Platinum Thermometry at Kew Observatory. 19 



tions, merely using the 20 ohms occasionally to furnish data from which 

 to calculate the heating effect under the normal conditions. To under- 

 stand how this is done we must glance briefly at the theory. 



Let E be the E.M.F., R' the internal resistance of the battery, K the 

 rest of the resistance in the battery circuit. Let r\ be the resistance in 

 either of the proportional arms, r the resistance in the bridge arm 

 containing the platinum thermometer, whose spiral has a resistance p. 

 Then if i denote the current in the spiral, H the heat given to it in 

 unit time, we have 



H = *> = E 2 r 1 2 P H-[(R + K')(r + r 1 ) + 2rr 1 p ......... (1). 



The heating of course is gradual, and theoretically it might be possible, 

 by rapid, skilful manipulation of the tapping key, to obtain a balance before 

 there is a sensible effect. In practice, however, this is hardly possible 

 in work of the highest accuracy. Only by the remotest chance does 

 one hit the balance at the first attempt, and, as a rule, the key must be 

 put down a good many times. Also, unless the key is held down a 

 sensible time, a small absence of balance may be overlooked. The 

 weaker however the current, the longer the time before sensible heating 

 exists, and with the 100 ohms in the circuit it seems possible to get a 

 fair balance before the heating effect is appreciable. Thus in comparing 

 platinum and mercury thermometers at high temperatures, where 

 accuracy of the order 0*01 C. is usually much above what is necessary, 

 the bridge has been regarded as balanced when no movement appears 

 in the galvanometer on depressing the key. 



In the fixed point observations, on the other hand, the resistances 

 have been adjusted until no movement appears on releasing the key. 

 Under these circumstances the current has exercised its full heating 

 effect. The platinum spiral is presumably heated to such small extent 

 above the surrounding temperature as is required for its gain of heat 

 from the current to balance the loss by radiation, conduction, &c. We 

 may pretty safely assume that this excess of temperature is proportional 

 to the heat given to the wire, but it must also depend on the specific 

 heat of the platinum, on its radiating and conducting power, and also 

 conceivably on the shape, dimensions, and material of the enclosing 

 tube. I understand that several authorities'* have proposed to keep i-p 

 constant in the spiral by suitably altering the battery resistance. This, 

 however, as the above reasoning shows, cannot secure constancy in the 

 temperature excess of the spiral at all temperatures. 



18. The application of the formula (1) presents difficulties. We 

 know at least, very approximately the resistance r\ of the propor- 

 tional arms, and the resistance p of the spiral, at any "fixed point" 

 temperature, but it is not customary to measure directly the resist- 



* For instance, Waidner and Mallory, 'Phil. Mag.,' July, 1899, p. 14. 



c 2 



