G. K. Gubert—Special Processes of Research. 469 
the comparative strength of the different members of a certain 
group of alloys, he has platted the strength by means of an 
isogram whose points are fixed by three codrdinate lines, each 
representing the ratio in which an ingredient enters into the 
alloy.* But the ratios of the three ingredients are not inde- 
pendent variables, since any two being. known, the third may 
be determined. His method of platting employs three coérdi- 
nate axes arranged in the form of an equilateral triangle, but 
one is redundant; the same result would be attained if the 
ratio of one ingredient were ignored and the ratios of the other 
two were referred to two coordinate axes intersecting at an 
angle of sixty degrees. I would not be understood to criticize 
this method of projection unfavorably—it is a singularly happy 
adaptation of a general method to a special case ; I merely claim 
it as essentially anormal isogram. It may be added that in 
the general theory of projection by trilinear codrdinates the 
redundancy of one set of codrdinates is recognized by mathe- 
maticians. 
Prof. Davis’s composite portrait (fig. 2) is the rational equiva- 
lent of a group of equations, each containing three variables, 
and all agreeing in two variables which they hold in common. 
It differs from the normal isogram in that the lines representing 
the third variables of the several equations are undrawn. One 
of the common variables is distance from the middle path of 
the storm, the other is distince from the line of rain-front; the 
remaining variables, which are severally functions of these two, 
are the phenomena of wind, temperature, thunder, lightning 
stroke, ete. — 
The composite photograph devised by Galton also finds place 
here. In his method a number of pictures, over-printed on the 
same sheet of paper, have two points in common. This is 
equivalent to giving them the same origin of codrdinates, the 
same directions of codrdinate axes, and the same scale. 
There is also a type of graphics bearing the same relation to 
the isogram that Prof. Call’s group of points bears to the nomo- 
gram. It is illustrated by charts of geographic distribution in 
which the data platted either do not admit of, or are not sub- 
jected to, quantitative gradation. Of this nature is a chart 
showing the positions of the volcanoes of the world. 
The graphic processes thus outlined and classified constitute 
essentially the graphic method as employed in research, but 
there are numberless details and devices, having the general 
nature of short cuts, in the invention of which any one will be- 
come fertile who makes extensive use of the general method. 
* The strongest of the bronzes, a newly discovered alloy of maximum strength. 
By Robert H. Thurston. Jn Rept. U.S. Board appointed to test iron, steel and 
other metals. Vol. ii, p. 133. 
