80è 



4. The above considerations can be applied in oalonlating the 

 oritical opalescence. For that piiij>ose we use the simple method 

 indicated by Lokentz'), which consists in superposing' Ihe iiglit- 

 vectors caused b}' the inthience of every individual molecule in a 

 ])oint at great distance. 



Consider in the substance through which a beam of light passes, 

 a volume I" great with respect to the wave-length, and take a distant 

 point P, the direction VP forming an angle (4 with the incident 



ray. 



All molecules lying in one plane perpendicular to the line which 

 bisects the angle <i , will cause equal phase in P. Take therefore a 

 system of axes with the Z-axis parallel to this line, then the con- 

 tribution of one molecule will be 



j? sin — {d -\- 2z cos i (f) 

 (i). 



where /? depends only on the kind of molecules, on / and on the 

 distaiu'C V P, jLi being the index of refraction. 



The number of molecules in d.r dii dz amounts to 



((( + V) d,i; ill/ dz. 



The total light-vector in P thus becomes 



r 2.T 



I? I («-| Ï') •*""'' — {ct-\-2z cox }^(f) da: di/ dz. 



V 



and the intensity 



^'— I dt I l{a~\ V,) [a f iv) sin ^ {<i + 2z, cos i (f) 

 VV 



sin — {cf-j- -^r cos i q) 



d.v^ di/^ dz^: d.v- dy- dz-. 

 Integrating with resp. to /. we get 



— ,i'^ I I [a- -\-a (iv-j- V-) -\- I'jrrj ens \ — (r, — S-) cos \ f f | d.^^.y^jlz-dx-dy-dz.. 

 V\' 



The mean value of this must be calculated. The term with r^ + iv 

 vanishes, and that with a'^ yields no contribution proportional to V. 

 We introduce the value of v^Vz from formula (10), and for = t 

 from form. (9). This gi\'es 



1) H. A. LoRENTZ, On the scattering of light by molecules. These Proceedings 13 

 y. 92 (1910). 



