THERMO-ELECTRIC DIAGRAM FROM - 200° C. TO 100° C. 



749 



The sum of the errors in this calculation was +7*50 — 7*53, again verifying its 

 accuracy. These gave for the probable error ±1'31^ or ±2 '6 rnicro-volts. The agree- 

 ment between the calculations of 1898 and 1908 is worthy of notice, and a comparison 

 of the two shows the effect of replacing 15*20 by 15*12 as the value of cot «: the 

 result is — an increase of "53 per cent, in the value of tan « diminishes a by '053 per 

 cent., p by '057 per cent., and increases k by "0086 per cent. ; or the percentage altera- 

 tions of a and p are each one-tenth of that of tan w, while for k it is only one-sixtieth. 



In fig. 3 the curves of platinum (Callendar's) leading to equations (17) and (19) are 

 shown. The A-curve is the facsimile of the one drawn by hand from the recorded 

 observations. A series of mid-points of fifteen chords parallel to the short line a on the 

 diagram are shown, as well as the line on which they appeared to lie (as already stated), 

 and which gives cot w= 15 '20. From this curve also, previous to the calculation, a series 

 of sixteen values of dM/dt were measured by means of the stretched thread as formerly 

 described ; their values are given in the adjacent Table II. From equation (17) the 

 B-parabola was drawn, and along it the original observations, represented by small crosses, 

 are plotted. Similarly, from equation (19), the Tait-line was drawn, and along it the 

 sixteen measured values of dE/dt are shown by means of small circles. The closeness 

 thus exhibited between theory and observation is remarkable ; and the test by means of 

 the Tait-line, considering the difficulty in measuring the temperature associated with 

 any particular value of dJZ/dt, and further that this measurement is made from the 

 hand-drawn experimental curve, is so severe as hardly to leave any doubt as to the 

 truth of the theory. 



Table II. 



t". 



dE/dt. 



f. 



dE/dt. 



78-5 



-515-4 



- 45-5 



- 136-2 



57-5 



-457-6 



- 65-0 



- 55-0 



44-2 



-422-2 



- 78-1 



o- 



25-7 



- 370-0 



- 963 



+ 77-4 



7-8 



-317-2 



-113-6 



167-6 



- 4-7 



-279-4 



-145-8 



344-6 



- 26-2 



-206-4 



-158-4 



424-0 



- 32-4 



-184-4 



-171-5 



523-4 



Fig. 4 is the entirely new set of curves for this same metal calculated in 1908. 

 Here again in the A-curve we have a set of mid-points of nine chords parallel to the 

 short a-line shown on the diagram, making an angle tan" 1 '5 with the axis of 

 temperature. The straight line on which they are assumed to lie is shown, and its slope 

 was found, in the same way as for the 1898 curve, to be cot a> =15*12. Hence 

 equations (22) and (24) were found; and from them the B-parabola and Tait-line were 

 drawn. The original observations are plotted along the B-parabola. A fresh set of 

 determinations of thirteen values of dE/dt were measured from the A-curve, and plotted 



