364 Transactions. — Chemistry and Physics. 



given conditions at a given temperature was, roughly, pro- 

 portional to the diameter of the wire raised to the power 

 three halves, the current was more nearly proportional to the 

 first power of the diameter if the wire were thin." Later on, 

 on page 395, after pointing out that their formulae for emis- 

 sivity may not be safely extrapolated, they assert that to 

 assume the emissivity to be constant would be to make " an 

 error of hundreds per cent, in the case of some of them " (i.e., 

 wires of diameters " from a small value up to 1 in."). 



This is an evident criticism of Sir W. Preece's work, but I 

 am wholly unable to find any practical effect following from 

 it. And, finally, Sir W. Preece's tables are quoted without 

 remark in all the electrical pocket-books I have seen. 



The crux of the whole question is the value to be taken for 

 the emissivity which is concerned in the phenomena in the 

 following manner : — 



Let C = current in amperes, 



pO = specific resistance at the temperature of fusion, 



e = emissivity in absolute measure or in gramme 

 calories per second, per square centimetre, per 

 degree (at the temperature of fusion), 



J = Joule's equivalent, gramme calories (Watt- 

 seconds), 



D = diameter of wires, 



A = a constant, 



= elevation of temperature of wire at fusion, 



then fusion is reached if there is no cooling effect of the ter- 

 minals in a wire when — 



C 2 ^ 2 = A J € 0D ; 



[or] OV^^D"; 

 [or] C = Df /ja? 



Sir W. Preece assumes the quantities under the root to be 

 a constant (1642, D being inches). 



If, now, we take my values for and p6 to be correct, we 

 may calculate the constant value for c which is assumed by 

 Sir W. Preece. It is — 



e — 0-00176 absolute units (approximately). 



Ayrton and Kilgour (I.e.) give the formula — 



e == 00011113 + 0-0143028 D-imils for a temperature 

 difference of 200° C. for platinum. 



The accompanying diagram (Plate XIV.), of which the 

 ordinates are values of e, the abscissa? values of ~ in., shows 

 clearly the relation between Sir W. Preece's law, Ayrton and 



