is necessary, in order to make a neat joint, to feather edge each sheet; this is done by carefully cutting with a knife half way through the paper near the edges, and on the sides, which are to overlap each other; then strip off a feather-edged slip from each, which, being done dexterously, the edges will form a very neat and efficient joint when put together.

The following method of mounting and varnishing drawings or prints was communicated some years ago by Mr. Peacock, an artist of Dublin. Stretch a piece of linen on a frame, to which give a coat of isinglass or common size. Paste the back of the drawing, leave it to soak, and then lay it on the linen. When dry, give it at least four coats of well-made isinglass size, allowing it to dry between each coat. Take Canada balsam diluted with the best oil of turpentine, and with a clean brush give it a full flowing coat

GENERAL RULES APPLICABLE IN ALL GEOMETRICAL

CONSTRUCTIONS.

In selecting black-lead pencils for use, it may be remarked that they ought not to be very soft, nor so hard that their traces cannot be easily erased by the India rubber. Great care should be taken, in the pencilling, that an accurate outline be drawn; the pencil marks should be distinct yet not heavy, and the use of the rubber should be avoided as much as possible, for its frequent application ruffles the surface of the paper, and will destroy the good effect of shading or colouring, if any is afterwards to be applied.

The following seven useful rules are taken from Mr. Thomas Bradley's valuable work on Practical Geometry:

"1. Arcs of circles, or right lines by which an important point is to be found, should never intersect each other very obliquely, or at an angle of less than 15 or 20 degrees; and, if this cannot be avoided, some other proceeding should be had recourse to, to define the point more precisely.

"2. When one arc of a circle is described, and a point in it is to be determined by the intersection of another arc, this latter need not be drawn at all, but only the point marked off on the first, as it is always desirable to avoid the drawing of unnecessary lines. The same observation applies to a point to be determined on one straight line by the intersection of another.

"3. Whenever the compasses can be used in any part of a construction, or to construct the whole problem, they are to be preferred to the rule, unless the process is much more circuitous, or unless the first rule (above) forbids.

"4. A right line should never be obtained by the prolongation of a very short one, unless some point in that prolongation is first found by some other means, especially in any essential part of a problem.

"5. The larger the scale on which any problem, or any part of one, is con structed, the less liable is the result to error; hence all angles should be set off on the largest circles which circumstances will admit of being described,

and the largest radius should be taken to describe the arcs by which a point is to be found through which a right line is to be drawn; and the greater attention is to be paid to this rule, in proportion as that step of the problem under consideration is conducive to the correctness of the final result.

"6. All lines, perpendicular or parallel to another, should be drawn long enough at once, to obviate the necessity of producing them.

"7. Whenever a line is required to be drawn to a point, in order to insure the coincidence of them, it is better to commence the line from the point; and if the line is to pass through two points, before drawing it the pencil should be moved along the rule, so as to ascertain whether the line will, when drawn, pass through them both. Thus, if several radii to a circle were required to pass through any number of points respectively, the lines should be begun from the center of the circle; any error being more obvious when several lines meet in a point.

PART II.-ON OPTICAL INSTRUMENTS.

UNDER this head our principal object will be to consider the construction, and principles of action, of such instruments as are indispensable to assist the vision in making observations upon distant objects, whether upon terrestrial objects for the purposes of the surveyor, or upon celestial objects for the purposes of astronomy and navigation. We propose, however, to add a few words upon such other optical instruments, as by their utility, or by the frequency with which they are brought before us, appear to demand our attention.

We shall thus be led, in the first place, to review briefly the properties of prisms, lenses, and plane and curvilinear reflectors, and shall then proceed to give descriptions of the following instruments, viz.,

Microscopes.
Telescopes.

The Camera Lucida.

The Camera Obscura. J

Such as are adapted to surveying and astronomical instruments, rather fully.

Very briefly.

THE PRISM.

A collection of straight lines, either conical or cylindrical, representing rays of light, is called a pencil of light, and the axis of the cylinder or cone is called the axis of the pencil.

The term medium is used in optics to signify any transparent substance, that is, any substance into which a portion of the light falling upon it can pass.

The term prism in optics is used to signify a portion of any medium bounded by plane surfaces which are inclined to one another. The bounding surfaces are called the faces of

the prism; the line in which the faces intersect is called the edge of the prism; and the angle at which the faces are inclined is called the refracting angle.

The prism is to be placed so that the axis of the pencil, by which an object is seen through it, be in a plane perpendicular to the edge of the prism; and the axis of the pencil during and after its passage through the prism still remains in this plane.

One effect of a prism of denser material than the surrounding medium is to bend every ray of light passing through it, and, consequently, the whole pencil, further from the edge of the prism.

Another effect of such a prism is to decompose each single ray of white light into several rays of different colours, which rays are bent at different angles, so as to form a lengthened image of different colours, of the point from which the ray proceeds. This image is called the spectrum, and these colours the colours of the spectrum.

When, then, any object is viewed through a prism, the two following effects

are produced. S

1stly. The ap

parent position of

K

M

the object is changed, so that, if the prism be held with its edge

-L

downwards, as in the accompanying figure, the object appears lower than it really is, while, if the prism were held with its edge upwards, the object would appear in a position higher than its actual position. 2ndly. The boundaries of the object are indistinctly defined, and fringed with colours.

Our figure represents the section of the prism made by the plane of incidence, that is, by the plane which is perpendicular to the edge of the prism, and contains the incident ray of light PQ, forming the axis of the pencil under consideration, which proceeds from one point of an object P. AQ and AR are sections of the faces of the prism; A is a point in its edge; and the angle QAR is its refracting angle. Now the ray of light, PQ, proceeding from the object at P through the medium of the atmosphere, is bent, upon entering the denser medium of the prism, from the direction Q T into the direction QR, nearer to LQ K, the perpendicular, at the point of incidence q, to the face Aq of the prism; and, upon emerging

from the prism into the rarer medium of the atmosphere, is again bent from the direction QR into the direction Rs, further from M RN, the perpendicular to the face AR at the point of emergence R. The eye, being placed at s, sees the point P, therefore, by means of a pencil of light of which 8 R is the axis, and P consequently appears at p' on the prolongation of the line SR. A similar effect being produced upon every other point, the entire object is apparently depressed, as represented in the figure.

The angle TES, or PEP', between ERS, the direction of emergence, and PET, the direction of incidence, is called the angle of deviation *.

The consideration of the properties of the prism is of great importance, as exhibiting in the simplest manner the principles of the refraction and dispersion of light. The prism is also used in optical instruments, to change the direction of the pencils of light by which an object is observed, in order to make the apparent place of this object, as viewed through the prism, coincide with the actual place of other objects seen directly, as in the prismatic compass †, or for the mere purpose of convenient observation, as in the Newtonian telescope +

The amount of refraction when a ray of light passes from one medium into another varies with the angle of incidence, so that the sine of the angle of refraction bears a constant ratio to the sine of the angle of incidence. This ratio varies for each different medium, and is called the refracting power of the medium. The deviation of a ray in passing through a prism varies also with the angle of incidence, and has a minimum value when the angles of incidence and emergence are equal: and the refracting power can be determined by finding practically this minimum deviation, as follows:-Place the prism with its edge downwards, so as to receive a small beam of solar light, admitted into a dark room through a hole in a shutter, and let the beam of light, after refraction, be received upon a screen behind the prism. The prism must then be turned round an axis parallel to its edge, so as to vary the angle of incidence, and, consequently, the position of the bright spot upon the screen; and, in one particular position, we shall find the bright spot to remain stationary for an instant, though the motion of the prism is continued. The deviation will then be a minimum, and will be equal to the sum of the sun's altitude and the inclination of the emergent beam to the horizon. Let s represent this minimum deviation, and ▲ the refracting angle of the prism, and let the

LENSES.

A portion of any medium bounded by two spherical surfaces having a common axis, or by a spherical surface and a plane one, is called a lens.

The effects produced by lenses upon pencils of light depend both upon the form of the lens itself, and upon the direction in which the pencil is proceeding with respect to the lens. Lenses consequently receive distinguishing names, to mark either different forms, or different positions with respect to the light falling upon them. These distinguishing names are the following, and the forms and positions of the corresponding lenses are represented in the accompanying diagram, the light being considered to be proceeding from left to right.

( X X MU ) S

8

10

5. Plano-convex. 6. Convexo-plane.

9. Concavo-convex. 10. Convexo-concave.

The rays forming any pencil of light must either be divergent, parallel, or convergent; and when a pencil of light passes through an essentially convex lens, that is, one which is thicker in the middle than at the edges, as 1, 2, 3, 5, 6, the rays are made more convergent, so that a pencil of converging rays becomes still more convergent, a pencil of parallel rays becomes convergent, and a pencil of diverging rays becomes either less divergent, parallel, or convergent: but when a pencil of light passes through an essentially concave lens, that is, one which is thinner in the middle than at the edges, as 4, 7, 8, 9, 10, the rays are made more divergent, so that a pencil of converging rays becomes either less convergent, parallel, or divergent, a pencil of parallel rays becomes divergent, and a pencil of diverging rays becomes still more divergent.

The sensation of vision is produced by pencils of rays proceeding from every point of the visible object, and entering