doubtful whether an angle can be measured by it even to that degree of accuracy: c is a prism, which the observer looks through in observing with the instrument. The perpendicular thread of the sight-vane, E, and the divisions on the card appear together on looking through the prism, and the division with which the thread coincides, when the needle is at rest, is the magnetic azimuth of whatever object the thread may bisect. The prism is mounted with a hinge joint, D, by which it can be turned over to the side of the compass-box, that being its position when put into the case. The sight-vane has a fine thread stretched along its opening, in the direction of its length, which is brought to bisect any object, by turning the box round horizontally; the vane also turns upon a hinge joint, and can be laid flat upon the box, for the convenience of carriage. F is a mirror, made to slide on or off the sight-vane, E; and it may be reversed at pleasure, that is, turned face downwards; it can also be inclined at any angle, by means of its joint, d; and it will remain stationary on any part of the vane, by the friction of its slides. Its use is to reflect the image of an object to the eye of the observer when the object is much above or below the horizontal plane. When the instrument is employed in observing the azimuth of the sun, a dark glass must be interposed; and the coloured glasses represented at G, are intended for that purpose; the joint upon which they act, allowing them to be turned down over the sloping side of the prism-box.

At e, is shewn a spring, which being pressed by the finger at the time of observation, and then released, checks the vibrations of the card, and brings it more speedily to rest. A stop is likewise fixed at the other side of the box, by which the needle may be thrown off its centre; which should always be done when the instrument is not in use, as the constant playing of the needle would wear the point upon which it is balanced, and upon the fineness of the point much of the accuracy of the instrument depends. A cover is adapted to the box, and the whole is packed in a leather case, which may be carried in the pocket without inconvenience.

The method of using this instrument is very simple. First raise the prism in its socket, b, until you obtain distinct vision of the divisions on the card, and standing at the place where the angles are to be taken, hold the instrument to the eye, and looking through the slit, c, turn round till the thread in the sight-vane, bisects one of the objects whose azimuth, or angular distance from any other object, is required; then, by touching the spring, e, bring the needle to rest, and the division on the card which coincides with the thread on the vane, will be the azimuth or bearing of the object from the north or south points of the magnetic meridian. Then turn to any other object, and repeat the operation; the difference between the bearing of this object and that of the former, will be the angular distance of the objects in question. Suppose the former bearing to be 40° 30' and the latter 10° 15', both east, or both west, from the north or south, the angle will be 30° 15'. The divisions are generally numbered 5°, 10°, 15°, &c. round the circle to 360°. A stand can be had with the instrument, if required, on which to place it when observing, instead of holding it in the hand.

THE VERNIER.

This is a contrivance for measuring parts of the space between the equidistant divisions of a graduated scale. It is a scale whose length is equal to a certain number of parts of that to be subdivided, depending on the degree of minuteness to which the subdivision is intended to be carried; but it is divided into parts which in number are one more or one less than those of the primary scale taken for the length of the vernier in modern practice, the parts on the vernier are generally one more than are contained in the same space on the primary scale.

If it is required to measure to hundredths of an inch, the parts of a scale which is graduated to 10ths, it may be done by means of a scale whose length is nine tenths of an inch, and divided into 10 equal parts; or by one whose length is eleven tenths of an inch, and divided into 10 equal parts; for in either case the difference between the divisions of the scale so made and those on the primary scale is the hundredth of an inch. Such a scale made to move along the edge of that to be subdivided is called a vernier; and we shall explain how by its application, either to straight lines or arcs of circles, the subdivisions of graduated instruments are read off. For this purpose, let us take as a general example the method of reading the sextant, as a person acquainted with the graduations upon this instrument will find no difficulty in becoming familiar with those on any other.

It will be observed,* that some of the divisional lines on the limb of the instrument are longer than others, and that they are numbered at every fifth, thus, 0. 5. 10. 15, &c. the 0 being the start

* The reader is supposed to have an instrument before him while perusing these instructions..

ing point, or zero. The spaces between these lines represent degrees; and they are again subdivided by shorter lines, each smaller space representing a certain number of minutes. For instance, if the spaces are subdivided into four parts, then there will be three short lines, each of which will indicate the termination of a space of 15 minutes; if there are six parts, there will be five short lines, and each will be at the end of a space of 10 minutes, reckoned from the commencement of the divisions. Likewise it will be observed, that some of the divisions on the vernier are longer than others: these indicate in the same manner single minutes, and they are numbered from right to left: the extreme right one is the zero, or commencement of the index divisions, and it is marked 0 or ◊; the shorter divisions shew fractions of minutes. If the spaces between each minute (or long division) contain three lines, each space will be 15 seconds, and if five, 10 seconds; the number of subdivisions between the minutes of the vernier is usually, but not necessarily, the same as between the degrees on the limb, so that if the limb is divided into 20′ the vernier is divided into 20"; if the former is divided to 10' the latter is divided to 10", &c.

The limb of the instrument now before us is divided to 10', and the vernier reads to 10", and by shewing the manner of reading it off, we shall explain sufficiently the method of reading verniers in general. If the zero division of the vernier coincide (or form a straight line) with any line on the limb, then that line indicates the required angle; thus, if it coincide with the line marked 60, then sixty degrees is the angle; if with the next long division, then 61 degrees will be the angle; but if it coincide with one of the shorter lines between 60 and 61, then the angle will be 60 degrees and a certain number of minutes, according to which of the short lines it coincides with. If it be the first, (of the instrument before us) the angle will be 60° 10′, but if it coincide with the second, it will be 60° 20′, if with the third, 60° 30′, &c. But when it happens that the zero division of the index does not coincide with any division upon the limb, but stands between two of them, we must observe how many degrees and minutes are denoted by the division it has last passed, and look for a line on the vernier that does coincide with one on the limb; and the number of minutes and seconds from that line to the zero of the index, added to the number read off upon the limb, gives the angle required. Thus, supposing the index to stand between 10' and 20′ beyond 60°, and the line on the vernier denoting 6′ 10′′ (which is the line next beyond the one marked 6) coincides with any one on the limb, then this quantity, added to 60° 10', gives 60° 16' 10", the angle required.

When the arc of excess on the limb of a sextant (the nature of which will be explained hereafter) is required to be read off, observe what quantity is passed to the right of zero by the zero division of the vernier, and find the remaining minutes and seconds to be added to it, by reading the vernier backwards; that is, consider the last numbered division to the left hand as the zero: thus, suppose that (on our instrument) the index stood beyond the third short division on the arc of excess, this would be 30′, and if the third long

division from the last numbered one on the left hand (marked 10), coincided with a line on the limb, this would denote 3' to be added to the former, making 33′ for the reading on the arc of excess.

On the limbs of small theodolites, the spaces between the degrees are generally divided into two parts, consequently the short division represents 30', and the divisions on the vernier are single minutes; a smaller subdivision must be estimated by the eye, which by a person accustomed to the instrument can be done to 15".

The subdivision of a straight line, as the scale of a mountain barometer, is likewise effected by a vernier, and is read off in the following manner. The scale is divided into inches, which are subdivided into 10 parts; these tenths are again divided into two, by a shorter division, which will be 5 hundredths of an inch. The long divisions upon the vernier shew each of them one hundredth of an inch, and they are numbered at every fifth; these are again subdivided by shorter lines, representing thousandths. Now to read it off, observe where the zero division of the vernier stands on the scale; suppose a little above 30 inches and 4 tenths, and as it does not reach the short line denoting 5 hundredths, observe what line on the vernier coincides with one on the scale: if it is a long division, then it is so many hundredths to be added, and if a short division, it will be so many hundredths and thousandths to be added, to make up the measurement, and the readings are written decimally thus, 30.435 inches.

In the subjoined figures, which are given for the purpose of illustration, A B represents a portion of the graduated limb of an instrument, and C D a portion of the vernier scale, the zero point being at C.

In the first figure, the limb is divided to 15', and these divisions are subdivided by the vernier to 15". In the second figure, the limb is divided to 10', and subdivided by the vernier to 10". In the third, the limb is divided to 20', and subdivided by the vernier to 30"; and in the fourth, the limb is divided to 20', and subdivided by the vernier to 20". E, on each figure, is placed where a division on the vernier coincides with one on the limb. In the first, the reading is 45° 46′ 30′′; in the second, 60° 21′ 20′′; in the third, 21° 23′ 30′′; and in the fourth, it is 17° 2′, and between 0" and 20", and as the 2' line is about as much in advance of the one on the limb near to it, as the 20" line is behind the one near to it, the reading may be taken as 17° 2' 10". The fifth figure represents the scale of a barometer, reading 30.435 inches, and is drawn much larger than the reality, to render it more intelligible.

30

THE THEODOLITE.

As an angular instrument, the theodolite has from time to time received such improvements that it may now be considered as the most valuable instrument employed in surveying. Instruments of this kind, of the best construction, may to a certain extent be used as altitude and azimuth instruments; and several astronomical operations, such as those required for determining the time, the latitude of place, &c. may be performed by them, and to a degree of accuracy sufficient for most of the purposes that occur in the ordinary practice of a surveyor.

There are various modes of constructing theodolites to suit the convenience or the views of purchasers; but we shall confine ourselves to a description of one of the most perfect, as a person acquainted with the details of its adjustments and use, will find no difficulty in comprehending those of others.

Description of the Theodolite.

This instrument (as represented in the next page) consists of two circular plates, A and B, called the horizontal limb, the upper, or vernier plate, A, turning freely upon the lower, and both have a horizontal motion by means of the vertical axis, C: this axis consists of two parts, external and internal, the former secured to the graduated limb, B, and the latter to the vernier plate, A. Their form is conical, nicely fitted and ground into each other, having an easy and a very steady motion; the external centre also fits into a ball at D, and the parts are held together by a screw at the lower end of the internal axis.