GENERAL EXPERIMENTS. 1. ESTIMATION OF TENTHS. Apparatus. Two scales, N and M, are placed side by side, one being divided into millimetres, the other into tenths of an inch. Also a steel rule A, Fig. 5, divided into millimetres, and so arranged that it may be pushed past a fixed index B, by a micrometer screw, C. A spring, D, is used to bring it back, when the screw is turned the other way. A Experiment. Read the position of each tenth of an inch mark of scale M, in tenths of a millimetre, estimating the fractions by the eye. Thus if the interval is one half, call it .5, if a little less, .4, if not quite a third, .3, and so on for the other fractions. The .3 and .7 are the hardest to estimate correctly, as we are liable to imagine the former too great, the latter too small. They should always be compared with the fractions one and two thirds. Record your observations in five columns, placing in the first the readings of the scale M, in the second the corresponding readings of N, and in the third the first differences of N. Next,. subtract the first from the last number in column two, and divide the difference by the number of spaces measured, that is, the number of readings minus one. This gives the average difference, and should be equal to each number of column three. Subtract it from these numbers, and place the results or errors, with proper signs, in column four. Next, compute the probable B A Fig. 5. E error (see page 3) of a single observation, using the fifth column for the squares of column four. In this way you can read any scale much more accurately than by its single divisions, and your computed probable error shows how closely you may rely on the result. Next bring one of the millimetre marks of A, Fig. 5, opposite the index B. Read its position, as described on page 20. The scale E gives units, or number of revolutions, and the divided circle hundredths. Move the screw, set again, and repeat several times. Take the mean and compute the probable error of a single observation. Do the same with the next millimetre mark. Now move the scale until the reading shall be in turn .1, .2, .3, &c., of a millimetre, taking care to move the screw after each, so that you will not be biassed by your previous reading. Next compute what should be the true readings in these various positions. Thus let m' be the mean for the first millimetre, m" for the second; the reading for one tenth would be m' + (m"-m') 10, for two m′+ (m” tenths m' + 2(m” — m′) ÷ 10, and so on. See how these readings agree with those previously found. If any differ by a considerable amount repeat them until you can estimate any fraction with accuracy. This work must be carefully distinguished from guessing, since there should be no element of chance in it, but an accurate division of the spaces by the eye. By practice one can read these fractions almost as accurately as by a vernier. 2. VERNIERS. Apparatus. A number of verniers and scales along which they slide are made of large size. The best material is metal or wood, although cardboard will do. By making them on a large scale, as a foot or more in length, there is no trouble in attaining sufficient accuracy. Several different forms are given in Gillespie's Land Surveying, p. 228, from which the following may be selected. 1st, Fig. 225, Scale divided to .1, Vernier reads to .01; 2d, Fig. 227, Same Vernier retrograde; 3d, Fig. 228, Scale .05; Vernier .002; 4th, Fig. 229, Scale 1°, Vernier 5'; 5th, Fig. 230, Scale 30', Vernier 1'; 6th, Fig. 233, scale 20', Vernier 30"; 7th, Fig. 239, Scale 30', Vernier 1'; Double Compass Vernier. Experiment. A vernier may be regarded as a simple enlargement of one division of the scale. Thus if the scale is divided into tenths of an inch, and the vernier into ten parts, it will read to hundredths of an inch. Always read approximately by the zero of the vernier, taking the division of the scale next below it. The fraction to be added is found by seeing what line of the vernier coincides most nearly with some line of the scale. Thus in the first example, we obtain inches and tenths by seeing what division of the scale falls next below the zero of the vernier. If this is 8.6, and the division marked 7 of the vernier coincides with a line of the scale, the true reading is 8.6.07 8.67. To prove this, set the zero of the vernier at 8.6 exactly. Nine divisions of the scale equal ten of the vernier. Hence each division of the latter equals .09, or is shorter by .01 than one division of the scale. Accordingly the line marked 1 of the vernier falls short by .01 of the scale-division, the 2 line .02, and so on. If we move the vernier forward by these amounts these lines will coincide in turn. Hence when the 7 line coincides, as in the above example, it denotes that the vernier has been pushed forward .07 beyond the 8.6 mark. This method may be applied to reading any vernier. To find the magnitude of the divisions of the latter, divide one division of the scale by the number of parts contained in the vernier. Read and record the verniers as now set. Then set them as follows: 1st, 8.03; 2d, 29.9; 3d, 30.866; 4th, 4° 10′; 5th, 0° 17′; 6th, 2° 58′ 30′′; 7th, 2° 51′. The last vernier is a double one, reading either way, the left hand upper figures being the continuation of those on the lower right hand. This is best understood by moving it 5' at a time and noting what lines coincide. After each exercise the instructor should set all the verniers, and compare the record of the student with his own. 3. INSERTION OF CROSS-HAIRS. Apparatus. Some common sewing silk, card-board and mucilage, also a pair of dividers, ruler and triangle. Experiment. A great portion of the accuracy attained in modern astronomical work is dependent on the exactness with which we can point a telescope, or other similar instrument, in a given direction. This is accomplished by inserting two filaments of silk or spider's web at right angles to each other, at the point within the telescope where the image of the object is formed. In the astronomical telescope, where a positive eye-piece is used, this point lies just beyond the eye-piece, that is between it and the object-glass. A ring is placed at this point on which the lines are stretched. In telescopes rendering objects upright, as in most surveyor's transits, the lines are commonly placed between the object-glass and erecting lenses, and close to the latter. In the microscope, and other instruments where a negative eye-piece only is used, the lines have to be placed on the diaphragm between the field- and eye-lenses. This plan is objectionable, since the lines should be very accurately focussed, which can then only be done by screwing the eye-lens in or out. In the other cases the whole eye-piece may be slid in or out until the lines are perfectly distinct, and do not appear to move over the object when the eye is moved from side to side. Fig. 6. It is comparatively easy to insert the lines on their ring, where a positive eye-piece is used. The following experiment therefore includes the others. Take a negative eye-piece, Fig. 6, from a microscope or telescope, and unscrew the eye-lens A. C is the diaphragm which limits. the field of view, and on which the lines should be placed. Cut from the cardboard a ring, Fig. 7, whose inner diameter is a little greater than the opening of the diaphragm, and the outer diameter such that it will easily rest on C. Mark on it two lines at right angles to each other passing through its centre. Unravel a short piece of the silk thread until you have separated a single filament. This is best done by holding the thread with the forceps over a sheet of white paper. We now wish to stretch two of these filaments over the lines marked on the cardboard circle. Put a little mucilage on the latter, dip one end of the silk into it, and press it down with one of the radial strips of paper shown in Fig. 7. When this is nearly dry fasten the other end in the same way, taking care to stretch it so that it shall be straight, or the twist in the thread will give it a sinuous form. Attach the Fig. 7. |