466 G. K. Gilbert—Special Processes of Research. 
1840 
1850 1860 1870 
Looking at these curves 
from the algebraic stand- 
point, we see that they do 
not correspond to a single 
equation between three or 
more variables, but to a 
group of equations with 
one variable in common, 
and with one other varia- 
ble in each equation. If 
we combine two of the 
equations or curves in such 
way as to eliminate the 
common variable, we ob- 
| tain ap equation or curve 
showing the relation be- 
tween the two other varia- 
bles. It is frequently ad- 
vantageous to do this, but 
[het 
1840 1850 1860 ao 
Fie. 4.—A, number of auroras. 8, range 
of magnetic declination. C, relative extent 
of spots on the surface of the sun. 
not always; and it is not 
ordinarily advantageous to 
do it when the common 
variable is time. I have 
copied in fig. 4 a portion of Professor Loomis’ curves, and it is 
evident by inspection. that there is a marked correspondence 
between the maxima and minima of the three curves. I have 
also combined the data employed in the construction of the 
upper curve (auroral frequency) and the lower curve (extent of 
sun-spots) in such way as to eliminate the common element of 
time, that is to say, I have (in fig. 5) platted for each year the 
relation of auroral display to extent 
of sun-spots, the ordinates- repre- 
senting frequency of auroras, the 
abscissas the extent of solar spot- 
ting. It would hardly be suspected 
from the arrangement of these dots 
that the two phenomena are in ac- 
cord.* Looking again at fig. 4, we 
see that while the minima of the 
upper curve correspond very closely 
with the minima of the lower, the 
maxima lie farther to the right. If 
the phenomena are really connected 
in a causal way, it would seem that 
the auroras are the effect, and that 
they are brought about by some chain of causation involving time. 
* My illustration is subject to a qualification, which, though unessential, should 
be stated. In fig. 5 each ordinate represents the number of auroras observed 
Fig. 5.—Direct comparison of au- 
roras with sun-spots. 
