186 Dr. A. Schrauf on certain Objections to the 



cannot avoid a similar assumption. To prove this I will adduce 

 the following examples. 



From the latest treatise by Descloizeaux* (kindly sent to me) 

 I select the observations for octahedral arsenious acid, As 2 O 3 . 

 In this, 



Pp =l-748, ^=3-698, P=198, D(H 2 0)=1, 



^- L = 0-2022, P^-^m = 40-03. 



Now according to Haagen (loc. cit.), referred to the density of 

 water m p ( As) = 20*02 and ttt p (0) = 3-00. Hence, by calculation 

 from the elements f, we get for arsenious acid, 



2m(As) +3m(0) = m , (As 9 3 ( = 49*44), 



a number which differs from the observed one to the amount of 

 20 per cent. 



If, going further, we reckon the indices of refraction from the 

 elements, it follows from P = 198, d=3'698, m' = 49-4, that the 

 coefficient of refraction /a'(As 2 3 ) =1*916, while direct observa- 

 tion gives fx = 1*748. 



The hypothesis of factors, or, as I call it, condensation, is 

 therefore not superfluous. 



Another example, which is at the same time of importance for 

 the derivation of the elements, may be found in the terchloride 

 of phosphorus, PCI 3 . 



I have (1865) given D(H 2 0)=773, m (PCI 3 ) =0-0576, 

 m(P) =00243, J»(C1) = 0-0110; these numbers being derived 

 from direct observation. If now we reckon the value of the 

 compound from those of the elements, we find at once 



m(P) +3m(Cl) = m r (PCl 3 ) =0-0573. 



The difference between observation and calculation scarcely 

 amounts to \ per cent. If we put D(H 2 O) = 1, my data change 

 to m(P) = 18-81, m(Cl) = 8-58, and for chloride of phosphorus 

 we should get from observation m(PCl 3 ) =44-52, and from cal- 

 culation m' = 44-55. 



It is seen that no better agreement can be imagined between 

 direct observation and calculation by means of the elements. And 

 yet this very body (PCI 3 ) induced M. Haagen [loc. cit.) to derive 

 for phosphorus in combinations the value tti/(P) = 14*6, a number 

 which departs considerably from that obtained by the direct ob- 

 servation of free phosphorus, m = 18-8 [if D(H 2 0) = 1]. The 

 reason of this deviation is to be sought for in the fact that 



* "Nouvelles reclierches sur les proprietes optiques des Cristaux," 

 Memoires de T Academie, vol. xviii. Paris, 1867. 



f The functions derived from direct observation are denoted in the sequel 

 by m, those obtained by calculation by m'. 



