From the data given in the last table three sets of curves were plotted. One set to show the variation due to the temperature, another the effect of speed in the amount of heat radiated, and the third showing the effect of the fields.

We come first to a consideration of the effect of temperature on the amount of heat liberated per square inch per degree rise in temperature. This is shown in Figs. 4, 5, 6 and 7. The curves plotted in these figures show the relation of the temperature (plotted along the vertical), to the amount of heat liberated per square inch per degree rise in temperature (plotted along the horizontal). In Fig 4 are shown four curves, I, II, III and IV obtained with the 100%, 75%, 50% and zero fields respectively. All

.002 .004 .006 .008 .010 .012 .014 .016 .018 .020 .022 .024 .026 .028 .030 .032
HEAT RADIATED PER SQ. IN. PER DEGREE RISE IN TEMPERATURE, WATTS.

FIG. 4.

are with a peripheral velocity of 3,000 ft. per minute, or about 1895 revolutions per minute. All of these curves are of the same general form, curve I being the steepest, and the others less and less so in the order in which they run. On examination we can very readily see that as the rise in temperature increases, the amount of heat radiated per sq. inch per degree rise in temperature also increases, but the rate of increase diminishes. It seems probable from the curves obtained, that somewhere along them the rate of increase becomes zero; that is the amount of heat liberated per sq. inch per degree rise in temperature becomes constant, and the total amount of heat liberated will thus become

proportioned, at the higher temperatures, to the rise in temperature. But this point is probably far beyond the range of temperatures allowable in armatures. In the experiments it was found that the hard rubber, used for insulation, became quite soft at about 140° centigrade.

A study of Figs, 5, 6 and 7 brings us to the same conclusion. In Fig. 5 are plotted curves similar to the preceding, but with a peripheral velocity of 2,000 ft. per minute, which is a speed of 1263 revolutions per minute. In these as in the previous set the amount of heat liberated per sq. inch per degree rise in temperature increases as the temperature, but the rate of increase gradu

ally diminishes. In the previous case we found that the curves became less steep as the amount of the armature covered by the field became less. In this case, however, the curves become very nearly parallel, except in the case of curve IV. which seems to follow rather an opposite law (if it may be so called), that is, it becomes less steep than any of the other curves, less steep even than that plotted for no field.

We also ascertain from this set of curves a fact that at first seems rather remarkable, namely, that curve IV crosses curve III; which means that while at the lower temperatures the amount of heat radiated with the 100 per cent. field, is less

than that radiated with the 75 per cent. field, at the same temperature, still as the rise in temperature increases, these two quantities gradually approach each other, become equal, and then the amount of heat liberated with the 100 per cent. field becomes greater than the amount liberated with the 75 per cent. field.

The curves plotted in Fig. 6 are for a peripheral velocity of 1,000 feet. per minute or a speed of 632 revolutions per minute. Here again we notice the same effect of temperature as in the previous case, and also the same peculiarity as regards the position of the curve for the 100 per cent. field. In this case, however, the curve for the 100 per cent. field lies entirely to the right of the curve for the 75 per cent. field, except for very small rises in temperature when it almost coincides with curve III. When we compare the curves shown in Figs. 4, 5 and 6, we find that as the speed is decreased, the difference between the curves for no field and for the 50 per cent. field becomes greater as compared with the difference between the 50 per cent. and 75 per cent. fields.

In Fig. 7 are shown curves similar to the above, but with the cylinder at rest, that is with a zero peripheral velocity. We see from these that the curve for the 100 per cent. field, lies entirely to the right of the curve for the 75 per cent. field, which means that the amount of heat liberated at any temperature, is greater with the former than with the 75 per cent., at the same temperature.

By comparing these four sets of curves (those given in Figs. 4, 5, 6 and 7) we find that as the speed is increased, the amount of heat liberated per square inch per degree rise in temperature is also increased; and that the rate of increase in the amount of heat liberated in any given case becomes smaller as the speed is increased. This is evident from the fact that with the lower peripheral velocities the curves are steeper, or are more nearly perpendicular to the horizontal, at the higher temperatures.

In every one of the preceding cases (16 in number), that is, with every speed and every field, we find that as the rise in temperature increases, the amount of heat liberated per degree rise in temperature also increases; and the rate of increase in the amount of heat liberated decreases as the rise in temperature increases.

Owing to the fact that the smallest amount of heat generated in the cylinder during any run was 100 watts, the curves are not accurate below a corresponding point. The above amount of

heat gave under the most favorable condition a rise in temperature of 23.5° centigrade as a minimum. Of course in drawing the curves as shown in Fig. 2 all should go through the origin, but the exact curvatures between the points for 100 watts and the origin are somewhat uncertain. Nevertheless the portions of the curves, below the points mentioned above, must be approximately correct. All the points of the curves below 25.5° to 30° C. in Figs. 4, 5, 6 and 7 were plotted by calculating from points obtained from such curves as are shown in Fig. 2.

It is probable that all of the curves shown in Figs. 4, 5, 6 and 7 pass through the origin; the calculations indicate that they do. But if we calculate the point at which the curve cuts the horizontal axis, we find that it is indeterminate. Because the cylinder does not radiate any heat when its rise in temperature is zero, it does not follow that the amount of heat liberated per degree rise in temperature at that point is zero. The curve cannot cut the vertical axis either above or below the origin, nor the horizontal axis to the left of the origin. If the curve cut the axis above the origin, the cylinder would radiate no heat when its temperature was above that of the atmosphere. It cannot cut the vertical below

the origin for a similar reason. And it cannot cut the horizontal to the left of the origin for in that case it must necessarily cut the vertical. There is a curve (perhaps similar in form to those shown) lying below the horizontal and to the right of the vertical axis, showing the effect of temperature on the amount of heat radiated or rather absorbed when the temperature of the cylinder is below that of the atmosphere. This curve must lie to the right of the vertical, because the rate at which heat is radiated must be a positive quantity. And it seems probable that the two branches of the curve form a cusp on the horizontal axis,

but whether this cusp is or is not at the origin we cannot say positively.

These curves also show that if the rise in temperature is small, the amount of heat liberated is also small, and most of the heagenerated, aids in raising the temperature of the cylinder or that of an armature. But as the temperature increases, the amount of heat liberated becomes very much greater, and but a small port tion aids in raising the temperature of the armature. This is one reason for the great length of time necessary to obtain constant temperature.