160 



f X 1 •• uo To* 

 i^) - = - = • "'■ 



lAoJ - u T* 



(4) XT = XoTo = constant. 



Wicn's displaccmont law may ho extended .so as to give a general formula 

 for the distril)ution (>( energy in the spectrum, viz., Ex = CX '^f (XT;, where EX 

 is the emissive power for radiation of wave-length X and C is a constant. To 

 prove this let ;-o change to r, then radiations of wave-lengths between X,, and 

 (Xo — dXuj will be changed to those of wave-lengths between X and fX — dX). 



r r dX r X 

 Also X = — Xi,, and a + dX = — (Xu + dX,,), whence = — = — . 



ro r„ dXu r,) X,, 



du fXol'' 



From (3) = — . But da is pro])ortionaI to E), dX. Therefore 



duo [ X I 



E'A dX du fXol* Ex Xu'' 



= = I — I , or = . Since ecjuation (4) holds we may write 



EXodXo duo [X J E/.o X-' 



(5) Ex = X-5 EXoX=o = CX"' f (XT). 



AH general distribution fornuihe must satisfy this eciuation. It remains 

 to determine the form of the function f(XT). The pai-ticular form will de- 

 pend upon the assumptions made. Wien found 



_SL _ Ci 



f(XTj = e XT, or Ex = CX'^e XT. 



For large values of X and T this formula fails. Lord Hayleigli proposed the 



formula EX = CiX-''Te XT. This formula fails for small \alues of X and 



7'. About lOOl Planck proposed ( he formula 



C,X-^ 

 EX = . 



f c, ] 



[eXT_]J 



'i'liis formula agrees with exiierimcnt and approaches the fornniho of Wien and 

 l^avleigh foi- the range of values for which each holds best. It has already 

 sujjplanted Wien's to a considerable extent in cduimcrcial i)raclice with high 

 tem])eratiuT furnaces. 



This foi'inula is based on a new and startling hypothesis which has come 

 to be known as the "(Quantum Hypothesis," to which refei'ence has already 

 been made. The importance of the new hypothesis is nuule a])parent by the 

 following (|Uol at ions. Ncrnst ' sa.\'s, "If Newton, when he created modern 

 mechanics, paved the wa.v to the results of theoretical ph,\sics, if Dalton in 

 the atomic theory gave |)liysics .and chemistry (heir most fruitful logical 

 «Prou-i.s. .\kal. Wis;., Hi-ilin, Sit',. Hoi. t, pp. (i.j-!H), lllll. 



