A NOMOGRAM FOR T H E VAN’T HOFF-ARRHENIUS TEMPERATURE EQUATION BY OSCAR W. RICHARDS
The use that the biologists are making of the van’t Hoff-Arrhenius temperature equation for the separation of various vital phenomena seems to warrant the construction of a nomogram or alignment chart with which one can readily discover the value of the thermal increment p . This equation is or
To use the accompanying nomogram a line is drawn connecting the two temperatures TI and TO. Since in the construction, which will be explained later, the absolute temperature values are given in degrees centigrade it is unnecessary to use other than the centigrade values. A second line is drawn thru the two velocities KOand K2 to the difference scale. Now, if a line is drawn from the point of iiitersection of the second line with the difference scale parallel to the first line to the p-scale is will indicate she numerical value of p . One must be careful to use the proper temperature and velocity scales. As will be seen from Table I the value found of p will be within 2-3% of the true value of p , or within, on the average about 300 units of the true value. An error of this magnitude is often of less importance as the characteristic values of p are usually at least a thousand units apart when vital processes are measured. However, the chart is only intended to be a ready aid to the experimenter during the process of an investigation rather than for the calculation of critical values. The data of Table I with the exception of the last set are from actual experiments and the calculated value was made with the aid of a five or six place logaiithmic table.
TABLE I Values of p from chart and from cahilation Ki
Tz
T1
Calc.
10.0
3.2
30
22.5
9.67
45
1.55
49
I39 15.7
c y
,r
Chart.
Eri cr
Error
27,175
27,600
+425
25
25,230
25,300
+70
+1.6 $ 0 . .3
38
22,526
23,500
+947
32
31,120
31,000
-120
1.7
38
26.0
16.1
30
22.5
11,431
33.8 31.6
26.5
30
22.5
28.2
5.7
30 30
22.5
10.0
5,806 31374 9,970
4.55
P
J !
KZ
20
,
+4.4 -o..t
11,200
-231
-2.3
6,000
+I94
$3.3
3,250
-124
-3.7
$30
+0.3
10,000
Average 2 7 1 Root-mean-square m o r 395.
2.06
.
I220
OSCAR W. RICHARDS
The noinograni was constructed from the folloving equation which is tlerived from equation ( I ) which i.
The left h m t l meiiiher of (31 may he repre+cntetl in the tlwiretl noii1ogr:mi :iq a sulitruction form, whcw t h e divitlentl vnlc T2 has divisions onc-h:tlf of the magnitude of thwc of the divisor kcale TI, nntl where lmth w n l ~ qhavv logarithmic ruling. The clifirrence scale i i graduntetl tqually t o r e d in tcriiis of the numerical differences of the logarithm
