38 A BICYCLE ERGOMETER WITH AN ELECTRIC BRAKE 



The left-hand member of this equation is proportional to the heat 

 generated per revolution of the disk, since the numerator represents the 

 rate of production of heat, while the denominator indicates the number 

 of revolutions per minute. We are thus in a position to obtain relative 

 values for the heat per revolution, based on magnetic data alone, which 

 can be compared, for the same current in the electro-magnet (1.25 am- 

 peres), with the calibration curve of the ergometer (fig. 13). Since k 3 

 is a constant and the temperature of the disk changed but little during 

 the magnetic tests, it is sufficient to compute the values of cocf> 2 at various 

 speeds and to plot these values as functions of the speed. The values of 

 wc/> 2 corresponding to the three observed values of <f> are given in table 7. 



In order to draw the entire curve, it was necessary first to find the 

 relation between (/> and (o. This relation, which can be derived from our 

 fundamental assumptions, is 



a, a 



where a and b are constants. The equation is roughly satisfied by our 

 observed values of $ and co, but we considered it better to obtain values 

 of 4> corresponding to various values of o from a curve connecting these 

 quantities. Since the curve was nearly a straight line over the observed 

 range, the interpolation was simple. To facilitate the comparison with 

 the ergometer calibration curve for 1.25 amperes, all of the values of w4> 2 

 were multiplied by a constant numerical factor, so that the maximum 

 of the calibration curve coincided with one point of the cw< 2 curve. In 

 fig. 13 the (#<f> 2 curve is shown as a fine line. It has the same general 

 form as the calibration curve, but its maximum comes at a lower 

 speed. This is no doubt due in large measure to the sources of error 

 already mentioned. But it may also be due partly to the fact that since 

 no attempt was made in the magnetic tests to reach thermal equilibrium, 

 the copper disk was, for the same speed, cooler during the magnetic tests 

 than during the calibrations. At low speeds, where $ is nearly constant, 

 the relatively small value of <r during the magnetic tests would make the 

 heat per revolution relatively high. But at high speeds a smaller value 

 of <r means a larger value of <f>', hence a relatively small value of <f>. 

 Since equation (5) shows that the heat per revolution varies as the square 

 of cf>, the result will be a relatively small value of &></>*. A rough calcu- 

 lation shows that the correction from this cause would amount perhaps 

 to 5 per cent, raising the ordinates to the right of the maximum of the 

 o)<f> 2 curve slightly, and reducing those to the left. 



Nevertheless, aside from minor discrepancies, the similarity of the 

 two curves is very striking, proving beyond a reasonable doubt that the 

 peculiarity^in the ergometer calibrations is due almost entirely to the 

 demagnetizing effect of the eddy currents in the disk. The increased 

 temperature of the disk at high speeds, by reducing the intensity of the 

 currents, enhances this peculiarity, but only to a minor degree. 



