PHYSICS: I. LANGMUIR 
253 
Now the area occupied by each molecule, which we will designate 
by a, is readily calculated. If w is the weight of oil placed on the sur- 
face and A is the area to which the film must be compressed before the 
surface tension changes, then the area a covered by each molecule is 
evidently a = AM/wN, where M is the molecular weight of the oil 
(oxygen = 16), and iV is the Avogadro constant (6.06 X lO^-"^ molecules 
per gram molecule). Furthermore, we may calculate r the length of 
the molecule (measured vertically), as follows: the volume of each mole- 
cule is M/pN, where p is the density of the oil. By dividing this vol- 
ume by a, the cross-section of the molecule, we obtain the length of 
the molecule, thus r= M/apN = W/pA. 
To measure A, a new method has been developed. A strip of paper, 
floating on the water in a long tray, is fastened to a horizontal balance. 
Oil is placed on the water on one side of the strip only, and leakage of 
oil past the ends of the strip is prevented by localized blasts of air from 
two small tubes. Thus the force tending to cause spreading of the 
oil is measured for different values of A. By plotting these results it 
is easy to extrapolate to zero force and thus obtain the maximum area 
completely covered by the oil film. 
TABLE 1 
Cross Sections and Lengths of Molecules 
SIIBSTANCE 
M 
CROSS 
SECTION 
a 
LENGTH 
T 
sg. cm. 
cm. 
cm. 
X 10-" 
X 10-8 
X io-» 
Palmitic acid CisHsiCOOH 
256 
24 
4.9 
19.6 
Stearic acid C17H35COOH 
284 
24 
4.9 
21.8 
Cerotic acid C25H51COOH 
396 
25 
5.0 
29.0 
Cetyl alcohol C16H33OH 
242 
21 
4.6 
21.9 
Myricyl alcohol CaoHeiOH 
536 
29 
5.4 
35.2 
Tristearin (Ci8H3502)3C3H6 
891 
69 
8.3 
23.7 
Cetyl palmitate C15H31COOC16H33 
482 
21 
4.6 
44.0 
Oleic acid C17H33COOH 
282 
48 
6.9 
10.8 
Triolein (Ci8H3302)3C3H5 
885 
145 
12.0 
11.2 
Trielaidin (Ci8H3302)3C3H5 
885 
137 
11.7 
11.9 
Ricinoleic acid Ci7H32(OH)COOH 
297 
90 
9.5 
5.8 
Linoleic acid CnHsiCOOH 
280 
47 
6.9 
10.7 
Linolenic acid C17H29COOH 
278 
66 
8.1 
7.6 
Castor oil (Ci7H32(OH)COO)3C3H5 
929 
280 
16.8 
5.7 
Linseed oil (CnHsiCOOaCaHg 
875 
143 
11.9 
11.0 
Table 1 gives the values of a and r, found for a number of different 
solid and Hquid films on distilled water at 16°C. Palmitic, stearic, 
and cerotic acids all occupy the same area (24. X IQ-^^ sq. cm.) per 
molecule. The length of the molecule in the vertical direction (r) in- 
