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other thread in the same way, and bending the four strips of paper down lay the cardboard on the diaphragm. To hold it in place cut a strip of cardboard or brass, and bending it into a circle push it into the tube. By its elasticity it will hold the paper strips firmly against the sides of the tube. If the experiment has been well performed, on replacing the eye-lens we see two straight lines at right angles, dividing the field of view into four equal parts. The cardboard should not project beyond the diaphragm, or it will give a rough edge to the field of view, and we must be careful that no mucilage adheres to the visible portions of the threads.

4. SUSPENSION BY SILK FIBRES.

Apparatus. The best method of suspending a light object so that it shall move very freely is by a single filament of silk. The only apparatus needed is a stand seven or eight inches high, some unspun silk (common silk thread will do, but is not so good) and some fine copper wire. We also need two pairs of forceps, such as come with cheap microscopes, some bees-wax and a sheet of white paper.

Experiment. Lay the silk on the paper and pick out a single fibre a little over six inches long. Bend pieces of the wire into the shapes A and B, Fig. 8. Pass one end of the filament through the ring of B, and fasten it with a little wax, twisting or tying it to prevent slipping. Fasten the other end to A in the same way, making the distance from A to B just six inches. Hook A into the stand, and lay the object to be suspended, as a needle on B.

5. TEMPERATURE CURVE.

A

B

Fig 8.

Apparatus. A beaker, stand and burner, by which water can be heated, a Centigrade thermometer, and a clock or watch giving seconds.

Experiment.

Place the thermometer in the water and record the temperature, dividing the degrees to tenths, as described in Experiment 1. Place the burner under the beaker at the beginning of a minute, and at the end record the temperature; repeat at the end of each minute, as the water is warmed, until the ther

mometer stands at 95°; at the end of the next minute remove the burner and the temperature will at first continue to rise, and will then fall rapidly. Record the time (in minutes and seconds) of attaining 95°, 90°, 85°, &c., taking shorter intervals as the temperature becomes lower, and the cooling less rapid. Record your results in two columns, one giving times, the second temperatures. Finally construct a curve in which abscissas represent times, and ordinates temperatures, making in the former case, one space equal one minute, in the latter, one degree.

When two students, A and B, are engaged in this experiment, the following system should be used. A observes the watch and records, while B attends to the thermometer. Five seconds before the minute begins A says, Ready! and at the exact beginning, Now! B then gives the reading which A records. This plan saves much trouble, and greatly increases the accuracy of any observations which must be made at regular intervals of time.

6. TESTING THERMOMETERS.

Apparatus. An accurate Centigrade thermometer is hung upon a stand, and close to it a Fahrenheit thermometer, which is to be tested, their bulbs being at the same height, and close together. A telescope with which they can be read more accurately is placed on a stand at a short distance, and their temperature may be altered at will by immersing their bulbs in a beaker of water, which may be either cooled by ice, or heated by a Bunsen burner. Some arrangement is desirable for stirring the water to keep it at a uniform temperature. One way is to use a circular disk of tin with holes cut in it, which may be raised or lowered in the beaker by a cord passing over a pulley, so that the observer, while looking through the telescope, can stir the water by alternately tightening and loosening the cord. A simple glass stirring rod may be used instead, if preferred.

Experiment. The problem is to determine the error of the Fahrenheit thermometer at different temperatures, by comparing it with the Centigrade thermometer, which is regarded as a standard. By means of the telescope read them as they hang in the air, estimating the fractions of a degree in tenths. Do the same when their bulbs are immersed in water, then cool them with ice and read again. This observation is important, as it shows the absolute error of each instrument. Next heat the water a few

ECCENTRICITY OF GRADUATED CIRCLES.

33

degrees with the burner, and then remove the latter. The temperature will still rise for a short time, then become stationary and fall. Read each thermometer at its highest point, stirring the water meanwhile. Repeat at intervals of about 10° until the water boils, and finally immerse again in the ice water, and see if the reading is the same as before.

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We have now two columns of figures, the first giving the temperature of the Centigrade, the second that of the Fahrenheit, thermometer. Reduce the first to the second, recollecting that 0° C. = 32° F., and 100° C. = 212° F.; hence F. = C. + 32°, calling and F the corresponding temperatures on the Centigrade and Fahrenheit scales respectively. Write the numbers thus found in a third column, and the errors will equal the differences between them and the readings given in column two. If the Centigrade thermometer does not stand at zero when immersed in ice water, all its readings should be corrected by the amount of the deviation, taking care to retain the proper sign. Now construct a curve whose ordinates shall represent the errors on an enlarged scale, and abscissas the temperatures.

7. ECCENTRICITY OF GRADUATED CIRCLES.

Apparatus. A circle divided into degrees carries a pointer with an index at each end, which turns eccentrically, that is, the centres of the pointer and circle do not coincide. It may be made in a variety of ways. One of the simplest is to place a pivot on one side of the centre of the circle, and on it a rod with a needle projecting from each end. Another way is to let the circle turn and cover it with a plate of glass, on which are marked two fine lines, with a diamond or India ink. The indices may also be made of fine wire, or horsehair. Lines of considerable length must be used, since the edge of the circle advances and recedes as it is turned. If greater accuracy is desired the plan shown in Fig. 9 may be adopted. The two indices (which may have verniers) are connected with the centre by the arms AC and CB. The circle turns around the pin D, and a rod passing through the guides EF, keeps the verniers in the proper position. Another good instrument for this experiment is the form of compass described under Magnetism in the latter part of the present work.

E

D

B

Fig. 9.

8

1

Experiment. Set the index A at 0° by turning the circle, and read B. Repeat moving A 10° at a time, until a complete revolution has been made. We have now two columns, giving the corresponding readings of A and B. Subtract 180° from the latter, and 1(A + B — 180°), or 1(A + B) 180°), or (A + B) — 90° will be the true reading; write this in column three; in the same way the error of each index is (A —B) — 90°, which should be written in the fourth column. Construct a curve with abscissas equal to the numbers in column three, and ordinates equal to those in column four, enlarged. At the highest and lowest parts of the curve the indices differ most from their true position, or the absolute error, if we read one only, is here greatest. Find these points by Curves of Error, p. 14. On the other hand, where the curve cuts the axis the two indices are opposite each other, and the abscissa gives the azimuth of the line CD. As the ordinates alter most rapidly at these points, the error, when reading a small angle by one index, is here a maximum. Draw tangents, as before, by Curves of Error, and from their direction we can compute the amount of variation. It is a very good exercise to deduce by trigonometry the theoretical curve, and constructing it on the same sheet of paper to compare the results with those obtained by your measurement.

We have heretofore supposed that the line connecting the indices passed through the axis around which they turned, or that D lies on EF. If, as often happens in practice, this is not the case, a second correction is necessary.

8. CONTOUR LINES.

Apparatus. No apparatus is needed for this experiment, except ordinary writing materials. It is, in fact, an exercise rather than an experiment.

Experiment. Mark in your note book nine rows of six points each, so as to form forty squares of about one inch on a side. Mark them with numbers taken from the adjoining table A. Now suppose these numbers represent the heights of the points to which they are attached, and we wish to draw contour lines to show the form of the surface passing through them. As the points are pretty near together we may assume that a line connecting any

two that are adjacent will lie nearly in the surface. Now regard your drawing as a map, as on p. 15, and suppose the ground

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75 80

94 80 81

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33 63 95 37 44 71 86

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71 58 61 82 96 70 59 7083 84 67 65 72 79 73 66 67 67 72 76 69 flooded with water to a height of 80. Evidently all the points in the upper line will be submerged except that on the left, and the shore line will come between 79 and 83, about a fourth way from the former. Also midway between 82 and 78 in the second line, two fifths of the way from 78 to 83, and a third way from 79 to 82. Several points are thus obtained in each square through which the contour line passes. After obtaining as many as possible, draw a smooth curve nearly coinciding with them all, paying special attention to the rules given under the Graphical Method. Construct in the same way other contours at intervals of ten units. Do the same with the numbers in table B or C.

This work is very well supplemented by procuring from the U. S. Signal Bureau at Washington, some of their blank maps (issued at $2.75 per 100), and filling them out from the weather reports for the day, according to their published directions. These maps may also be used for drawing isothermals, isogonals, &c., if a list is prepared in the first place of the temperature, magnetic variation, &c., of a large number of stations in the United States. The method adopted for drawing these lines is essentially the same as that given above, only the points are irregularly spaced.

9. CLEANING MERCURY.

Apparatus. But little apparatus is needed for this experiment, except such as is found in every chemical laboratory. Some bottles, funnels, &c., should be placed on the table, and the student should try as many of the following methods of purification as he can, and record in his note-book his opinion of their comparative value.

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