a solution of sulphate of soda, which dissolves the iodide of silver, and thus renders the image unalterable by the action of light.

This negative image once obtained serves to produce an indefinite number of positive ones. For that purpose, it is covered with paper impregnated with chloride of silver, and the two sheets being pressed between two plates of glass. the whole is exposed to the action of the light, so that the dark parts of the negative image cast their shade upon the paper with the chloride of silver. It then reproduces upon this a copy of the negative image, in which the light parts are replaced by the dark, and the dark by the light.

There is thus a positive image. It remains to fix it, which is done by washing the paper, as above described, in a solution of hypo-sulphate of soda.

Photography on paper was invented by Mr. Talbot, an Englishman, shortly after the disco ery of Daguerre. It has been since improved by M. Blanquart Evrard, of Lille. In reality it does not differ from the process adopted by Scheele, except in the fixing of the image.

Proofs on paper are less expensive than those on plates,

VOL. V.

to rectify the image, care should be taken to place the painted glass in the lantern in such a manner that the pictures are reversed.

The magic lantern was invented by father Kircher, a German Jesuit, who died at Rome in 1680. The magnifying power of this instrument is the same as that of magnifying lenses, that is, it is in the ratio of the distances from the lens C, to the image and the object. Consequently, if the image is 100 times or 1,000 times more distant from the lens then from the object, the magnifying power will be 100 or 1,000. Hence we perceive that with a lens of short focus, we can, if the screen is sufficiently remote, obtain images of extreme magnitude.

magic lantern, illumined by the solar rays, and is used to The Solar Microscope-The solar microscope is in reality a obtain greatly magnified images of objects which are extremely minute. This instrument works in a dark chamber. Fig. 333 represents it fastened to the window-shutter of the chamber, and fig. 334 exhibits the internal details.

"

receives the solar rays and reflects them on the convergent lens The plane mirror м, placed outside the dark chamber, A, and thence on a second lens E, fig 334, named the focus," object whose image we wish to obtain; it is placed between which concentrates them at its focus. At this point is the plates K K, that are pressed together by means of the spring two glass plates o, which are introduced between two metallic HH. The object being then strongly illuminated, and placed vergent, this lens forms an image ab, inverted and greatly very near the focus of the small lens L, which is highly con

magnified, on a wall or on a white screen placed at a convenient distance. The screws D and c serve to regulate the distances E and L from the object, so that the latter shall be exactly at the focus of the firs, and that the image formed by the lens L shall correspond exactly to the screen.

The direction of solar light varying continually, it is necessary that the reflector placed outside the window shutter of the chamber should change also, in order that the reflection may be constantly made in a line with the axis of the microscope. The more accurate plan would be to have recourse to the heliostat (p. 318); but as this apparatus is very expensive, we supply its place by inclining the mirror more or less by means of a perpetual screw B. and a pinion, and by turning the mirror about the lens a, which is accomplished by me ns of a knob A that moves in a fixed groove, and gives the mirror a rotatory motion about the axis of the instrument.

The solar microscope has the disadvantage of concentrating intense heat upon the object, which it soon alters. This is remedied by interposing a covering of water impregnated with alum, which arrests a part of the heat.

name given to a light produced by quicklime, kept white
hot by a jet of hydrogen gas, which burns by means of a jet
of oxygen gas-a light which possesses extraordinary bril-
liancy.

Fig. 335 represents the manner in which the apparatus is
arranged. In a wooden box is placed a piece of chalk c. In
front is a tube a in which are two concentrical conduits,
which do not communicate with one another, and which afford
a passage, one for the hydrogen and the other for the oxygen,
both which escape into two reservoirs. At the end of the
tube DL, at D are two plano-convex lenses, M and N, arranged
as represented on the left of the illustration, which concen-
trate the light upon the object. This is placed between two
plates of glass P, which are put between two disks, of which
one is fixed, and the other can be moved more or less by means
of the four handles E, so that we can introduce the plate P.
Finally, the two cocks o and H serve to regulate the flow of
the oxygen and the hydrogen, so that the volumes of these
two gases shall be nearly in the ratio of one of the first to
two of the second.

Fig. 333.

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The magnifying power of the solar microscope may be experimentally determined, by putting in front of the object a plate of glass on which are traced the divisions of distance in Fooo or so of an inch. Measuring, then, the intervals of these divisions on the image we infer the magnifying power. The same process may be employed in regard to the gas microscope and the megascope. According to the magnifying power to be obtained, the object-glasses consist of one, two, or three lenses, all achromatic.

The gas microscope has the advantage over the solar, inasmuch as it can act, whatever may be the state of the sky, at any hour of the day. Electric light is sometimes employed with this apparatus, and gives very remarkable results.

The Megascope. This instrument, invented by Charles, serves to obtain magnified images of objects which are not very small, such as a statuette, a medal, or a bas-relief. It has the same form as the magic lantern, only the object instead of being placed where the glass vis, fig. 332, occupies the Fig. 831.

MOTEX

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to obviate this inconvenience, lenses are constructed d échellons, or with gradations. These were contrived by Buffon, and improved by Fresnel. They are formed at the centre of a plano-convex lens c (figs. 336 and 337), surrounded by a series Fig. 336. Fig. 337.

are found at the same point. The whole of these rings then form with the central lens a single one, a section of which is represented in the figure 337. Our drawing is taken from a lens of about 27 inches in diameter, and the annular segments of which are formed out of a single piece of glass; but in larger lenses every segment is itself formed of several pieces.

Behind the lens is a support fixed by three triangles, on which are placed the bodies we wish to submit to the action of the solar rays, which fall upon the lens. The centre of the support corresponding to the focus, the substances which are placed on it are melted and volatilized by the high temperature which is produced. Gold, platina and quartz are rapidly melted. We should remark that these experiments prove that caloric is refracted according to the same laws as light, since the focus of heat is formed at the same point as the focus of light.

In ancient times they used parabolic reflectors to throw the light of beacons to great distances. At the present day they use only lenses with gradations. The fire is produced by a lamp with three or four central wicks. This fire being placed at the principal focus of a lens with gradations on the side of the plane surface, the emergent rays form a parallel pencil, which loses its intensity only in passing through the atmosphere, and may be seen at the distance of 40 or 50 English miles. In order that all parts of the horizon may be successively illumined by the same light, the lens is made to move round the lamp by means of a mechanism of clock-work, and makes its revolution in times which vary in different light-houses. Consequently there is a successive appearance and eclipse of the light at equal intervals, by which mariners are enabled to distinguish the beacon from an accidental light, and also to recognise the particular light-house, and consequently the coast which it illuminates.

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FEMALE EDUCATION.-No. III.

BY SILVERPEN.

the large class of shopkeepers, who usually supply the young female operative with her gown or shawl, trust to the deceptive glare of gaslight to set off an inferior, if gayer class of goods, than they would be unable to dispose of it viewed closely by daylight, or by those of more educated taste.

THERE are two habits, which, generally speaking, lie at the root of much of the female morality of the middle and upper classes of society, and at much of the female immorality of the operative masses. I allude to the fact, that, on the one hand, the young girl or young woman never, under any possible circumstances, enters a gin-shop or public-house, or is out alone in the streets after nightfall; whilst on the other hand, many young women more or less frequent these places, and carry on their courtships and gossiping acquaintanceships at lane-ends, and court ends, and in the streets, after the evening has closed around. Now, whilst many of our most important social questions can only be solved by the descent, as it were, of our higher and middle classes to a plainer, less ostentatious mode of life, so it is equally true that the same questions need a visible ascent through self-improvement and education of the moralities of the operative masses. And nothing would assist this great need further than that young women of the working classes should repudiate these habits with all the earnestness they can. What is immoral in the sight of, and distastetul to, one class, must surely be so for another; for 1 can neither believe in, nor understand, any natural inequality in the morals of progressive human creatures; and as I earnestly wish to give good counsel, let this habit of entering | public-houses, or of considering them as fitting places of amusement, be for ever set aside by those young women who can understand and really value in all their worth a pure reputation and a progress in refinement and morals. Of course I do not here include errands, or small matters of business, which may occasionally take a young woman within a public-house, as into a shop or other dwelling, for I undoubtedly address myself to many unconnected with the temperance question, viewed strictly in its relation to total abstinence; what I mean here is, the habitual or occasional frequenting public-houses and gin-shops as places of refreshment and amusement. But in neither sense are they worthy

of the name.

A habit of gossip and tittle-tattle is an intensely low and vulyar thing. To prate and be curious about other people's affairs is so mean and paltry as to merit the heartiest con tempt of any one ordinarily intelligent, or possessing any generosity of character; and I do not care if gossip be the habit of a duchess or a maid-servant, a mill hand or one calling herself a "gentlewoman," it is equally the mark of a mean spirit and of low breeding. Not that I ignore interest, and sympathy, and love. Let there be more of these, let every channel of human life fill to overflowing, for there is need; but those who would give proof of education, who aim at the moral advance that social interests require, can have no time, and should have no taste, for what is only fitted, to say the least, for the weak and trifling. What in the world can it matter to one young woman how many gowns and how many sweethearts another has? or to the Browns what the Smiths next door have for dinner, or whether they are prudent or imprudent in doing such and such a thing? Be sides, to say nothing of the waste of time, of the consequent neglect of duties, and of the invariability of a love of gossip being connected with other bad habits, it begets more or less a vicious love of scandal. And think what this scandal often is! Think that it is the defamation of one woman's character by another, and often for no worse cause than "devil's envy;" that the one defanied is purer, prettier, kinder-hearted, or is more a favourite. The whole round of human wrong-which is unfortunately a pretty wide one-has no more flagrant evil than this, of one woman speaking dispitefully of another, of putting the worst construction upon every action of judgment by mere hearsay. But the pure in act, the kindly in heart, the generous in spirit, will always speak and judge mercifully, especially of their own sex; and I know of no more lovely, more in the best senses religious, no more nobly feminine habit, than that women, young women especially, should speak and think of their own sex with kindness and mercy. Let the vice of evil-speaking and scandal be left to the painted dowagers of the higher classes, to the ill-conditioned spinsters and vulgar mammas of the middle class, to the low, coarse women of the working classes; but let the young women of the operative masses, the sisters, the future wives of thought'ul working men, give proof of a genial advance in the needed direction of moral habits and moral duties, by avoiding this low-bred vice of scandal; this vice of lane-ends, street-ends, and courtways; this vice which gentlemen who write Blue Books for parliament deplore as one of the signs of a low condition of the people.

As to courtships and acquaintanceships carried on in the streets after nightfall, they are not well. Even as to habits, generally speaking, they are out of place with womanly selfrespect, for though protected by a lover, much must be heard and seen by a young woman that it were best she was ignorant of. I know allowance must be made for those whose work confines them through the day, and who may have no cheerful, cleanly home to receive, or kind parents to invite a lover; yet I feel sure as a rule that young women of the operative classes are so unaware of the immense intellectual advance of many of the young men amongst whom they naturally look for admirers and husbands, as scarcely to bring fitting habits of reserve and womanly delicacy to bear upon the general fact of their intercourse. But let this matter be better understood. Men of the operative classes, men working in shops and factories in Birmingham, in mills and warehouses in Manchester, in milis in Leeds, Huddersfield, and Derby, are making an immense advance in intelligence, in clear far-seeing thought, in those self-restraints that honour body and soul; and would, I firmly believe, reverence and respect any advance young women might make in modest circumspection. Many such men are ultimately drawn down to the level of a woman's coarseness and low habits; but there are others, and the number must necessarily increase as they make intellectual advance, who would rather remain single than trust their own and children's future welfare to those who lightly pace the streets at nightfall, even though with themselves, or who can find charms in the low conviviality of the beer or gin-shop. It only as a matter of prudence, it therefore behoves young women of the operative classes to shape their habits and behaviour in accordance with the moral and intellectual advance of those amongst whom they look for husbands. It may be said that those who have little or no time through the day, are necessarily led into the streets by night by their need Visiting shops for the purchase of apparel, and other things. asionally such a want may arise; but, generally speaking, tion of the noon-day hour would be better spared for ses of this sort, particularly when it is recollected that

Nor can I pass from this question without a word as to a habit worthy of the utmost condemnation by all good and earnest young women. I allude to the love of impure conver sation, either as listener or speaker. Such conversation may he said to be in jest, or in fun; its purpose may be hidden like an evil face with a fair mask, by words expressing one thing but really meaning another; but it is not the less impure for that; and if such "jokes" are habitually indulged in or listened to, the end may prove terrible in its earnestness; because I firmly believe that no individual can indulge in any kind of gross conversation without acquiring a proportionate depravity of character. I do not wish it to be thought for a moment that I am writing a series of moral sermons to the working classes; I am only speaking earnestly from my heart, what my experience of life and my knowlede of books have taught me, and to declare with pride, which nothing could shake or bow, that in all which is most lovely in the feminine character God made all women akin; and be her heart and conversation but pure, and her efforts after self-improvement earnest, the poorest mill-girl that Manchester may hold, stands side by side, in all the best moral aspect of human life, with the highest, purest lady in the land. It makes me proud to think and know this; let it make those rightly proud who will read what I now write; let them strive for this pure heart, these pure lips; let them avoid as companions and friends all who indulge in gross habits or gross conversation, whether at home, in the mill or shop, or in the street; and if

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