330 



Mr. W. H. L. Russell on 



[Jan. 27,. 



compounds has two values, and he comes to the conclusion that it has 

 the value 3*35 where the oxygen is attached to a carbon atom by a 

 double linking, but 2*76 inhydroxyl and where the oxygen is united to 

 two other atoms.* This is deduced from experimental data: but there 

 are other results which present difficulties. Thus the refraction of no 

 substance is more certainly known than those of water, wood spirit, 

 and alcohol. But the oxygen in H 2 (5*9) appears to have the higher 

 number 3' 3, notwithstanding its union to two atoms of hydrogen, 

 while in CH 4 (131), C 2 H 6 (20'8), as well as higher alcohols, and 

 the diatomic ethene alcohol, C. 2 H 4 2 (23" 7), and the triatomic glycerol, 

 C 3 H 8 3 (33*9), the oxygen is not 2" 76, but 2"9 or 3 - 0, the numbers 

 originally assigned to this element. 



Nitrogen. — ISTitrogen has two values, 4*1 and 5*1, or thereabouts. 



The lower value, 4*1, is that originally deduced from cyanogen and 

 metallic cyanides, and it seems to be generally confirmed by the 

 observations on organic cyanides and nitriles. The higher value, 5*1, 

 is deduced from all my observations on organic bases and amides, such 

 as diethylamine (39*4), triethylamine (54'6), formamide (17 - 4), &c. 



The determination of the value of nitrogen in nitro-substitution 

 products presents some peculiar difficulties. The observations are not 

 accordant. Even were the value of N0 2 obtained with certainty, it 

 would not be easy to say how much should be attributed to the oxygen, 

 especially when it is remembered that combination with oxygen alters 

 very materially the refraction of the analogous elements, phosphorus 

 and arsenic. 



I hope shortly to submit to the public the data for these calculations, 

 and in fact the whole of my recent observations on the refraction of 

 organic compounds, together with a fuller discussion of the conclusions 

 that may be drawn from them. 



II. " On certain Definite Integrals." No. 8. By W. H. L. 

 Russell, F.R.S. Received January 6, 1881. 



I commence this paper with some general reflections on the theory 

 of definite integrals. A definite integral may be written thus — 



f/3 



dxf(a, b, c . . . #)=0(a, b, c . . ). 



If we expand in terms of (a) and equate the coefficients of a n we shall 



have 



jjfaj/^M, &, e . . x) =(/), 0, &, c. . ). 

 * These have been calculated for line A. 



