468 G. K. Gilbert—Special Processes of Research. 
besides its verbal statement. It is expressed by the equation, 
by the curved surface, and by the system of plane curves, or 
the projection on a piane of the contours of the curved surface. 
The allied process in the conduct of research is as follows: 
Upon a sheet of paper two systems of lines representing 
equidistant values of two variable phenomena are drawn or 
conceived to be drawn. Points representing observations are 
then added, their positions with reference to the two systems 
of lines being made to indicate the quantitative observations of 
the two phenomena, and figures, or other equivalent notation, 
being employed to indicate the simultaneous quantitative 
observations of the third phenomenon. Lines are then drawn 
connecting those dots which bear the same figures, and it is 
arranged, by the aid of interpolation, that these lines represent 
equidistant values of the third variable. The chart thus pre- 
pared shows by inspection the relations of the third phenome- 
non to the other two. The isobars on our weather maps are of 
this nature. Space in two of its dimensions constitute in this 
case two of the variables; we may say for convenience that one 
variable is latitude and the other longitude. The third varia- 
ble is barometric pressure. The lines representing meridians 
and parallels may or may not be drawn upon the map, and if 
they are drawn, their character, as straight or curved, will de- 
pend upon the nature of the projection of the map. Another 
illustration is found in Davis’s rain-front map, (fig. 1.) 
It will be convenient to have distinctive terms for the line, 
corresponding to two variables and for the system of lines cor- 
responding to three, and I venture to propose for the first the 
name nomogram, or line representing a law, and for the second 
isogram, a title connecting it with its familiar examples in the 
isobaric, the isothermal and the isohyetal curves. 
Tsograms adinit of combination in the same manner as nomo-- 
grams, but in their case it is essential that two of the variables 
be common to all. Upon our daily weather maps the isobars 
and isotherms are both platted with reference to latitude and 
longitude, and we are thus enabled to compare in a direct and 
simple manner the areal phenomena of temperature with the 
areal phenomena of pressure. The weather map is the logical 
equivalent of two equations, each including three variables, the 
equations agreeing in two variables and differing in a third. 
The general case of an equation of four variables has not yet 
found graphic expression, although some special formule with 
four or even five variables have been reduced to graphic form 
for the purposes of the computer. 
T am not aware that the graphic method has been used in re- 
search to express a relation involving more than three inde- 
pendent variables. In an investigation by Prof. Thurston into 
