LENSES PROPER FOR THE PURPOSE.

Sir,-In reference to Mr. Cumberland's suggested improvement in the Daguerreotype process, vol. xlii. p. 421, I beg to observe, that metal specula for taking daguerreotype portraits have been in use for three or four years, or more; but at the same time, I believe it would not be difficult to show that cameras constructed with a speculum were before known. The great expense and impossibility of making them accurate has, however, hitherto precluded their general use. One of Mr. Beard's patents includes the speculum camera.

Mr. Cumberland observes: "The mode at present practised is by refraction of the sun's rays through a convex lens, which, unless composed, as I have sometimes constructed them, of two planoconvex lenses, is always subject to limited aberrations, and, indeed, in all cases, gives a distorted image to a certain degree, although not always perceptible to the eye." This conveys the idea that Mr. Cumberland has, by combining two plano-convex lenses, succeeded in doing away with the aberration that has always been known to attend the images given by lenses of any, and every form. It would be a pity for any one to be led astray by such remarks to waste his time and money in fruitless experiments to accomplish an impossibility viz., to cause any convex lens or any combination of lenses, however shaped, to make a clear, sharp, distinct image. No lenses or combination of lenses can do this, unless made of different refracting substances none but achromatic lenses will do it. All those daguerreotypes made by specula

*

35

that I have seen have not the sharpness peculiar to those made by achromatic lenses. We all speak by comparison. Mr. Cumberland may have found that his arrangement of lenses was the best he had tried. Mr. Hunt considers that a periscopic lens is the best. I have tried almost all the lenses and likely combinations in Sir David Brewster's volume on Optics (Lardner's Cyclopedia), and I simply beg to state the fact, that neither such lenses as have hitherto been known, nor any combination of them, have ever given or ever can, give a sharp image (except those called achromatic). But an achromatic lens 34 inches diameter, and 15 inches focus, will not give an image clear and distinct enough for daguerreotype purposes; part of it must be stopped out so as to leave an aperture of only 1 inch diameter; if the aperture is made 1 inch diameter, the image will be so sharp, that any further diminution of the aperture does not perceptibly improve the sharpness of the image. Any one who has used an achromatic lens and seen the clear image produced by it, cannot afterwards call the images produced by other lenses sharp. If it was possible to form a correctshaped parabolic lens, it would give a perfect image.

I am, &c.

Carmarthen, July 10, 1845.

HOMO.

P. S. Will any of your readers be kind enough to furnish a description of "Storer's Delineator"?

BAROMETRIC PRESSURE AT THE ANTARCTIC CIRCLE.

Sir, The discovery of Sir James Ross, mentioned in your periodical of the 5th instant, "that a permanently low barometric pressure prevails over the whole of the antarctic ocean," however difficult to explain by modern modes of philosophising, presents no difficulty on principles truly natural.

The principles are these: Matter is inert; so must all bodies be inert; inertia implies want of ability to perform any kind of act to produce any kind of effect. Motion is not natural to anything material, moving being acting. There can be no

*For reasons, see any elementary work on Optics.

motion without previous impulse, nor continuous motion without equally constant impulse. In empty space there is nothing to impel the planets. Planetary motion implies the existence of a medium occupying the whole of the regions of planetary space; and as the common effect, motion, requires but the same universal cause, so is all motion caused by the pressure of the all-pervading motion space.

of

Now, considering the natural fact, that space contains a medium which keeps the planets in motion, and that all motion has no other cause-how this medium makes bodies fall to the ground, and why the direction of descent tends towards the centre of the earth, induce the idea, that somewhat of a centripetal flow of the medium of space takes place, to produce the descent and direction of descent.

A centripetal flow of the medium of space into and from the globe of the earth, may take place under the following circumstances. During the different motions of the earth, the centre of motion may be at the axis or some proximate diameter. There the pressure of the medium of space will be less than at the surface of the globe, which will promote a flow centripetally of the same medium through all parts of the surface towards the centre of motion, and which will pass along the axis to have exit at the poles or at the polar circles.

Only by means of such a flow can we account for descending motion and its peculiar direction, and that all motion out of that direction is retarded, but in it is accelerated. It is by a flow of this kind the atmosphere is retained to the earth, which, otherwise would be left behind and pressed after the planet as in the tail of a comet, and the planet itself forced out of its orbit to become a comet. This flow makes the atmosphere heavy, and all' terrestrial bodies have weight; and in the direction of the centripetal flow do all bodies ponderate. Weight is not natural to matter. Besides, something in continued flow must force from the polar circles the elementary matter of which the boreales consists. The compass needle indicates the act of a directing current; and whether the magnetic effect, as it is termed, depend on a polar flow of medium of space, or on some other elementary matter involved in it, subject to occasional interruption in its

course by the non-conducting polar ices, certain it is, that a constant flow must have an equally constant supply.

The inferior, or minus-pressure effect on the barometric fluid at the polar circles, arises from the elementary matter of the boreales mixing with and becoming part of the atmosphere, and from the general pressure on it being as the size of its elementary atoms, which evinces the boreales emanations, than of the atmogreater rarity of the atmosphere with the sphere within the tropics; just as fire, flame or rarefied air at the top of a tube, the lower end of which is immersed in water, mitigates or intercepts, in degree, the force of the general pressure on the included water, so do the boreales on the barometric fluid for the above-mentioned

reasons.

Thus, adventurously, in the teeth of the established philosophy of the age, are my opinions on the subject of pressure in the polar regions laid before your learned readers for their edification or correction. T. H. PASLEY.

Jersey, July, 1845.

CURIOUS PROPERTY OF THE PYTHAGOREAN ABACUS, OR COMMON MULTIPLICATION TABLE.

If the table be divided into compartments by vertical and horizontal lines, produced till they meet as in the opposite diagram, the sum of the numbers in each compartment, will be equal to the cube or third power of that number which indicates the place of that compartment. Thus, the number in the first cell or compartment at the top of the table on the left hand is 1, which is the cube of 1; the numbers in the second compartment, are 2, 4, 2, the sum of which is 8, or the cube of 2; the numbers in the third compartment, are 3, 6, 9, 6, 3, the sum of which is 27, or the cube of 3; the numbers in the fourth compartment, are 4, 8, 12, 16, 12, 8, 4, the sum of which is 64, or the cube of 4, and so on throughout the table carried to any extent we please. It therefore appears, that the sum of all the numbers in the table, is equal to the sum of the cubes of the series of consecutive numbers, 1, 2, 3, 4, 5, &c., carried to the extent of the table; hence an easy way of summing the series 13, 23, 33, 43, 5a3, &c., to n3, where n denotes the number of terms.

It is obvious that each horizontal row of numbers forms an arithmetical series of which the common difference is equal to the first term; the sums of these series, will therefore form another arithmetical series, the common difference of which is equal to the first sum or term, or the sum of the numbers in the upper row, the last term being equal to the sum of the numbers in the lower row. Now, by the rule for summing an arithmetical series, the first term or the sum of the numbers in the upper row, is (n + 1) × = 2+, which is also the

x

n

2

2

n

common difference; but the last term of

96 108 120 132

144

Sir,-Having seen a letter in one of your late Numbers on the subject of

yacht building, and as it is one in which I feel great interest, and have availed

myself of every opportunity, both of observing different models, and practically testing the results as to their sailing qualities an amusement to which I did always "most seriously incline"-and having on two occasions reduced my ideas on it into practice in two small vessels-I think, too, with rather a successful result I send you a few observations on the subject, for insertion in your Magazine, should they seem likely to be of service. It is not my intention at present to make any observations on the wave line, nor on the remarks made on that subject in the letter of your correspondent "Forrester;" not that I underrate the importance of that point, or the assistance which a scientific investigation would afford in laying down the most eligible lines for the construction of vessels, but because I wish to confine my remarks to some other points, which seem to me of considerable importance, and yet not to be sufficiently considered, or to occupy so prominent a position in the scientific treatment of this question, as their practical importance would seem to entitle them to."

Persons in general seem to me to consider it too much as if vessels were impelled forward by some inherent principle of motion, acting horizontally, and not, as is the case in sailing vessels, by a force acting in a peculiar manner, and modified in its effects by a great variety of causes. Their different states, when in motion under sail, I will class under two heads. The first is, when the wind is more or less astern. In this case, the boat is propelled by the pressure of the wind acting altogether, or nearly, in the direction of her course; but as the resistance offered by the sails acts on a considerable lever, the mast, the tendency of the moving power is to bury the bows until they are sufficiently sunk to offer the necessary resistance. Now in this case the effect of a long fine bow, from whose facility in heading the water so much is expected, differs materially from those that were calculated on, because, from the sinking forward and rising aft, the theoretical lines have ceased to be the practical ones, and her horizontal section at the water line would now probably be an oval with large end foremost, instead of the reverse, as it was before. Again, an equal mistake would be made if the run should be made too

fine; for vessels built thus, in scudding, are apt to settle by the stern, and are counted very dangerous. The second state is, where a vessel is said to be, on a wind; that is, when the direction of the wind is at either a right, or less than a right angle, with that of her course. In this case, her progress results from a less resistance being offered by the water to her moving ahead than laterally; in fact, its rapidity is proportionate to the comparative difference between the amount of both. I am aware that the difference of the angle at which the wind strikes the sails, and other matters of detail, cause irregularities of various degrees in the practical application of these general principles; but as these modifications are incidental to all forms, and do not particularly affect the principles themselves, I shall not dwell on them.

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Vessels intended to go near the wind, or fast on it, are therefore generally constructed sharp in the bottom, with a deep draught of water, and a sharp entrance and run; this form being regarded as the one calculated to offer the greatest resistance to any motion in a direction at right angles to the vessel's length, and the least to one in the direction of it. Experience shows that it is a form which does not produce the full effect anticipated, besides being attended with some drawbacks. No boat sails upright (even the mere spars, lying to one side or other, tilts her, and the more so the sharper she is,) but in proportion as she is pressed with canvass throws up her side; the draught of water is thereby reduced, and the line of her side, from being tolerably perpendicular, is brought nearly horizontal. Thus the resistance her side offered to the water is greatly diminished, while the flat of her bow being sunk in it, her way is greatly retarded; and these tendencies, it must be recollected, increase in proportion as the wind does,-just the reverse of what would be desirable. The following sections will explain this better (See next page). No. 1 shows the vessel as she is intended to be; No. 2, as she really becomes. A B, elevations; D E, depth of bearing when upright; BC, as reduced; DFE shows the angle at which the resistance acted on the side, and BIC, the less favourable one to which it changes; causing manifestly a much greater lis

bility to drift sideways, the water from the direction in which it is acted on, yielding with great facility. The very sharp entrance and run, when the draught of water is very deep, must greatly interfere with any length of floor, and therefore injure her seaworthy qualities, diminishing the ability of carrying sail, her steadiness and tightness in a seaway. The resistance, too, of a deep keel, acting at the extremity of the lever, must of course increase the disposition of a vessel to heel under sail, besides losing its effects in proportion as she does. Of late, I know, yachts have been built of great length to meet many of these difficulties; but, inasmuch as this renders it necessary greatly to reduce the beam, they are seldom able sea-boats. They are, no doubt, often very fast, and may answer very well for racing or river practice, under favourable circumstances; but beyond that I would not trust them much.

And

as people are apt to mast vessels more according to their length than their beam, they are in general quite oversparred for going to sea. Now it is not because I regard the defects to which I have alluded as capable of being completely remedied, that I have made these observations, but because I look upon them as inevitable, or at least to a certain extent more or less incidental to every form of vessel; and ought, therefore, to be more kept in mind in their construction than is done, and greater provision should be made for meeting the conséquences of such disturbing causes, and moderating their effects. With this view, another gentleman and I constructed for our amusement a small boat of the form we thought most calculated to diminish or correct

generally the objectionable tendencies. She was a small open boat, of about 21 feet on the keel, something about 7 on the beam, not drawing over 3 feet of water with two or three persons on board. The particulars of her mould are shown by the sketches figs. 1, 2, and 3. (See next page.)

She was what is commonly called a yawl, and therefore, of course, flatter on the floor than a cutter-built boat. The greatest breadth, as will be seen by fig. 1, was at, or just immediately below, the water line A B, from which she tumbled into the gunwale; the difference being about 2 inches of a side. Her floor, E, was straight, and she was turned up sharp at F. CD represents her water line when heeled under sail. The form of this section was adopted as the most likely, under general circumstances, to be the most affected by the lateral resistance of the water, as it secured the sides, being, when submerged by the listing of the boat from the pressure of the wind, in the position most sure of rendering that resistance effective; that is, nearly perpendicular. The stronger, too, the pressure was, the greater would become the surface of the side acted upon, the spread and straightness of the floor giving her great steadiness and power for carrying sail.

Fig. 2 represents a side view, in which A B is the water line, and CDE an imaginary one, pointing out the particular line throughout her length when the side is what is technically called turned up, and equally showing the position of her greatest bearing. The lines marked with the small letters, a, b, c, d, e, f, g, h, are to give some idea of the form of the