44 PHYSIOLOGICAL CHEMISTRY 



It is obvious that it often will be impossible to observe the 

 rotation produced by a substance under these standard condi- 

 tions. Many substances are not sufficiently soluble to dissolve 

 1 gram in 1 cubic centimeter of solvent. To avoid this difficulty, 

 a formula has been developed for use under general laboratory 

 conditions. Let oc be the observed rotation of a solution under 

 question. Under standard conditions [ oc ] = <x . Let g = grams 

 substance per c.c. of solvent. If g is not equal to 1, we can 



easily find the value of [ oc ] by dividing oc by g. [ oc ] = - 



We must also introduce the length of the observation tube, as 

 naturally a column of liquid longer or shorter than the specified 

 1 decimeter will give respectively a greater or a smaller rota- 

 tion. Our formula will now be [ oc ] = - 



As it seldom is convenient to work with 1 c.c. of solution, it 

 will be advisable to revise our formula for use with solutions 

 calculated on the basis of 100 c.c. Let c equal the number of 



r* 



grams substance in 100 c.c. solvent, then g = -^- Substituting 



1UU. 



this value of g in the above equation we have 



100. oc 



[ a ] = Tc~~ 



Now the amount of rotation which a given solution will pro- 

 duce is influenced by various factors, among them the tempera- 

 ture of the solution, the color of the light used in the observa- 

 tion, etc. Unless there are special reasons for other procedures, 

 it is customary to make observations at 20 C. and with sodium 

 light, corresponding to the D line in the spectrum. These two 

 influencing factors also are included in our formula, which 

 we now have in its final form. 



20 100. oc 

 D : l.c 



This value is called the specific rotation of a compound and 

 is a constant for each optically active substance. The specific 

 rotations of most of the sugars have been determined, and may 



