a half wave length long, a second resonating circuit ought to be found by increasing each side of the rectangle by a half wave length, making the circuit 3 half wave lengths long, and a third when the circuit is 5 half wave lengths long, and so on.' This is evident from a consideration of the accompanying diagram. segment and the points marked 1, 3, 5, are always nodes.

0

O is the center of a central

From the results that he obtained, Bjerknes concluded that the change of period, if there was such a change, by the use of iron in place of copper, could not exceed two per cent.

The difference in length between a copper and an iron circuit of the same period would be very small with circuits a half wave length long, but this difference would be three times as great with circuits 3 half wave lengths long, and there might be a cumulative difference that would finally become measurable by the use of circuits of still greater length. This theory was tested in the following way. A copper wire (diameter 0.1201 cm.) was used as the secondary circuit in Figure 5. The sides were taken 15 cm. long, and then gradually lengthened to 875 cm., and bolometer readings observed for each addition. The results are shown graphically by the upper curve in Figure 4 of the Plate. The critical points in the curve are the results of many separate determinations. The unsteadiness of the spark in the vibrator made the determinations somewhat laborious, though a single series of observations would locate a maximum very closely. After this had been done, a space of about a meter including the maximum point was worked over forward and back, changing its length 2.5 to 5 centimeters at a time in the region of the maximum. To assure the steadiness of the spark during such a series of observations, some convenient length of circuit was chosen as a point of reference, and observations taken before and after the series; if these showed that the activity of the spark was practically the same, the readings of the

* J. J. Thompson, Recent Researches in Electricity and Magnetism, § 297.

series were retained. The results here given rest upon such readings.

An examination of the curve shows four maxima, E, F, G, H, occurring when the sides of the rectangle were 45, 306, 562.5, and 818 cm. long. The additions of wire for the successive maxima after the first were 261, 256.5, and 255.5 cm. These additions should be a half wave length; the last two are nearly the same, but the first differs by 5 cm. from the average of the last two, which is 256 cm. With the sides fixed 818 cm. long, the wave form along the circuit was determined by sliding the exploring terminals over the wires by short steps, and observing the bolometer throws for each position. The result is shown in Figure 3 of the Plate. The critical points were determined several times, and a method similar to that described above was used to assure the constant activity of the spark. The curve shows three minima, occurring at 240, 496, and 752 cm. Starting from the point O these give half wave lengths of 255, 256, and 256 cm., with an average of 255.6 cm. The third minimum at 752 was determined with care, as it was to be used as a basis for calculating the half wave length. A small error in determining the position of this miniumm would be divided by 3 in obtaining the result, since its distance from O was 3 half wave lengths. The total length of the circuit was 7 half wave lengths. From the third minimum to the end it was one fourth of a wave length, the capacities bring each equivalent to 62 cm. of the wire. By fixing the length of the rectangle at 562.5 and 306, a similar investigation showed the circuits to be respectively 5 and 3 half wave lengths long.

An explanation of the fact mentioned above, that the distance between the first and second maxima was anomalously large, may possibly be this: the sides of the rectangle for the first maximum were but 45 cm. long, so that the effect of the closed end in increasing the self-induction was relatively large, and the maximum appeared earlier than it otherwise would; but when the rectangle was 300 cm. long, the influence of the closed end became relatively small, and the second and future maxima came in the normal positions. In the first case the capacity was mostly local, while in the second it was largely distributed, and the length of the circuit was greater than the wave length. This same effect appeared in every case, and seemed to be a constant phenomenon.

The maximum I, omitted from the above discussion, was not constantly present, but appeared when the primary spark was particularly active, and seemed to belong to a circuit whose period was to the

period of the primary as 5 to 3. The side of the rectangle was 127.5 cm., and the end capacities equivalent to 62 cm. of wire. The half wave length was

30+127.5 x 2 + 62 × 2 = 409. 409 255.6 = 1.6, nearly.

This was the only indication observed of complexity in the vibration of the oscillator. It appears that, when the oscillator is especially active, it can excite a circuit having this ratio to itself, or that the vibration is not a simple one. Time was not at disposal sufficient to decide this point, which is left for future investigation.

A comparison of the curve (Fig. 1 of Plate) obtained from the plain wire circuit with the curve (Fig. 3 of Plate) obtained when capacities were fixed on the free ends shows a quite satisfactory agreement in the results, which tends to create confidence in both methods. The half wave length by the first is 254.3 cm., by the second it is 255.6 cm., values which differ by about one half of one per cent. There is a marked difference, as was to be expected, in the form of the curve for the quarter wave length next the free ends. When end capacities were used, the accumulation of charge seemed mainly confined to those out of reach of the exploring terminals, while with the plain wire it seemed distributed over a greater distance, and could be detected by the exploring terminals. In each case the effect of the ends was to make the curve depart from its normal form along the free wire.

the

An annealed iron wire (diameter 0.1186 cm.) was put in place of copper, and the same series of observations was made as with the copper. The results are shown graphically in the lower curve of the upper pair in Figure 4 of the Plate. The maxima E, F, G, H, appear at 42.5, 301, 553, and 805 cm.; in each case before the corresponding maxima with the copper, and the difference increases with the length of the circuits, as is evident from an examination of the curves. The successive additions after the first maxima are 258.5, 252, and 252 cm.; the last two agreeing, while the first, as with the copper, is larger. With the sides of the rectangle fixed at 805 cm., the form of the wave was found as shown in Figure 2 of the Plate. The third minimum occurs at 740 cm. Calculating its half wave length as before, 740 + 15 =755. 755 ÷ 3 = 251.6 cm. This agrees well with the value 252 cm. given above by the last two additions, but differs by 4 cm. from the value found when the copper was used.

The same series of observations was repeated with a second pair of finer wires (diameter of copper wire 0.07836 cm., diameter of iron

0.07850 cm.). The results are shown in the lower pair of curves in Figure 4 of the Plate, the upper one, as before, being the copper. A comparison of the curves shows the same general result, which appears more distinctly from the following table.

The successive differences should be in the ratio of 1, 3, 5, 7, if the theory of the investigation is correct. The differences for the first two maxima are very small, so that the experimental error in their determination would be relatively large.

In the case of the fourth maximum, the damping was so great that it was difficult to fix the point with certainty. The difference for the third maximum was relatively large, and the determination of the maximum point was sharp. Taking this difference as a point of reference, the calculated and observed values are shown in the following table.

The observed half wave lengths for the four wires were as follows:

S Copper (diameter 0.1201 cm.), 255.6 cm.

Iron (diameter 0.1126 cm.), 251.6 cm.

Copper (diameter 0.07836 cm.), 251.6 cm.

Iron (diameter 0.07850 cm.), 246.8 cm.

The wires in each pair were as near the same diameter as could be found, the iron of the larger pair having slightly the smaller diameter,