G. K. Gilbert—Special Processes of Research. 471 
tary rate of heating is the differential of the temperature, and 
the momentary increment to the rate of heating is the differ- 
ential of the rate of the heating, or the second differential 
of the temperature. If then the variation of pressure is 
proportional to the increment of the rate of . 
heating, it is also proportional to the second 2 6 Noo 6 2 
differential of the temperature; and an equa- 
tion or curve expressing the law of the diur- 
nal oscillation of pressure should by a dou- 
ble integration yield the equation or curve ® 
expressing the law of the diurnal oscillation 
of temperature. This being the theory, I 
sought to test it by twice integrating an ex- 
pression for the observed law of pressure 
change. 
Trinking to diminish the disturbing effect 
of local conditions, I combined for my test 
observations made at San Francisco and Gir- 
ard College. To avoid complication from 
the annual variation in the character of the 
diurnal oscillation, I used only the observa- 
tions for the equinoctial months of March 
and September. Making the combination 
and giving it graphic expression, there ‘re- 
sulted the curve shown in figure 6. This 
curve I undertook to integrate, and wishing 
to avoid the labor of converting it into an 
equation, I devised a graphic method of per- 
forming the operation. It is evident that, 
regarding the curve as an equation, the area 
contained between any two of its ordinates is 
the definite integral beween the limiting val- 
ues represented by the corresponding abscissas. 
On cross section paper it is easy to estimate such 
an area by the counting of squares. Selecting 
twenty-four equidistant ordinates I ascertained 
the definite integrals contained between the 
first of these and each of the others severally, 
and this gave me twenty-four equidistant val- 
ues of the integrated function. Assuming an i Noon 612 
arbitrary scale, I platted them as the ordinates 
of the integrated curve, obtaining figure 7 as the result. A 
repetition of the process produced the curve in figure 8, which, 
if the theory was correct, should express the diurnal variation 
of the temperature of the atmosphere. It has the general form 
of a temperature curve, but its maximum is several hours later 
than the maxima shown by the observations at San Francisco 
and Philadelphia. 
