430 M. Wladimir Michelson on the Distribution 



It is towards a law of this sort that the distribution ot 

 radiant energy in each spectrum must tend as its continuity 

 becomes more and more perfect, that is to say, as the elective 

 absorptions along the path of the rays diminish. To obtain a 

 more complete expression of the law it would still be neces- 

 sary to determine the value of p and the form of f{6) ; but 

 our formula is capable of giving some interesting results 

 without our even having to make such a specialization. 



It is evident that, under this general form, our law embraces 

 as particular cases all the empirical laws of emission proposed 

 hitherto, such as those of Newton, of Dulong and Petit, and 

 of Stefan. 



If we were to attribute to 6 a constant value, and if we were 

 to take X as abscissa, and I A as ordinate, equation (10) would 

 be the equation of the curve of energy in the normal con- 

 tinuous spectrum of a solid source at the temperature 6. 

 These are the curves which M. Crova has called "isothermic 

 curves."* In order to study the general properties of these 

 curves, we will suppose 6 constant and take the derivative of 

 the expression I A . 



2. Limits of the Spectrwn. — It is easy to see, from formula 

 (10) and its derived formula, that if/(0) and p have definite 

 values, we shall have for \ = and X=co , 



I,=0 and§=0. 



This signifies that all the curves of energy represented by 

 equation (10) are tangents to the axis of \ at the origin of 

 coordinates, and that they have this axis as an asj-mptote. At 

 the two extremities of the spectrum the radiant energy dimi- 

 nishes to zero ; but whilst towards the violet it disappears 

 almost suddenly because of the rapid diminution of the factor 



c 



e" 0k2 , the less refrangible energy extends indefinitely towards 

 the side of increasing \. This fact has been recently observed 

 by Prof. Langleyf. 



3. Maximum Intensity. — Each of the curves represented by 

 equation (10) presents only a single maximum defined by the 

 condition 





(11) 



We see that the position of maximum intensity in our spectra 



* A. Crova, " Etude des Radiations," &c. {Ann. de Chim. et de Phya. 

 [5] t. xix. p. 472). 



f S. P. Langley, " Sur les Spectres invisibles " {Ann. de Chim. et de 

 Phys. Dec. 1886). 



