into a number of small squares, by a large number of straight lines drawn at right angles to one another. The distances of the points measured horizontally from oy (Fig. 26) should be taken to represent the deflections on the galvanometer G, and the distances of the same points measured vertically from o x the corresponding amounts of gas produced in a given time—that is, the corresponding values of the current.

It may be asked how distances along a line can represent the angular deflections on a galvanometer, or the amount of gas produced in a given time. What is meant is this: the line ox is subdivided into a number of equal divisions by the ruling on the squared paper; one, or any convenient number, of these subdivisions is taken arbitrarily to stand for 1°, then any deflection is represented by this number of divisions that we have arbitrarily taken to stand for 1°, multiplied by the number of degrees of the deflection. Similarly one, or any convenient number, of the divisions along o Y is taken arbitrarily to stand for one cubic centimetre of gas liberated per minute, then any number of cubic centimetres liberated per minute in a test will be represented by the number of divisions along oY that has been taken to stand for one cubic centimetre per minute, multiplied into the number of cubic centimetres liberated in that test per minute.

If the galvanometer is being calibrated only relatively the unit volume of gas may be that of unit length of the tube or its whole volume, and in that case a convenient number of divisions along o y will be taken to represent one such volume of gas liberated per minute.

And as these results, rather than the training of the experimenter, were the most important part of the investigation, the paper was very accurately divided, and sold at a high price totally out of the reach of students. It became, therefore, necessary to have squared paper specially made, cheap, and at the same time sufficiently accurately divided for students' purposes; and such paper, machine-ruled, can now be obtained at between a farthing and a halfpenny per sheet, or at about one-twentieth of the cost of the older squared paper.

P

5

10°

65°

15° 20° 25° B30° 35 40 A 45° 50° 55° 60° Galvanometer deflection in degrees.

Fig. 20.

70°

75°

In the same way a curve may be drawn to record the height of the barometer from hour to hour, or the variation in the price of some commodity from day to day, or the depth of the sea from point to point along some section of the ocean, and generally to give a picture of the way in which any two things vary with one another.

In selecting the scale-that is, in determining the number of divisions along o x or along o y-that is to be taken to represent 1° deflection, or unit volume of gas liberated per unit of time in the preceding experiment, we must remember that it is desirable that the curve, which we are about to draw, shall be as large as possible, since the larger it is the more accurately we can draw it. The scale should, therefore, be so selected that the maximum deflection of the galvanometer that has been used in the experiment should be represented by nearly the whole of o x, and the corresponding maximum quantity of gas developed in the given time by nearly the whole of o Y, since with this arrangement the curve would occupy nearly the whole of the sheet of squared paper. For example, suppose that the length ox is divided by the ruling of the paper into 170 equal divisions, and o y into 100, and suppose that the maximum galvanometer deflection was 79°, and that when that deflection was produced the liquid ascended from the zero mark at the bottom of the tube to the top mark in 22 seconds, then, if one minute be the fixed time decided on, the most suitable scales for distances measured along ox and along o y would be selected as follows :—

2.15 divisions per 1° would, however, be a little awkward to employ when deflections of 17°, 291°, &c., had to be represented; 2 divisions per 1° would therefore be better. 37 divisions along o Y, to represent one volume of the tube per minute, would just enable the maximum rate of liberation of the gas, corresponding with 2.7 volumes of the tube in the minute, to be represented by the whole of o y; but 37 divisions for unit rate of liberation would be a little awkward to employ when other rates had to be represented; probably, therefore, 30 divisions along o Y, to stand for the unit rate, would be more convenient.

Having obtained a sufficient number of points by experiment, a curve should be drawn connecting these points. Such a curve can be drawn by bending an elastic piece of wood, and holding it so as to pass as nearly as possible through all the points that are plotted on the squared paper to record the results, and then using the bent piece of wood as a ruler, along which to draw a line. A better way is to bend a piece of soft brass strip, bit by bit, until the edge of the strip passes through the average position of the points.

Unless, however, the experiment has been performed with great accuracy—to attain which requires, not merely the careful attention of those engaged in making the experiment, but a certain amount of practice in experimenting-it must not be expected that a curve so drawn will pass through all the points; some of them, b, are sure to be a little too low, meaning that the deflection on the galvanometer has been read too high, or that the rise of liquid in the graduated tube has been read too low, from, perhaps, an error having been made in taking the time, or from the current not having been kept on for a sufficient time before the pinch-cock c (Figs. 22, 23, 24) was closed for the gas to have commenced to come off regularly. Some of the points e (Fig. 26), on the other hand, are sure to be too high, meaning that the deflection on the galvanometer has been read too low, or the rise of

liquid in the graduated tube too high; or it may be that the experiments were fairly well made, and that b and e are merely plotted incorrectly, and so do not represent the results of the experiment.

14. Practical Value of Drawing Curves to Graphically Record the Results of Experiments.-It may be asked, But is it not possible that the points b and e, although not on the curve, may be quite correct? The answer is, No, because experience makes us quite sure that the connection between the deflection of the galvanometer G and the current strength must be a continuous one, and, therefore, that the points correctly representing the true connection must all lie on an elastic curve, or on such a curve as can be obtained by bending a thin piece of wood or steel, and, consequently, that if no mistake has been made in plotting the points b and e, some mistake must have been made in taking the observations. But what is even more important, we are also sure that the points b' and e' on the curve, obtained by drawing lines through and e respectively parallel to o Y, give far more accurately the relative strengths of the currents producing respectively the two deflections in question, than the currents obtained directly from the experiment itself. Drawing the curve, then, corrects the results obtained by the experiment. But it does something more than that—it gives, by what is called "interpolation," the results that would have been obtained from intermediate experiments correctly made; that is to say, it tells us. what would be the relative strengths of the currents that would produce deflections intermediate between the deflections that were actually observed. For example, suppose it be required to know the strength of current which will produce a deflection of 41°, for which deflection no experiment has been made, compared with that which will produce a deflection of, say 281°, for which deflection also no experiment has been made, then all that is necessary is to draw a line parallel to o Y, through the point A in ox corresponding with 41°, similarly to draw a