Read

ing the magnitude of the divisions of its scale in the following manner; focus it on the steel scale, placing it so that two divisions of the latter shall be in the field at the same time. each of them by the scale in the eye-piece, and take the difference; the reciprocal is the magnitude of one division in millimetres. Repeat a number of times and take the mean. To make any measurement, place this microscope with one of the others over the points to be determined, and take the reading with its scale, estimating tenths of a division; then substitute the steel scale as before, and read the millimetre mark preceding, also that following. By a simple interpolation the distance is obtained from these three readings with great accuracy.

Try both these methods with the objects to be measured, and then test the scale of tenths of an inch by measuring the distance of each inch mark from the zero, and reducing the millimetres to inches. Measure also in the same way the ten divisions of one of the inches.

One of the best ways to measure off a large distance, as ten or twenty metres, with accuracy, is by means of a couple of reading microscopes. A steel rule is used, the ends being marked by the microscopes, as they are in rough measurements, by the finger. In all cases where the graduation extends to the end of the rule it is better to use.the mark next to it, both as being more accurate, and as affording a better object to focus on.

21. DIVIDING ENGINE.

Apparatus. This instrument rests on a substantial stand ABED, Fig. 17, like the bed-plate of a lathe. A carefully constructed micrometer screw moves in this, and pushes a nut Ở from end to end. The screw should have a pitch of about a millimetre, or a twentieth of an inch, if English measures are preferred. The head of the screw is divided into one hundred parts, and turns past an index which is again divided into ten parts, as in Fig. 4, p. 24. The screw may be turned by a milled head or a crank. The nut must have a bearing of considerable length, a decimetre is scarcely too much, as any irregularities are thus compensated. It should be split so that it may be tightened by screws, or better, by a spring, and slides along two guides, AB formed like an inverted V, and DE, which is flat. A scale is cut on the latter to give the whole number of revolutions of the screw. The nut

should move with perfect smoothness from end to end, but not too freely. A certain amount of back-lash is unavoidable (that is, the screw may always be turned a short distance backwards or forwards without moving the nut), but this does no harm, as when in use it should always be moved in the same direction. A second screw similar to the other, but smaller, and at right angles to it, is attached to C,.so that its nut may be moved backwards or forwards about one decimetre. It carries a reading microscope R, made of a piece of light brass tubing, by inserting an eye-piece above, and screwing a microscope objective into the lower end. It may be focussed by sliding the tube up and down by a rack and pinion. Cross-hairs should be placed in the eye-piece, but in some cases a fine scale, or eye-piece micrometer, is preferable.

To use this instrument as a dividing engine, the microscope must be made movable, so that it can be replaced by a graver for metals, or a pen for paper. The micrometer head F has ten equidistant holes cut in it, in which steel pins can be inserted. These strike against a stop which they cannot pass unless it is pushed down by the finger. A sheet of thick plate glass DSTE serves as a stand on which to lay objects, and under it is a large mirror to illuminate them, but it may be removed when desired.

Experiment. This instrument may be applied to a great variety of purposes. Several experiments with it will therefore be described.

A

B

E

M

T

1st. To test the screw. Lay a glass plate divided into tenths of a millimetre on DSTE, and bring the microscope. over it. Use a moderately high power, as a 1′′ objective, and focus on the scale; the want of a fine adjustment may be partly remedied by varying the distance of the eye-piece from the objective. Bring the first division of the scale to coincide with the cross-hairs of the microscope by turning the micrometer

S

Fig. 17.

head F. Read the whole number of turns from the scale on DE, and the fraction from F. Move it one or two turns to the right, and set again; repeat several times, and compute the probable error

Turn the The differ

of one observation. It equals the error of setting. screw the other way, and bring it back to the line. ence between this reading or the mean of ten such readings, and that previously obtained, gives the back-lash. Set in turn on several successive points of the scale. The first differences should be equal. Mark two crosses on a plate of glass with a diamond, three or four centimetres apart. Measure the interval between them with different portions of the screw, and see if they agree. If not, the defect in the screw must be carefully examined, and corrections computed. The screw M should be similarly tested.

Procure a

2d. Determination of the pitch of the screw. standard decimetre (or other measure of length) and measure the distance between its ends. The temperature should be nearly that taken as a standard, or if great accuracy is required, allowance made for the difference of expansion of the screw and decimetre. From this measurement, which should be repeated several times, compute the true pitch of the screw, and the correction which must be applied when distances are measured with it.

3d. To measure any distance. Lay the object on the glass plate and bring the cross-hairs of the microscope to coincide first with one end of it, and then with the other. The difference in the readings is the length. Apply to it the correction previously determined.

4th. To determine the form of any curved line. For example, use one of the curves drawn by a tuning fork, in the Experiment on Acoustic Curves. Bring the cross-hairs to coincide with several points in turn of one of the sinuosities, and read both micrometer heads. These give two coördinates, from which the points of the curve may be constructed on a large scale, and compared with the curve of sines, the form given by theory. The relative positions of a number of detached points may also be thus determined, as in the photographs of the Pleiades and other groups of stars by Mr. Rutherford.

5th. Graduation. For a first attempt, make a scale on paper with a pencil or pen. Replace the microscope by a hard pencil with a flat, but very sharp point. It must be arranged so that it can be moved backwards or forwards a limited distance, but not sideways. Every fifth line should be longer than the rest, which

should be exactly equal to each other in length. Fasten the paper securely on the glass plate so that it shall not slip. Suppose now lines are to be drawn at intervals of half a millimetre. Insert a pin in one of the holes in F, and turn the latter to the stop. Draw a line with the pencil for the beginning of the scale, depress the stop to let the pin pass, give F one turn, bring the pin again to the stop and draw a second line, and so on. If the lines are to be a millimetre apart, draw one line for every two turns. In the same way, by inserting more pins a finer graduation may be obtained. Instead of using the pins a table may be computed beforehand, giving the reading of the screw for each line to be drawn, allowing for the errors of the screw, if great accuracy is required. The scale is then ruled by bringing the nut successively into the various positions marked in the table, and drawing a line after each.

A most important application of this instrument is to the measurement of photographs of the sun taken during eclipses. The position of the moon at any instant is thus obtained, with a degree of precision otherwise unattainable. In this, and other cases where angles must also be measured, the plate of glass ES should be removed, and the object laid on a rotary stand, with a graduation showing the angle through which it is turned.

22. RULING SCALES.

Apparatus. In Fig. 18, two strips of wood A and B, rest on a smooth board, and are held in place by the weights C and D. The ends of a string are attached to them, which is stretched by means of a weight F, so that if C and D are raised A and B will slide. A peg is inserted in B, which moves between two steel plates fastened to A, one being fixed, the other movable by means of a screw G. If, then, either weight is raised, the strip of wood on which it rests will be drawn forward by F, but will be free to move through a space equal to the difference of the diameter of the peg and the interval between the two steel plates. If desired, G may be a micrometer screw, by which this interval may always be accurately determined. It may be fastened in any position by a clamp or set screw. A steel rod H is used to draw the division lines. It is fixed at one end, and carries at the other a pencil, pen, graver or diamond, according as the lines are to be drawn on paper, metal or glass. By this arrangement there is little or no

lateral motion of the graver, but unfortunately it draws a curved line. To remedy this defect, the rod may be replaced by a stretched wire, to the centre of which the graver is attached, or the latter may slide past a guide against which it is pressed by a spring.

Experiment. For many purposes in using a scale, it makes but little difference what the divisions are, provided that they are all equal, and this is especially the case in all accurate measurements, since as a correction must always be made for temperature, we can readily at the same time correct for the size of the divisions. The instrument here described will probably give divisions more nearly equal than those obtained by a micrometer screw, but it is more difficult to make them of any exact magnitude, since any deviation is multiplied by the number of divisions.

To draw a scale, lay a piece of paper on B and fasten it with tacks or clips. To secure uniformity in the length of the long and

A forward a distance equal to the interval between the two plates near G, minus the thickness of the peg. Lay C down and raise D. A will now remain at rest, but B will move through the same distance. Draw a second line with the pencil, and repeat, making every fifth line about twice as long as the others. They will be found spaced at distances which may be regulated by the screw G. Try making short scales in the same way, with large and small divisions. It is always safer to keep the hand on one weight while the other is lifted. The magnitude of F should be such that the strain on the cord will be greater than the friction of repose when the weights are up, but less than the friction of motion when they are down. If F is too light, when C is raised A will not start; if too heavy, it will strike so hard that it will move B. To test the accuracy of the machine draw a single line, take a hundred