466 Mr. W. Sutherland on the 



liquid of index n 2 , we have its index n given by the Lorenz- 

 Lorentz formula 



1 n 2 ~l _p 1 n 1 2 -l p 2 n 2 2 -l . 



Pl < + 2 "^ 2 V 2 rc 2 2 + 2 Pl n l 2 + 2r K } 



so that (n 2 — l)/(Vi 2 + 2)p, say R, is a linear function of £>2 r 

 therefore we shall tabulate the values of this expression at 

 different temperatures for water and the values of p 2 from 

 Table I. side by side, and also the values of their respective 

 successive differences denoted in the next table by AR and 

 Ap 2 . The indexes n for water are those of Ketteler (Wied.. 

 Ann. xxxiii.) and for ice that of Pulfrich (Wied. Ann. xxxiv.), 

 and the densities are the mean values given by Mendeleeff. 



Table II. 



Ice. Water. 



t 0° 0° 20° 40° 60° 80° 100° 



10 6 R 209680 206342 206208 206108 206051 206016 206015 



lO 3 ^, 1000 375 321 284 255 234 217 



10 6 AR 3338 134 100 57 35 1 



10 6 ARcalc... 3338 185 95 52 9 -12 



10 3 Ap 2 625 54 37 29 21 17 



It will be noticed that the values of A(n" — l)/(n 2 + 2)p 

 and of Ap 2 run a similar course, but that the former tend to 

 diminish to a value more rapidly than the latter. This is 

 connected with an interesting fact that water differs from 

 ordinary liquids in showing a diminution of (n 2 — l)/(n 2 + 2)p 

 with rising temperature, whereas it usually increases. Thus 

 Lorenz (Wied. Ann. xi.) finds it to increase by the following 

 number of parts in 10,000 for the following liquids from 10 

 to 20° : — ethyl oxide 8, chloroform 4, ethyl iodide 5, ethyl 

 acetate 11, carbon disulphide 12. It appears, therefore, that 

 in water this normal temperature effect of an increase has- 

 superposed on it a diminution due to the changing composi- 

 tion of water; the result being that in water (n 2 — l)/(n 2 -t-2)p 

 is nearly stationary at 80° and 100°. In the case of water 

 then A(?i 2 — l)/(n' 2 + 2)p consists of two parts, one propor- 

 tional to increase of temperature At like those just given for 

 ordinary liquids, and the other proportional to A/> 2 , thus 



A(n 2 - l)/(n a + 2)p = -00000515 A* + -00534 Ap 2 , 



