DIPLEIDOSCOPE

DIPLEIDOSCOPE, an instrument invented by Mr Bloxam, whose name has already been mentioned in the article on CLOCK AND WATCH WORK, for ascertaining the time of solar noon more exactly than can be done by a common sun-dial. It can also be used when the sun is covered with thin clouds, not thick enough to hide it, though sufficient to prevent it casting a distinct shadow. The name is compounded of δπλός double, ἔδος an image, and σκοπέω I see, because in all positions except one it presents a double image of the sun. The instrument is to be fixed by a chronometer so that it may be in the position of showing the single image of the sun exactly at noon; and then at about a minute before noon the two images make their first contact, and at the same time after noon they completely separate, and the times of these contacts and also of the complete coincidence can be observed within two or three seconds. The following is the principle of the construction.

Let ABC be the rectangular section of a prism set so that a ray of the sun SI, and its reflected ray IR₁, lie in the plane perpendicular to the axis of the prism. It is not solid, but composed of three small glasses of which AB, AC, are mirrors, but BC is only a plain glass not silvered. Consequently, the ray SI will be partly reflected from BC in the direction IR₁, but part of it will pass through the glass and be reflected by the mirror AC on to AB, and there reflected again and sent through BC in the direction aR₂, making some angle $\backslash alpha$ with BC. Suppose the angle of incidence, and therefore of first reflection to R₁, to be $A-\backslash delta$ ($A$ being the opposite angle of the prism), and the other angles as marked in the figure; and let us see what $\backslash alpha$ the angle of the twice reflected ray will be.

Now, $\backslash beta\; =\; \backslash pi\; -\; (C\; +\; A\; -\; \backslash delta)$, in the small triangle near C; therefore, in the one near A, $\backslash gamma\; =\; \backslash pi\; -\; (A\; +\; \backslash beta)\; =\; C\; -\; \backslash delta$; and in the triangle near B, $\backslash alpha\; =\; \backslash pi\; -\; (B\; +\; C\; -\; \backslash delta)\; =\; A\; +\; \backslash delta$. And, therefore, the difference between the directions of the once

reflected and the twice reflected rays is $2\backslash delta$; and if the prism is so placed that the angle of incidence = the opposite angle of the prism at noon, the rays will then emerge parallel at noon, and the two images of the sun will be seen as one; as noon approaches, the images converge, and after noon diverge, with a velocity double that of the sun itself.

But the plane of incidence and reflection can only be perpendicular to the axis of the prism twice a-year. Still the same result will take place if it is once set properly. For suppose it to be set perpendicular to that plane at the equinox: then at midsummer the incident and reflected ray IR₁ will lie in planes making the angle $\backslash omega$ (the obliquity of the ecliptic) with the equinoctial plane; but SI and IR₁ will be sections of two other planes parallel to the axis of the prism, in which the incident and reflected rays also lie. And, in like manner, the ray reflected from AC will lie in a plane at the angle $\backslash omega$ below the equinoctial plane; and that reflected from AB to R₂ also; and the projections of these rays on the equinoctial plane will lie in the same direction as before; and, therefore, the twice reflected and the once reflected rays will emerge parallel, as before, when SI is in the plane of the meridian.

The prism is inclosed in a small solid brass box in the shape of an irregular pyramid about two inches high; and it is made so that it only requires fixing on a horizontal bed. They are only made by Mr Dent, as he is the proprietor of Mr Bloxam's patent. Instead of fixing them and so leaving them exposed to the air, he has lately adopted the plan of fixing a brass plate on the window-sill where the instrument is to stand, with a raised edge against which one side of the diploidscope is laid when it is first set by the chronometer, and afterwards whenever it is used. It is generally necessary either to smoke the front glass, or to look at it through a piece of smoked or coloured glass, which is supplied with it, as well as the necessary table of the times of first and last contact for every day in the year. Mr Dent has also lately made them to revolve upon an axis parallel to the earth's axis, and with a graduated hour circle, so that they may be used for any other hour as well as noon. But in this case the instrument can only be used (except at noon) for the latitude for which it is constructed, like a sun-dial, unless it has an adjustment for latitude also, as some of them have.

Some instrument of this kind ought to be kept by everybody who thinks it worth while to have a good clock, and yet has no other means of occasionally obtaining the real time, more accurately than from railway clocks, or public clocks of ordinary quality. For those who feel any difficulty about using the diploidscope, or who wish to be quite independent of the setting by a chronometer in the first instance, Mr Denison recommends, in his Treatise on Clocks, the following simple and independent construction of a sun-dial on a larger scale for noon only, which is quite sufficient for the occasional correction of a tolerably good clock:—Fix a thin plate of metal (protected against rust in any way you please) with a small hole in it, facing the south as nearly as you can, and inclined to the horizon at about $50^\backslash circ$ (not that the inclination is material), with the hole about nine inches above a stone slab set quite firm and level. Mark the point on the slab exactly under the hole by means of a pointed plumb-bob, and call it C. About 11 o'clock see where the bright spot falls on the slab, and call that A, and with radius CA draw as much of a circle as is likely to be wanted for the bright spot again to reach it about 1 o'clock. Mark the place where it does reach it $\backslash alpha$, and bisect the arc A$\backslash alpha$ in M suppose, and draw a straight line CM, as long as the slab will hold, from C through M. That line is the meridian, and the spot will always fall upon it at solar noon. Before you mark the line strongly, it will be as well to take several observations of this kind at different times, before and after noon, and on different days;

Diplomacy, and if their bisections agree in falling on the line CM you may be sure it is right. We have seen one of these dials with the gnomon only six inches high, and the time can be taken from it perhaps as accurately as from a dipeidoscope, and certainly with far less trouble.

In order that the bright spot may fall on the slab in winter, the distance of its northern edge from C must be rather more than four times the height of the hole above the slab. If this size is inconvenient, there may be a second hole made at half the height, the plate or gnomon not being finally fixed; then on any fine day in the summer half of the year, move the gnomon until the spot from this second hole also falls on the line CM at noon (it can be done in a moment), and there fix the gnomon. The lower spot will then always

fall on the slab if it is made only half the size above mentioned, though in winter the upper one will fall beyond it. It is best to make the slab a light colour, and an equation-table may as well be cut upon it. (x. n. d.)