394 



SCIENCE. 



of reducing matter increases, the value of diminishes, 

 and vice versa. Nos. 14 and 17 show extreme cases of 

 this law. Nos. 3, 18 and 20, because of their high- speci- 

 fic gravities, should not be included in the above gener- 

 alization. Having thus established the law that the per 

 cent of reducing matter is in general inversely as the 

 value of 0, it is next proposed to investigate the relation 

 between these two quantities, and determine whether it 

 is constant or variable. 



From Nos. 1 and 2, of table II, it is seen that for a 

 value of = 91.50, the percentage of reducing matter is 

 52.78. Let us say for convenience in calculation that 

 6 = 91.50 corresponds to reducing substance — 53 per 

 cent. Let us consider next, some of the cases which the 

 value of differs widely from 91.50. No. 17 of above 

 table affords an example. 



The difference is, 109.99—91.50 = 18.49. The differ- 

 ence in the per cent of reducing substance is 53 — 39.22 

 = 13.78. Thus an excess of the value of of 18.49 cor- 

 responds to a deficit of 13.78 in the percentage of reduc- 

 ing matter. 



Therefore a variation of each degree in the value of 

 is equivalent to 0.745 > n the percentage of a reducing 

 matter. By similar calculations with the other data fur- 

 nished by the table, I have found, not including Nos. 3, 

 18 and 20, marked by the high specific gravity, that this 

 number lies between 75 and 78. 



I will give the calculation for the first of these num- 

 bers, and compare them with the numbers obtained by 

 analysis. 



Table III. 



Number. 



Variation of 



e 



% Glucose 

 by 



0.75 Factor. 



% Glucose 

 .by 

 I' ehlmg s Sol. 











00 



53 



00 



53.20 











00 



53 



00 



52.36 



3-- 





— 12 



08 



62 



06 



61.73 



4- 





—16 



°3 



65 



03 



62.50 



5-- 





— 7 



53 



58 



64 



59-35 



6 





— 8 



75 



59 



57 



61 .40 



7- ■ 





- s 



07 



56 



81 



58.80 



8 





— 7 



44 



58 



58 



58.55 



9-- 





— 4 



30 



56 



21 



56.60 



10, 





— 2 



14 



54 



62 



53 5° 



11 





— 3 



77 



55 



82 



5 6 -49 







— 1 



73 



54 



29 



56.18 



13- 





— 20 



66 



58 



32 



69-93 



14.. 





— 22 



10 



69 



56 



69.30 



I5-- 





- 3 



83 



55 



88 



56.09 



16 





+ 18 



49 



39 



14 



39.22 



17.. 





— 1 



75 



54 



32 



54 05 



18 





— 



19 



S3 



14 



56.81 



19.. 





+ 6 



60 



47 



15 



54.60 







+ 1 



66 



5i 



75 



57-14 



In the above table, Nos. 18, 19 and 20 are the three 

 specimens with high specific gravity. We will, there- 

 fore, exclude them from the discussion. In the other 

 numbers the percentage of reducing matter, as calculated 

 from the reading of the polariscope, falls short of the 

 amount obtained by the alkaline copper test ten times, 

 and by an average of 1.018. It exceeds that amount 

 seven times with an average of 0.75. We thus see that 

 the polariscope will e.iable us to compute the reducing 

 matter present in a glucose with a probable error of less 

 than one per cent. This is quite accurate enough for 

 practical purposes. 



Perhaps a larger number of determinations should be 

 made before constructing a formula for determining the 

 amount of reducing in substance a " straight " glucose. 

 The following formula:, however, are given provisionally, 

 subject to some slight correction derived from more ex- 

 tended data. 



We 'may have three cases : 



1. The value of 9 = 91.50 



2. V *' < 91.50 

 3- " " > 91-5° 



In the first case the percentage of reducing substance 

 in a glucose, if not far from 1.410 sp. gr., will be nearly 

 53- 



In the second case the required percentage may be 

 found by the following formula, in which a = difference 

 between the value of and 91.50, and g = per cent re- 

 ducing required — 



g = 53 + °-75 a or °-7% a. 

 In the third case we have 



g = 53 — 0-75 « or 0.78 a. 

 In order to make the principle of more general appli- 

 cation, I have modified the calculations so as to apply 

 the formula directly to the cane sugar scale of the instru- 

 ment. 



To this end, for instruments using 26.048 grammes for 

 100 divisions, it is convenient to use only 10 grms. of the 

 glucose. If 26.048 grms. are employed, the neutral point 

 is thrown entirely beyond the limit of the icale. Ten 

 grammes is the quantify which has been employed in the 

 following table. 



The average reading of the sugar scale for ten grammes 

 is about 50. 



In the following table will be found the results of the 



experiments. 



Table IV. 



Number. 



Scale. 



% Reducing 

 Substance 

 by Cal- 

 culation. 



% Same by 

 Cu. Test. 



Difference. 





5 2 



65 



53-43 



53 



20 



+ 0.23 





52 



65 



53 43 



52 



36 



+ I.07 



3 



46 



07 



61.66 



61 



73 



— 0.07 



4 



43 



°5 



64.90 



62 



5° 



+ 2.40 



5--- 



48 



04 



58.75 



59 



35 



— 0.60 



6 



47 



70 



59 63 



61 



40 



—I.77 



7 



49 



80 



57.00 



58 



80 



—1.80 



8 



48 



45 



5856 



58 



55 



+ 0.01 



9 



5° 



26 



56.45 



55 



60 



+ 0.85 





51 



50 



54.88 



53 



50 



+ 1.30 





5° 



57 



56.04 



56 



49 



— o.45 





5i 



74 



54 -58 



56 



18 



— 1.60 



13 



40 



83 



68.21 



69 



93 



— 1.72 



14 



4° 



00 



69.25 



69 



80 



—0.05 



15 



5° 



53 



56.09 



56 



34 



— 0.27 



16 



63 



80 



39-5° 



39 



22 



+ 0.28 



17 



5i 



73 



54-37 



54 



°5 



+ 0.32 



18 



52 



63 



53 46 



56 



81 





19 



56 



53 



48 -59 



54 



60 







53 



70 



52.10 



57 



14 





The above calculations were made from the following 

 data. 



Starting with Nos. 1 and 2, and discarding small frac- 

 tions, we find that 53 divisions of the cane sugar scale 

 correspond to 53 per cent of reducing matter nearly. 



By a method of calculation entirely similar to that em- 

 ployed in determining the reducing matter from the 

 fluctuations of 9, I have found that a variation of one 

 degree in the. sugar scale corresponds to an inverse var- 

 iation of nearly 1 .25 per cent of reducing substance. 



We may have as in the previous calculation three cases. 

 1st. The reading of the scale = 53 

 2d. " " " ' " > 53 

 3d. " " " " < S3 



In the first case 53 = 58 per cent nearly. 



In the second case, placing a for the reading of the 

 scale, we have 



g = 53 — («— 53) 1-25 

 In the third case we have 



g — 53 + (53— «) i-25 



