’ G. K. Gilbert—Special Processes of Research. 465 
shell from the geologic deposit. The two relations might have 
been exhibited upon separate sheets, but as they are relations 
between similar quantities, we can by employing the same scale 
plat them upon the same sheet, and thus platted, we are en- 
abled to compare them with each other. 
It is a general principle that if we have a series of observa- 
tions showing the relations of phenomena A and B and another 
series showing the relations of A and C, we may by platting 
them upon the same sheet and employing the same scale in the 
representation of the vaiues of the common phenomenon, A, 
make a sort of comparison between B and C. The units of 
measurement for B and C may be of different kinds, and even 
if of the same kind, may be of different orders of magnitude, 
and it is not ordinarily necessary to establish any correspon- 
dence in their scales. Neither is it necessary that the zeros of 
their scales have the same position. 
In this manner Professor Loomis has compared the mean 
daily range of the magnetic declination with the relative extent 
of dark spots on the surface of the sun by the aid of their com- 
mon relation to time ;* that is to say, using time for his scale 
of abscissas and the relative extent of spots as a scale of ordi- 
nates, he has platted a curve showing the relation of spot ex- 
tent to time. Then upon the same sheet and with the same 
scale of abscissas he has platted a curve in which the ordinates 
represent the daily range of magnetic declination. The second 
curve shows the relation of magnetic declination to time, and 
the two curves exhibit to the eye whatever correspondence or 
discordance there may be between the time relation of the mag- 
netic declination, and the time relation of the extent of sun- 
spots. Again he has made the ordinates represent frequency 
of auroral displays, and has thus produced a curve showing the 
relation of auroral frequency to time, and this curve he is able 
to compare with each of the others. There is indeed no limit 
to the number of relations which may be compared in this way, 
provided only that one system of codrdinates, either abscissas 
or ordinates, remains unchanged in meaning and scale. Mr. 
Schott in his discussion of the temperatures of the United 
States has compared the sun-spot curve with four curves repre- 
senting secular changes of temperature at as many stations, the 
abscissas representing the common factor time, and the ordi- 
nates standing for temperatures in the case of four of the 
curves, and for relative frequency in the case of the other.t 
* This Journal, III, vol. v, p. 346. 
+ Tables, distribution, and variations of the atmospheric temperature in the 
United States, etc.; by Charles A. Schott. Smithsonian Contributions. Plate 
facing p. 310. : 
Am. Jour. Sci.—-THIRD SwRiEs, VOL. XX XITI, No. 198 —JuNnz, 1887, 
29 
