462 G. K. Gilbert—Special Processes of Research. 
equation. It has many of the properties of an equation and 
may be discussed in a similar manner. 
The subsidiary or dependent laws deduced algebraically from 
the written equation have a quantitative definiteness to which 
the platted curve can afford only approximations, but the 
curve yields to the minds of most men a clearer conception of 
the nature of the relation of the two variables than is conveyed 
by the equation. Its advantage is that it appeals to the eye, 
and thus brings a sense impression to the aid of the imagina- 
tion. This however is by the way, for the application of the 
platted curve in research is somewhat different. 
When the investigator, suspecting that two phenomena are 
mutually related in a constant and necessary manner, has made 
a series of observations affording him simultaneous quantitative 
values of the phenomena, there are open to him two general 
ways for the classification of his observations and the drawing 
of the proper inferences. Pursuing what may be called the 
written or mathematical method, he writes the observed quan- 
titative values of one phenomenon in a column in the order of 
their magnitude, and the corresponding quantities expressing 
the other phenomenon in a parallel column. He then inspects 
the numbers of the second column to see whether they consti- 
tute a series. If their arrangement is quite irregular, he infers 
that the two phenomena-have no constant relation; but if he 
detects a greater or less amount of order among the numbers, 
he assumes the existence of a law, and endeavors to ascertain 
its nature by discovering its mathematical expression. He first 
assumes more or less arbitrarily or hypothetically the general 
form of the equation expressing the relation of the phenomena, 
and by substituting the observational values successively in this 
forma! equation, he obtains a number of numerical equations 
from which a single one is deduced by the method of least 
squares. The resulting formula expresses the law connecting 
the phenomena with a degree of precision which depends on 
the consistency of the observations ; and by another mathemat- 
ical process he can obtain a numerical expression representing 
this degree of precision. ‘The two expressions will enable him 
for any given value of one variable or phenomenon to compute 
the corresponding value of the other, and also to compute the - 
probable error of this value. 
If on the other hand he employs the graphic method, his 
procedure is ordinarily as follows: Upon a sheet of cross- 
barred paper he assumes the lines running in one direction.to . 
represent equidistant values of one of the observed phenomena, 
and the lines running in the transverse direction to represent 
equidistant values of the other phenomenon. The scale assigned 
upon the page to the numerical values is unessential, and is 
