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form in which the results should be tabulated, are given, together with “ Inferences" to be deduced. These latter, if conscientiously worked out, are calculated to cause the experimenter to think and reason for himself. Following the series of tests is an Appendix containing the algebraical solutions of the various formulæ used in the tests, and these the student is strongly recommended not to refer to until he has tried by all the means in his power to solve the inference for himself. The Appendix also contains complete descriptions and sketches of almost all the apparatus which may be employed in carrying out the tests, and it is such as will be found, to a large extent, in almost every college and testing

Useful tables and data, which are constantly needed in physical and electrical engineering work, are added at the end of the book.

It is sincerely hoped that the general arrangement of the present work will be found both helpful and conducive to systematic and valuable results.

A considerable amount of the apparatus illustrated has been constructed by the mechanical assistants, Messrs. John Watkinson and Herbert Addy, of the Physical and Electrical Engineering Departments of the Yorkshire College respectively.

In conclusion, I wish to express my sincere thanks to my. valued friend Mr. Charles Mercer, M.A., for the very considerable amount of trouble he has taken in producing the greater proportion of the photographs from which the illustrations are obtained, to Dr. John Henderson for permission to use the tables of squares and reciprocals of numbers, to Mr. S. Joyce for allowing me to use his tables of sines and tangents, to Messrs. Kelvin & James White for permission to use the table of doubled square roots, to Her Majesty's Stationery Office for allowing me to use the tables of logarithms and antilogarithms, and also to Messrs. Nalder Bros. & Co., R. W. Paul, Kelvin & James White, and W. & J. George for their kindness in lending me the blocks of some of the illustrations of the very excellent apparatus made by them.


January, 1901.

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1. Curve Plotting. Introduction. It is of paramount importance in a great many kinds of work, but perhaps more especially in physics and electrical engineering, to thoroughly grasp, firstly, the great convenience, advantage, and practical utility of representing the results of any experiment, when possible graphically (as well as in tabular form), by means of a curve, which will show the variation of one quantity with another; secondly, the method of accurately and rapidly plotting such curves to the most convenient scales for future reference.

By means of a curve, the way in which two quantities vary together can not only be seen at a glance far more easily than from the table of results, but there is the enormous advantage that any intermediate values between those actually obtained from experiment can be easily, quickly, and accurately deduced, providing the curve is drawn as it should be. In order to more fully illustrate the method and principles involved in plotting curves, tables of results obtained from two totally different experiments, together with their corresponding curves drawn on squared curve paper, are shown in Figs. 1 and 2.

Instructions.-(1) After having neatly entered up the results of the experiment in a “finished” table, note carefully the magnitudes of the two sets of quantities to be plotted, and on which axes OA and OB (Figs. I and 2) each is to be plotted. Distances measured from OB along lines parallel to OA are called "ordinates," those parallel to OB being termed "abscissa."

(2) Choose the numerical value of the lengths of the axes so

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as to obtain as large a curve as possible, for this will enable it to be drawn more accurately, and will magnify experimental errors and the desired result.

(3) Number the axes at well-defined and equal intervals, and at no other points, choosing as convenient a scale as possible for readily reckoning intermediate values.

(4) Write along each axis the denomination of the quantity plotted thereon, as shown in Figs. 1 and 2.

(5) Plot the points by mentally following out the right axes to their point of intersection, using a convenient notation for the points. Thus, if several curves are to be plotted on the same sheet of curve paper, they may or may not be very close together, and even cross one another. Hence, to avoid confusion, the following notation for points might be used :



(6) Draw a probable or mean curve through as many of the points as possible in the way shown (Figs. I and 2), endeavouring to get as many of the erroneous points on one side of the curve as on the other, but, of course, as many on the curve itself as possible.

Note.—The curve line should be thin and clear, and, unless otherwise authorized, the curve sheet must bear no other numbers than those mentioned in (3) above.

On no account should any other curve than the mean one be drawn. Some of the points, all of which, whether erroneous or not, must be plotted, are sure to be experimental errors, and would give an irregular and erroneous curve if the latter was drawn through all of them. Thus we see that a curve corrects experimental observations, and in addition enables the nature of the law of the instrument to be observed.

Fig. I shows the relation between the deflection and current producing it in a certain galvanometer.

Fig. 2 shows that between the magnetic induction produced in a sample of iron and the magnetizing force causing it.

The first-named is what is called the “relative" calibration curve of the galvanometer. If, however, the values of current, c,

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