346 W. A. Norton—Force of Effective Molecular Action. 
FART. XLIL—On the Force of Effective Molecular Action ; by 
Professor W. A. Norton. 
[An abstract of this paper was read before the National Academy of Sciences, 
April 18, 1878.] 
In my paper on the variability of the ultimate molecule, pub- 
lished in the March number of this Journal, I gave the follow- 
ing theoretical expression for the force of effective action of 
one ultimate molecule of a body on another contiguous to it, 
deduced from certain fundamental conceptions which were 
succinctly stated : 
a n(3r’+-2re)  _ m (1) 
(r2)(2rfay 2 
in which x denotes the distance between the electric envelopes 
of the contiguous molecules; r the distance between the center of 
emanation of the attractive force, f, represented by the first 
term, and that of the repulsion /’, represented by the second 
term; n the coefficient of the attraction /, and m that of the repul- 
sion /’. The expression has been simplified by making one or 
two assumptions that do not strictly accord with fact, but 
which can occasion no material error in the general discussion 
now proposed ; as will be shown on another occasion. 
If we put e=ur, — =k, and =P; it becomes 
k(3+-2u) 1 
F= peraeotiy Fy 2 
(appara — x 
If this be a true theoretical expression for the force of effec- 
tive molecular action, it should comprise the essential mechani- 
eal theory of solids, liquids, and gases, as well as the special 
mechanical features of individual substances; and should suc- 
cessfully withstand all the quantitative and qualitative tests that 
ean be applied to it. I propose now to give the result of the 
application of a number of such tests ; and to show that the char- 
acteristic features and laws of the three different states of aggre- 
gation are deducible from it. : 
Theory indicates that in the comparison of different solids, 
liquids, or gases, among themselves, at the same temperature, 
P (= “) may be regarded asconstant. In fact we shall for the 
resent assume that both m and r, as well as p, are constant for 
substances in the same state of aggregation, when the tempera 
ture is the same. Upon this assumption one substance will dif- 
fer from another, in its essential molecular condition, only in 
the value of &, that is of the ratio — of the coefficients of the 
