398 ME. J. C. MAXWELL GAENETT ON 



If I s denote the volume of the gold particles, so that I is given in the 8th or 9th 

 column of the Table II., according as p., the gold content, is taken from the 6th or 

 7th column, then the number 91 of gold particles per cubic (10" 1 centim.) is given by 



We have said that for our analysis to be applicable there must be many spheres to 

 a wave-length. Since the spheres in glasses A, B, Ca, Cb, Cc (Table II.) can be 

 separated by a Zeiss -r^th objective, they must be at a distance apart greater than 

 2/x., or half a wave-length of violet light. We shall therefore not expect our 

 analysis to apply to them. It is further apparent that the particles are more widely 

 separated in Da than Db. If we take for I the mean of the two numbers given, we 

 have 



'$'= -019, 91,, = 2-48. 9?, , = 6-24, ' 5R = 8'40, = 6'35, 



so that, since 9?,,, 9f, ; , and 9?,, are larger than 9t Db and 9? E , the glasses F, G, H 

 satisfy our condition best. 



But here we are presented with a difficulty. The wave-length of the yellow light, 

 \= -0000589 centim., is in our glass (v = 1'oG) only, X' = '00003775 centim. or 

 '3775/A. Thus to find the number of gold particles in X' 3 , we must multiply 91 by 

 ( - 3775) 3 = '0538. We shall thus, even for glass G, have less than one particle to a 

 wave-length. < >n the other hand, SIEDKNTOPK warns us (loc. cit., p. 27) that the 

 linear dimensions of the particles are only to be taken as upper limits and may be 

 three times too large. 



Suppose this is the case, then the number of particles in a yellow wave-length in 

 the glass is 27 X '0538 (= l - 45) times the above numbers, 91, with of course a still 

 greater value for red light. 



On this hypothesis then the glasses F, G, H alone of the series satisfy our 

 condition. If, therefore, the theory is coiTect, it should explain the colour and other 

 optical properties of these three glasses as set out in the first five columns of 

 Table II. 



Let us, for instance, consider the colour of glass G. From equation (15) we have 

 as the distance <l in which the intensity of light of wave-length X is reduced to 

 1/7 '4 of its original value X/QTTfj.v/3 given by (15). 



From the Table 1. we have, supposing v = 1 '5G, 



/3 = -5854, for yellow light X = 10~ 7 '589 centim. 

 ft = "2501, for red light X = lO" 7 "630 



The value of yu. found by colorimetry is 72.10" 7 . Consequently we have 



Yellow, d = '48 centim., nearly. 

 Red, d = 1 - 19 centims. ,, 



Since the latter number is greater than the former, it follows that this glass, and 



