BY J.C. BRUNNICH, EMG. 35 
tical lines and diagonals. Lallemand, another French 
mathematician, was the first to construct hexagonal graphs, 
in which, with the aid of a transparent sheet, on which 
the three diagonals of a hexagon are drawn, the value of an 
unknown may be found from two given variables. He 
further extended the principle by making each of the scales 
a system of two variables and thus producing a graph on 
which the relation of six variables is recorded. On Table IT., 
Plate I), which represents one of Lalanne’s hexagonal graphs, 
we have thus three double systems, one with the variables, 
u and v, the second with the variables, y and z, and the third, 
with the variables w and 2, and for uw=30, v=20, y=50, 
z=20 and w=20, we find z=4. In the reading of these 
hexagonal graphs, attention has to be paid that the diagonals 
of the transparent sheet cut the systems perfectly perpen- 
dicular. With the help of similar tables, Lallemand 
succeeded in the general topographical survey of France 
to reduce to quite simple reading off, long complicated 
calculations, which previously occupied for days the time 
of several persons. 
As a practical example of such a hexagonal graph, I give 
here a Table (III., Plate I), for the calculation of com- 
pound interest, constructed by Prévot, which for a given 
amount of capital, a given rate of interest and given time 
in years, allows to read off the amount of capital plus 
compound interest. For instance, £225 at 3 per cent. will 
increase in thirteen years to £328. 
One of the greatest authorities on graphical calculations 
of the present day is the French enginneer, Maurice d’ Ocagne, 
who proposed the term Nomographie for this science, which 
term is now generally used in Europe, on which he published 
several works. He was the first to extend and simplify 
the principle of graphical calculations by inventing a system 
by which the three factors are read off on a straight line. 
I will give here an instance of this principle by showing a 
Table (IV., Plate 1), published only a few months back, 
constructed by Fischer for the calculation of the amount of 
alcohol in wine. A wine with a specific gravity of 1.0520 
yielded an alcoholic destillate with a spec. gr. .9778, con- 
tained in accordance with this table 13.84 per cent. by weight 
of alcohol. 
