LXX. On the Fitting-up of Microscopes for the Examination of Opaque Objects requiring high powers; and on the Construction of a Focimeter. By Mr. G. DAKIN.

To the Editors of the Philosophical Magazine and Annals. Gentlemen,

AS microscopes are now fitted up by the opticians, a nu

merous and beautiful class of objects is entirely lost to observers; viz. those opaque objects which require a high power. My single microscope, which I had purposely fitted up with the highest powers both opaque and transparent, is almost useless for this purpose, as the highest opaque eye-piece is 1-6th of an inch focus. I have seen the scales of the diamondbeetle as an opaque object through a lens which I think Dr. Goring said was 1-60th of an inch focus. He has certainly carried it quite to the maximum, as there was rather a want of light and distinctness, which I attribute in a great measure to the best part of the speculum being lost by the introduction of the deep convex cup which holds the lens; nevertheless the beautiful lines on the scales were plainly to be seen, even with this high power. I have made the whole of my transparent eyepieces answer as opaque ones, in which the lenses are placed on the outsides of the speculums; consequently the whole of the central and best part of the speculum is brought into action. Opticians seem to forget that the light which is thrown on the speculum is already condensed, and that such large ones are not necessary, unless it be to compensate for the clumsy manner in which they generally fit up the opaque slides. Objects of this sort ought to be fixed on small cylinders of jet or ebony, and these glued on slips of glass: by this means little or no light is lost. The speculums I made were about,,,, and th of an inch diameter: they should be fitted into a brass ring (fig. 1.), to which should be soldered a piece of wire, fitting a hole in a larger piece of wire (fig. 2.), which should slide easily through the stage (fig. 3.); or they may be laid on the slips of glass over the objects (fig. 4.), provided the cylinders are adjusted to bring the objects into the focus of the speculums. When the highest powers are used, take a very small piece of the object and lay it on a small cylinder, which must have a fine hole in the side, for the purpose of fixing it on the point of a fine needle; place the object in the centre of the stage, and bring the speculum down so as to illuminate the object as much as possible. The eye-piece must then be brought down close to the hole in the speculum, the eye being now placed in its right position. The eye-piece may be raised

to

to its true focal distance; this will prevent the lenses being injured by coming in contact with the speculum.

The highest power in my microscope is about 1-46th inch focus; but a lens of 1-30th inch focus may be used by a novice with ease and very great advantage, and the object will be as well illuminated as by one of the large speculums. As they are very easily made, I shall describe the method of making a 1-4th inch one. Melt a little fine silver by the blowpipe into a globule about 1-10th of an inch diameter; hammer it out till it is full 1-4th inch wide, and as thick as stout foolscap paper: take a piece of brass wire, barely 1-4th inch thick, and file one end of it hemispherically; then lay the silver on a piece of lead about 1-4th inch thick. Hollow the silver to the shape of the wire, and then drive it quite through the lead, turning the wire at the same time: make a small hole in the centre, and fix it on the end of a stick of sealing-wax; then file a piece of slate-pencil, barely 1-4th inch diameter, to fit the silver cup, and grind them together with fine emery, till it is of a uniform figure quite over the surface; then wash the emery off, and grind the scratches out with the pencil, washing the mud away with clear water. To polish it, cover the pencil with thin silk, rub a little tallow and jeweller's rouge on the silk, and work them together till the speculum is beautifully polished.

1

4

5

I strongly suspect that the focal distances of lenses are ge

nerally

nerally underrated by opticians. To prove mine, I made what may be called a Focimeter. It consists of a flat piece of brass, which fixes on the arm of the microscope (fig. 5.); at the end is a female screw that has exactly fifty threads to the inch, to which is fitted a male screw about half an inch long, with a hole drilled quite through it, and a large ivory head (fig. 6.), with twenty divisions fixed on its lower end; consequently one division on the head is equal to the 1-1000dth of an inch. After the end of the screw and the brass plate are ground together on a flat hone, there must be glued over the hole in the male screw, a small piece of the outer membrane of the eye of the Libellula grandis, and a piece of very thin foil with a small hole in its centre laid over the female screw. When used, fix it to the arm of the microscope, and throw the light up the hole by the mirror; lay the highest power on the foil, turn the screw up till it just touches the foil, and set down the number of turns and divisions that it takes to bring the object down to the focus of the lens.

Proceed in the same manner with the rest of the powers; they may then be easily reduced to the nearest fraction having one for a numerator: by this means I found that my highest power, which I considered 1-60th of an inch focus, was only 1-46th inch focus, and the rest in proportion. I have made a double convex lens, which is the smallest I have ever seen, and is only 1-100dth inch focus, as it took but half a turn of the screw to bring the object down to the focus. The thickness of the foil may be neglected even in the highest powers; as it does not amount to the 1-1000dth of an inch.

Dr. Goring uses the scales of the Lepidoptera as test-objects: but the most beautiful and delicate test-objects that I have ever seen are the scales of the Lepisma saccharina; they are so very thin, and the lines upon them are so very fine,that they will bear almost any power. The beautiful green convex scales of the small English diamond-beetle, which is very common in the summer months, is a very good opaque test-object.

The focal distance of large lenses for telescopes, &c. is reckoned from the centre of the body of the lens (under half an inch focus); but in my opinion the focus of microscopic lenses ought to be computed from the surface next the radiant object, otherwise another operation is necessary; viz. taking the thickness of the lens and adding half of it to the focal distance: but as small lenses are so very apt to be lost or cracked, it is much safer and better to reckon from the surface. I beg to remain yours, &c. G. DAKIN.

'Ninesham, Oct. 23, 1828.

LXXI. On

LXXI. On the Method in the Trigonometrical Survey for finding the Difference of Longitude of two Stations very little different in Latitude. By J. IVORY, Esq. M.A. F.R.S. &c.*

IN

N this Journal for October last, I endeavoured to prove that the method in the Trigonometrical Survey for finding the difference of longitude of two stations, not much different in latitude, was insufficient, and led to erroneous results. The principle of the method is this, That the latitudes being the same, the difference of longitude is independent of the excentricity, or it is the same on the surface of a sphere and a spheroid of small oblateness; which, in reality, is consistent neither with experience, nor with other methods of investigation of undoubted accuracy. We are told indeed, that the incorrectness of the method, and its want of success in practice, is now allowed on all hands; but the date at which the delusion was dissipated is not mentioned. As my intention was merely to overturn an insufficient method of calculation, not to establish a new rule, I neglected such small quantities as could not be distinguished from the unavoidable errors of observation. Thus the small quantity in the value of ß, which I neglected (p. 243), would be produced by a small variation in the length of the chord y, amounting to about 18 feet in the distance between Beachy Head and Dunnose, more than 65 miles. Assuredly a method of calculation which requires such nice accuracy in the data of observation is not a very solid foundation on which to place any conclusion respecting the figure of the earth. There is also an omission in the equations (x) (p. 243), arising from supposing R = a (p. 242), which, however, will affect the azimuths only a small fraction of a second in the ordinary circumstances of the problem; that is, when one azimuth is greater, and the other less, than 90°. In the extreme case, of which there is no instance that I know of, when the azimuths are both less than 90°, and nearly equal, the last-mentioned omission will affect the accuracy of my formula, because the quantity neglected does not vanish when the two latitudes become equal. There is, however, no doubt that, in the ordinary circumstances of the problem, my method, which takes the excentricity into account, comes nearer the truth than the method in the Survey, which entirely neglects the figure of the earth; and this seemed sufficient to answer my purpose. But it is not easy to put down an authorized error; although I shall now attempt to accomplish this task by new investigations, to which it will be impossible to object.

* Communicated by the Author.

Using

Using the same symbols as in this Journal for October, the two following equations, which are rigorously exact, contain the full solution of this problem; viz.

▲= √1-e2 sin2 λ, A'= √1—e2 sin2 λ', Q=

sin a

A

sin λ'

These equations express the condition that two vertical planes, one at each station, intersect in the chord joining the stations. As the investigation is merely elementary, it may be omitted. The two equations, although very simple, are alone sufficient for the solution of the problem, since the excentricity and the difference of longitude are the only unknown quantities they contain. In order to simplify, I shall put a sin λ-sin ';

on the right-hand sides. The equations coincide with the surface of a sphere when e2 = 0, and when x = 0; and as is always very small in the practical application of the problem, it is with difficulty that the quantities on the right-hand sides enable us to distinguish between the sphere and a spheroid of small oblateness. It is here indeed that the difficulty of the problem lies; and it will easily be conceived that, without nice discrimination, one case is apt to be confounded with the other, as it actually is in the method of the Trigonometrical Survey. In order to solve the equations so as to give full effect to the excentricity of the spheroid, it would be requisite to free them from the almost evanescent factor ; but this is what I shall not at present attempt to accomplish. As I write in haste, I shall not inquire how the value of the excentricity is to be deduced, but shall confine my attention to the difference of longitude, supposing that the observations have been made upon a spheroid of a known figure.

The two equations may be brought to a form fit for calculation by the following transformation: viz.