High Temperatures hy the Method of Colour Identity. 51 



and in most cases is considerably less than 1 per cent. — i. e.. 

 within the possible error of the experiments. Further, it is- 

 shown later that a very large extrapolation of the tungsten 

 curve by this formula indicates a value for the melting-point 

 of tungsten which is not inconsistent with that found by 

 other observers. The formulae indicate that the maximum 

 attainable efficiency would occur in the region of 6000° CL, 

 which is quite in accord with accepted theories. 



The origin of the constants in equations 7, 8, and 9 should 

 be particularly noted. The watts-temperature relationship 

 for a lamp has been found to be of the form Wcc T m (equation 

 1), m being a constant which appears in equation (7). The 

 constant p of equation (7) is equal to n + u— 1, where iC — n" 

 is the index of \ in equation (2) of the " Wien " form, which 

 is assumed to give the power distribution curve for the 

 filament throughout the visible part of the spectrum, and 

 where "a" is derived from Nutting's equation for the sen- 

 sitivity of the eye, and has the value 181. B=-^- (see 



equation 6), where Q is the other constant in the assumed 

 Wien equation for power distribution, " a, " has the value as 

 before of 181, and \ m is the wave-length of the energy to 

 which the eye is most sensitive, i. e., 0*55 /jl. Hence 



B= qq.k^ . For a true black or grey body ??i = 4, ?i=5, 



/3=185, Q = 14,500, and B = 145'0 approximately. 



Before leaving the consideration of these equations con- 

 necting lumens per watt ;md temperature, it is desirable to 

 discuss one or two points which at first sight may appear to 

 have an important bearing on the deductions that can be 

 made from the foregoing results. 



Firstly, as regards " n" in equation (5) and "m" in 

 equation (7). For a black body the value of "n' J in equa- 

 tion (5) is 5, and it will also be 5 for a true grey body whose 

 radiation in all wave-lengths bears a definite proportion to 

 that of a black body. It will not necessarily be 5, however, 

 for selective bodies, although, as in the selective bodies under 

 consideration, they appear to radiate very much like grey 

 bodies over the visible spectrum. 



In equation (7) the constant " m" which is derived directly 

 from equation (1), can only be regarded as connected with 

 "w" (?z = m + l) in equation (5) if the latter represents the 

 distribution of power throughout the whole spectrum, and not 

 merely in the visible spectrum. This latter is the assumption 

 made in using equation (5) in this investigation, and the 



E 2 



