to be founded upon a false análogy. The eye sees with a distinctness which agrees with the distance of the object: a result which can be determined only by the aculty of vision itself, without any correspondent variety of the focal power. That the focal powers of the eye undergo no change in order to produce vision at different distances, appears from this fact, namely, that we are enabled to see a great variety of objects at all distances, within a range of A perhaps from three yards to three miles at the same time. thousand objects may be interspersed in this range. Can there, then, exist a correspondent number of distinct focal powers in the eye at the same time? The eye requires a determinate focal power: its only movements are for the purpose of regulating the axis of vision: and perceptions are formed according to the relation which subsists between light at various approximations to a focus, and the faculty of vision allied with the retina. Bath, April 4, 1815. SIR, V. Proposed Road over Hounslow Heath. (To Dr. Thomson.) AN Act of Parliament has passed for the inclosure of Hounslow Heath, and the commissioners have already begun to act upon it. It may not, however, be too late to induce them to lay down one of their roads in the line on which Gen. Roy measured his base. The plan seems unobjectionable, and it certainly would be attended by circumstances which make the execution of it highly desirable. The suggestion of it in the Annals can at least do no harm, and will oblige A CONSTANT READER. VI. On Mr. Lockhart's Imaginary Cube Rools. By Dr. Tiarks. (To Dr. Thomson.) SIR, Having seen in the last number of your Annals a paper by Mr. Lockhart, which contains this most extraordinary assertion, that every cubic equation has more than two imaginary roots, I beg leave to state to you that the imaginary expression which Mr. L. supposes to be a root of 4, different from the two well-known roots, is nothing but a different form of one of them. 3+ √ 3 3) is the square The above expression, therefore, is, (2 + 2 √ 3), which is (2 ± 2 √ − 3) really one of the two imaginary roots of 4, 5, Bateman's Buildings, Soho-square. J. L. TIARKS. VII. Another Communication on the same subject. SIR, (To Dr Thomson.) My attention was arrested by the seventh article of scientific intelligence in your last number (p. 315). Some mathematicians have denied the universality of the doctrine of there being as many roots to an equation as it has dimensions, but none have been able to maintain that there are more. I therefore examined Mr. Lockhart's proof with some attention; and I conceive that he cannot take it ill if I endeavour to point out the source of his mistake. I think, likewise, that you will be indebted to me for doing so; since the "method for approximating towards the roots of cubic equations belonging to the irreducible case," has justly given some weight to the author's opinions; and you must be desirous of not being the means of propagating an error which can only be supported by the authority of his name. I must begin by laying down 3 + that 2 √ - (13 3 is not a cube root of 64, but of S. To show this in the simplest manner, we will substitute + √ 3 in the place of ✔ - (1 - √3, for these two quantities may easily be shown to be equal by the rule for extracting the roots of binomial surds; and then 2 3 + = − 1 + √ — 3, which, when cubed, will be found to make up 8. But it may be asked how a mathematician so well acquainted with algebraical processes, and especially with cubic equations, can have made such a mistake, and in what part of his reasoning the fallacy lies? This question I think admits of a complete answer; for the error will be found in his manner of bringing 3) √ - ( − ÷ √ 2 +6√ out the value of ( 1 3 It is perfectly clear that a√ is equal to the square root of a2 b; but it escaped Mr. L. that by squaring his quantity he introduced an ambiguity, since the square root of a b is a ; and in this instance he ought to have taken the negative instead of the positive 288, instead of root; the value then would have been 36 36 + 28 = 64. To show that this is so, we have only to take the and then we shall value above assigned to ✔ find that (-2 +6 √ − 3) · ( ÷ + 3 √ − 3) = − 28. There are some particulars in your last number which would not deserve a separate communication, and on which I may yet take this opportunity of offering some short remarks. In your account of Count Rumford you have omitted to mention the memoirs which he published abroad, and the medal which he entrusted for distribution to the Royal Society. To the last query of M. (p. 314), it may be answered that he will find the subject mentioned at p. 31 of Smith's Optics, and at p. 148 of Dr. Jurin's Essay on Distinct Vision (annexed to that work); and that a number of curious' experiments, which give greater precision to the inquiry, will be found in Harris's Optics, and in a paper of Dr. Herschell's in the Phil. Trans. for 1786 (vol. lxxvi.). N. R. D. VIII. Effect of Sulphuric Acid on Agates. What can be the reason that agate heated, or rather boiled, in concentrated sulphuric acid, becomes in its different layers differently coloured; the white strata becoming milk-white, and the greyish ones as black as pitch? I heard this from Mr. Banks, in Bath, and would not believe it; but Mr. Banks was so good as to make the experiment in my presence, and I was convinced of the fact. Saxon agate is more affected than the Scotch is: half an hour or one hour is generally sufficient for producing the effect. The colours penetrate to a considerable depth. I think this fact fully merits the attention and investigation of chemists and mineralogists. Glasgow, March 15, 1815. J. HAMEL, M. D. IX. Constituents of the Ribes Grossularia, (Green Goosberry.) We know from Scheele that the juice of this fruit contains citric and malic acids. Dr. John has lately subjected it to a more detailed analysis. This juice has a greenish, and somewhat thick consistence; but it does not gelatinize when exposed to the air. John could find in it hardly any traces of sugar, and therefore is disposed to doubt the possibility of converting it into wine; but this is often and successfully put in practice in this country. Indeed the taste of this gooseberry is very distinctly sweet. The following are the constituents found in this juice by John. Much water. Prunin or cerasin.* A salt with base of magnesia. Traces of phosphates of lime Trace of muriate of lime? This is a substance similar to gum in appearance; but it does not dissolve in water, only swelling up and becoming gelatinous in that liquid. X. Constituents of Angelica or Changelica. This plant, one of the greatest ornaments of cold countries, has been analyzed by John. The following are the constituents which he obtained from 300 parts of the dried plant. ROBERT DICKINSON, Great Queen-street, London; for certain improvements in the art of sadlery. Nov. 28, 1814. ROBERT DICKINSON, Great Queen-street, London; for certain improvements in the manufacture of barrels and other packages made of iron or other metals. Dec. 10, 1814. ROBERT SALMON, Woburn, Bedford; for improved movements and combinations of wheels for working of cranes, mills, and all sorts of machinery, either portable or fixed. Dec. 10, 1814. EDWARD GLOVER, Penton-place, Walworth, Surrey; for an apparatus for drawing or extracting bolts, nails, &c. and for various other useful purposes. Dec. 10, 1814. HENRY JULIUS WINTER, Dover; for a method of giving effect to various operating processes. Dec. 12, 1814. JOHN FRANCIS WYATT, Furnival's Inn, engineer; for a new kind of bricks or blocks, one of which is particularly adapted for the fronts of houses and other buildings, giving to them the appearance of stone; another is applicable to a new method of bonding brick-work; also a new kind of blocks or slabs for paving floors, and facing or lining walls, instead of ashler, which will resemble marble or stone, and which may also be applied to steps or stairs, and other parts of buildings. Dec. 15, 1814. JOSEPH C. DYER, of Boston State, America, now residing i Camden Town, Middlesex; for certain additions to, and improvements on, machinery to be made and applied in manufacturing cards for carding wool, cotton, silk, and tow, and other fibrous materials of the like description. Communicated to him partly by a foreigner residing abroad. Dec. 15, 1814. JAMES SMITH, Newark-upon-Trent; for a self-acting sash fastening. Dec. 20, 1814. WILLIAM EVERHARD, Baron von Doornich, Sun-street, Bishopgate-street, London; for improvements in the manufacture of soap. Dec. 20, 1814. JOHN VALLANCE, jun. Brighthelmstone; for an apparatus and method of so constructing and securing brewers' vats or store-casks as to prevent the vat falling to pieces, or even breaking, though every one of the hoops on it should be broken asunder, and consequently preventing the liquor from being lost; and also for preventing the loss of liquor, even if a cock or all the cocks of the vat should be broken off. Dec. 20, 1814. ROBERT DICKINSON, Great Queen-street, London; for certain improvements in implements applicable to the purposes of navigation, namely, an improvement or improvements in the ship's nunbuoy and beacon-buoy. Dec. 20, 1814. EDWARD JORDEN, Norwich, and WILLIAM COOKE; for an apparatus for the detection of depredators, which they denominate The Thieves' Alarum. Dec. 24, 1814. FREDERICK KOENIG, Castle-street, Finsbury-square; for certain further improvements in his method of printing by means of machinery. Dec. 24, 1814. JOHN WHITE, New Compton-street, Soho; for a method of making candles. Dec. 27, 1814. JOSEPH HARRIS, Shire-lane, Middlesex; for an improvement or improvements in the necessaries of clothing used for the military in general. Jan. 4, 1815. JOHN CATTLER, Great Queen-street, Lincoln's Inn-fields; for certain improvements applicable to fire-places, stoves, &c. Jan. 6, 1815. CHRISTOPHER DIHL, Brewers-street, Golden-square; for a method or means of making a mastic cement or composition, which he denominates Dihl's Mastic. Jan. 6, 1815. JAMES COLLIER, Grosvenor-street West, Pimlico; for an apparatus, machine, or instrument, intended to be called a Creopyrite, by means of which power will be very economically obtained, and advantageously applied to the raising of water, and other useful purposes. Jan. 16, 1815. FREDERICK Marquis de CHABANNS, Thayer-street, Manchestersquare; for a method of extracting from fuel a greater quantity of caloric than hath hitherto been acquired, and applying it to the purpose of warming the room in which the operation is conducted, and also other rooms by one single fire. Jan. 16, 1815. |