36 GRAPHICAL AND MECHANICAL AIDS TO CALCULATION 
D’Ocagne exiended the science of nomographie in 
every direction and he succeeded in laying before the French 
Academy of Science a method by which he constructed 
nomographs with ten and more variables. I will give here 
another example of one of d’Ocagne’s nomographs, as 
applied to higher mathematics, the graphic solution of the 
cubic equation, z?+pz+q=0, we find from Table VII. 
that for p=2, and q= —6, 7=1.46. 
As another instance of reading a result with the aid 
of a straight line, I will give here a very simple graph, which 
I constructed for use in sugar laboratories for the calcula- 
tion of the well-known value Pure Obtainable Cane Sugar, or 
P.O.C.S. in sugar cane (Table V., Plate II.) In cane juice, the 
amount of total solid matter is determined by a density 
determination with the aid of Brix or Beaumé spindle. 
The degree Brix express the percentage of total soluble 
solid matter in the cane juice, which value is read off in our 
table on the third perpendicular scale on the right. The 
amount of cane sugar in the juice is determined with the 
help of the saccharometer or polariscope, the value found 
is read off on the centre scale, by connecting the per cent. 
of brix and per cent. of cane sugar by a straight line, the 
amount of P.O.C.S. is read off on the left hand scale where 
it is cut by this straight line. I may be allowed to explain 
that the amount of sugar obtainable by the process of 
manufacture not only depends on the actual amount of 
cane sugar in the juice, but also on the amount of soluble 
impurities, and from practical experience the manufacturer 
estimates that one-half of these impurities have to be 
deducted from the per cent. of cane sugar in the cane. 
We have for instance two cane juices both nineteen degrees 
Brix, one with seventeen per cent., and the other with 
fifteen per cent. of cane sugar, the former has sixteen per 
cent. and the latter only thirteen per cent. P.O.C.S. 
I will now show a chart which I constructed for the use 
of dairies and butter factories, by the aid of which for a given 
quantity of milk containing a certain per centage of butter fat, 
the amount of commercial butter which should be obtained 
by churning, may be read off. (Table VI., Plate Il). A cow’ 
giving, say, 2llbs. of milk with a 3.8 per cent. test, would 
yield 140zs. of commercial butter a day. The formula 
