504 CHAPTER XXV 



The polarization, and also determination, of sucrose is affected by the 

 conditions discussed below : 



Concentration. The rotation of cane sugar varies slightly with con- 

 centration ; Nasini and Villavecchia 10 found for p 3 to 65. 



[ a ]J = 66-438 + 0-010312 p 0-00035449 P 2 > where p is the percentage 

 of sugar. 



In very dilute solutions the results of different investigators are very 

 discordant. Tollens 32 found very irregular values. Pribram 33 found a 

 decrease from p 3-659 to 0-222 and Nasini and Villavecchia 10 found an 

 increase from p I 253 to o 824. 



Schmidt's 34 tables, which still remain in use, are based on the formula : 

 [a] /) 2 = 66-514 0-0084150, where c is the grams of sugar per 100 c.c., and 

 should be abandoned. The most probable formula is that of Landholt 35 

 which combines the results of Tollens, Nasini and Villavecchia into the 

 formula : 



[a]5J = 66-438 + 0-00870 C. O-OOO235 c - 2 > f r c > to 65. 



Temperature. The effect of temperature on poiarimetric observation 

 is twofold : firstty, there is the effect of temperature on the quartz wedge 

 compensating system, and secondly the effect on the specific rotation of the 

 sucrose. As regards the first, three factors enter : the linear expansion of 

 quartz parallel to and perpendicular to the optic axis, the increase in the 

 specific rotation of quartz with rise of temperature and the expansion of the 

 scale, which becomes zero when the latter is engraved on the wedges. These 

 effects have been studied by Schonrock 36 and, as the result of his studies, it 

 is found : 



Rotation of quartz near 20 C. 



[a]i = [a] + [a] O-OOOI 4 3 (t ~ 20). 



Linear coefficient of expansion of quartz parallel to the optic axis, o 000007 

 Whence specific rotation coefficient, 0-000143 0-000007=0-00000136 

 Linear coefficient of expansion of quartz perpendicular to the optic axis, 

 0-000013. 



Linear coefficient of expansion of nickelin scale, o 000018. 

 Linear ,, ,, glass 0-000008. 



Whence the total temperature coefficients for the instrument alone 



become : 



Nickelin scale 0-000136+0 -000007 0-0000134-0-000018=0-000148 

 Glass scale 0-000136+0-000007 0-000013+0-000008=0-000138 

 Scale on wedge o 000136 +o 000007 o 000013 =o 000130 



and the following formulae result : 



Nickelin scale S 20 =S,+S, 0-000148 (t 20) 

 Glass scale 20=5, +S, 0-000138 (t 20} 



Scale engraved on wedge S 20 =S,+S, 0-000130 (/ 20), where S is the 

 reading at t C. and S 20 is that at 20 C. * 



The effect of temperature on the specific rotation of cane sugar was 

 first observed by Dubrunfaut 38 and, though disputed by various physicists, 

 a decrease with rise of temperature is now established. Schronrock 36 has 

 found that the coefficient varies with temperature and is as follows : 



10 C., 0-000242; 20 C., 0-000184; 30 C., 0-000121. 



