472 G. K. Gilbert—Special Processes of Research. 
This difference appeared to be susceptible of explanation, 
for the part of the atmosphere heated most rapidly is that in 
contact with the earth, and in the later part of the day the 
lower strata become so much warmer than the upper that a 
vertical circulation is produced, whereby cooler air is brought 
down and the rise of temperature near the ground somewhat 
checked. Thermometric observations near the ground there- 
fore fail to exhibit the variations in the amount of heat con- 
tained in the atmospheric column as a whole. 
To escape this difficulty I tried to discover the temperature 
of the air column as a joint function of insolation and radia- 
tion. Radiation to space was assumed to be at a constant rate. 
The rate of heating by the sun was assumed to be propor- 
tional to the sine of the angular height of the sun above the 
horizon. On these postulates the law of temperature incre- 
ment for the equinoctial day in the latitude of Philadelphia is 
expressed by the curve in figure 9. Integrating this, I obtained 
as the diurnal law of temperature variation the curve in figure 
10. This curve resembles very closely the one obtained from 
the curve of barometric oscillation (8), differing by less than an 
hour in the epochs of maximum and minimum. The theoretic 
curve of temperature increment (9) moreover possesses a gen- 
eral resemblance to that derived by one integration from the 
barometric curve (7). 
If no other test had been possible, I should have regarded 
the hypothesis as well sustained, but unfortunately for it there 
are widely different types of barometric oscillation in different 
parts of the world, and when the same integration was applied 
to curves of other types, the results were found to have little 
or no resemblance to temperature curves. I was compelled 
therefore to believe that either the theory or the method of 
testing it was inadequate; and I may add that I have since 
satisfied myself by independent reasoning that the relation of 
the temperature oscillation to the pressure oscillation is less 
simple than the one suggested by Espy. 
I have pursued the subject farther than was warranted by its 
use in illustration of graphic mett.od, and I have done this for 
the sake of a moral, with which I will close. The sun is the 
creator of the day. By alternately giving and withholding his 
light and heat he brings to pass an infinite series of events 
which agree in having a diurnal period of wax and wane. 
Were we to ascertain the quantitative elements in these cycles 
of events, and picture them by curves, it is to be anticipated 
that these curves, representing as they would a series of func- 
tions of the same periodic flux, would include a large number 
of close coincidences. For this reason the test I applied, 
though by no means a waste of energy, could not by itself 
