xvin THE CLASSIFICATION OF THE ELEMENTS 453 



Dobereiner was tested by Dumas in a memoir " On the 

 Equivalents of the Elements " (Ann. Chim. Phys., 1859, 55, 

 129-210), in which he sought to establish an analogy 

 between the "natural families" of elements and the 

 " natural series " of organic radicals. Dumas concluded 

 that : 



" In a family of three elements, the equivalent of the 

 intermediate element may be equal to the mean of the equi- 

 valents of the two extreme elements ; but the contrary may 

 also occur in regard to the most closely related elements " 

 (loc. tit. p. 163). 



Thus P ^ J 5 ^} M ean = 81*25, whereas Br = 8o'o. 



When dealing with the equivalents of organic radicals, on 

 the other hand, the averages are exact, and may, moreover, 

 be extended throughout a homologous series in the form of 

 arithmetical progression, as represented by the simple 

 formula a + nd^ e.g. 



H = i, CH 3 =1 + 14, C 2 H 5 =1 + 2x14, C 3 H 7 =1 + 3x14, etc. 



Dumas suggested that something similar might be recog- 

 nised in the equivalents of the following families of 

 elements : 



F =19 * 6 ' 8 



CI =19+ 16-5= 35-5 S = 8+ 8= 16 



Br =19+ 2x16-5+ 28 = 80 Se 8+ 4x8= 40 



I =19+ 2x16-5 + 2x28+19=127 Te = 8+ 7x8= 64 



N =14 1 Mg=i2 

 P =14+17= 31 Ca=i2 + 8= 20 



As=i4+i7+ 44=75 Sr =12+ 4x8= 44 



Sb =14+ 17 + 2x44=119 Ba=i2+ 7x8= 68 



Bi =14+17 + 4x44 = 209 Pb =24+10x8=104 etc. 



To Dumas belongs also the credit of recognising the 

 existence of numerical relationships between the equivalents 



1 The equivalents of the oxygen and magnesium families require to 

 be doubled in order to give the modern atomic weights. 



