4iS A. L. Day and J. K. Clement — Gas Thermometer. 



were computed by the method of least squares. In computing 

 these constants the observations marked* in Table II were 

 omitted in order to equalize the intervals between points. By 

 comparing the T(obs.) — T (calcul.) values (Table II, column 

 fi) of the various pairs of observations, it will be seen that any 

 two values at the same temperature agree within 0*1°. With 

 one exception, the differences between observed and calculated 

 temperatures are all less than 1°. The average difference is 

 0-37° and the probable error of a single observation is 0*25°. 



The foregoing table (Table II) contains a complete series of 

 76 observations, without omission, covering a period of more 

 than three months in timej in the order in which they were 

 made and with the control melting points through which the 

 constancy of the thermoelements was assured. If we now 

 regroup these observations in the order of increasing tempera- 

 tures and combine the pairs referred to above, the relation 

 between the observed and calculated curves appears in a new 

 and interesting light. (Table III.) The average difference in 

 column 5, Table III, is somewhat smaller than in Table II. 

 The most notable feature, however, of these differences is their 

 sytematic variation. Below 500° the observed values are less 

 than the calculated ones ; from 500° to 800° the observed 

 values are greater, from 800° to 1000° the calculated values are 

 greater and above 1000° the observed values are greater. If 

 the calculated temperatures be taken as the ordinates of a curve 

 of which the E.M.F's of element " W " are abscissas, the 

 resulting curve will be a parabola, slightly concaved downward 

 (fig. 8). 



If now the differences in column 5, Table III, be plotted on 

 their proper ordinates, measuring upward from this parabola 

 when the difference is positive and downward when it is nega- 

 tive, the second curve will cross the first in three points, form- 

 ing two loops of about equal length and area. In fig. 8 the 

 dotted curve represents the observed temperature curve, with 

 the deviation from the parabola plotted on an exaggerated 

 scale. From this diagram, as well as from the figures in 

 column 5 of Table III, it is apparent that a simple equation 

 of the second degree is no longer quite competent to express 

 the electromotive force of the thermo-couple as a function of 

 temperature with the full accuracy of the measurement. In 

 their paper on the electromotive force of metals of the platinum 

 group, Holborn and Dayf state that the "relation between the 

 thermoelectric force and the temperature in metals of the 

 platinum group could be represented, within wide limits, with 

 an accuracy of d=l'0° by a function of the second degree." 

 The results of our experiments are represented by a function 

 f This Journal (4), viii, 46, 1899. 



