468 On Complete Radiation at a given Temperature. 



in space, but to be distributed in time according to a similar 

 law. In comparing the radiations at various temperatures, 

 we should have to suppose that, as the temperature rises, not 

 only does the total number of elementary impulses (of given 

 magnitude) increase, but also the accuracy of aim of each 

 group. 



We have thus determined a kind of impulse such that an 

 arbitrary aggregation of them will represent complete radia- 

 tion according to Weber's law (5). One feature of this law 

 is that F(n) approaches a finite limit as n decreases. In this 

 respect W. Michelson's special law (4) differs widely ; for, 

 according to it, ^(n) vanishes with n. This evanescence of 

 Y(n) implies that the integrated value of each of our com- 

 ponent impulses is zero. If we wish to inquire further into 

 the law of the impulse, we have to determine 0(-'k) so that 



/i(«) = Cw^g-"'/'^' (23) 



By successive differentiations of (10) with respect to m, it 

 may be shown that 



c 2c^ J_, 



e ''''' (I — ^c^x^) cos uxdx. , (24) 



Thus, if we take 



<f>(x)=e-'''''\l-2c'x^), .... (25) 



/i('0 ^^^^^ ^^ of the required form. The curve representative 

 of (25), viz. 



y = e~'\l-2x'), (26) 



is symmetrical with respect to x=0, vanishes when ^= +oo 

 and also when a;—+2~'. The positive area between the 

 last-named limits is numerically equal to the negative area 

 lying outside them. 



Other proposed forms for /(?/), such as those included 

 in (2), might be treated in a similar way ; but the above 

 examples may suffice. The simplicity of (8) compared, e. g., 

 with (25), may be regarded as an argument in its favour. 

 But we do not know enough of the mechanism of radiation 

 to draw any confident conclusion. What we most require at 

 present is more complete data from experiment, such as have 

 been promised by Prof. Langley. As regards the radiation 

 of very low frequency, a question may arise as to whether it 

 is included in our present measurements. Some authorities 

 have favoured the view that, when the frequency is suffi- 

 ciently diminished, all kinds of matter become transparent ; 

 but the electric theory seems to point in the opposite direction. 



