1891.] The Thermal Emissivity of Thin Wires in Air. 171 



At 100 C. e = 0-0010360 +0-0120776CZ- 1 (1), 



200 e = 0-0011l] 3 +0-0143028d~ 1 (2), 



300 e = 0-0011353+0-016084 d~ l (3), 



where d is the diameter of the wire in mils, or thousandths of an 

 inch. 



The emissivities have been calculated in calories lost per second 

 per square centimetre per 1 C. excess temperature, in order that they 

 may be compared with the emissivities obtained by other experi- 

 menters, but we prefer to speak of the diameters of the wires in mils, 

 since a wire of 1 mil is about the finest that is drawn commercially. 

 Hence the statement that the diameters of wires are 1, 2, or 3 mils is 

 more suggestive to an engineer than saying that they are 0"0254, 

 0-0508, or 0-0762 millimetres. 



The statement, not unfrequently made, that the current required to 

 maintain a wire of a given material at a given temperature above 

 that of the surrounding envelope is proportional to the diameter of 

 the wire raised to the power three halves, is equivalent to stating 

 that the emissivity is independent of the diameter. Now from the 

 three formulae (1), (2), (3), given above for e, we may conclude 



That for a temperature of 100 C. the value of d in the formula 



e = 0-0010360 -f-0-0120776^- 1 



must be something like 220 mils, or 5'6 mm., in order that the neglect 

 of the second term may not make an error in e of more than 5 per 

 cent., and something like 1"15 inch, or 29'3 mm., if the error is not 

 to exceed 1 per cent. ; 



That for a temperature of 200 C. the value of d in the formula 



e = 0-0011113 +0-0143028<T 1 



must be something like 244 mils, or 6'2 mm., in order that the neglect 

 of the second term may not make an error in e of more than 5 per 

 cent., and something like 1'28 inches, or 32'5 mm. if the error is not 

 to exceed 1 per cent. ; 



And that for a temperature of 300 C. the value of d in the 

 formula 



e = 0-0011353 + 0-016084(T 1 



must be something like 267 mils, or 6"8 mm., in order that the 

 neglect of the second term may not make an error in e of more than 

 5 per cent., and something like 1*39 inches, or 35 '3 mm., if the error 

 is not to exceed 1 per cent. 



Generally, then, we may conclude that to assume that the emissivity 

 is a constant for wires whose diameters vary from a small value up to 

 1 inch is to make a large error in the case of the greater number of 



