TRANSACTIONS OF SECTION B. 457 
in one hour, are by no means proportional .to speeds during the first minute, or 
under like conditions. Prof. L. Meyer has recently published an excellent work 
entitled ‘Dynamik der Atome;’ and yet both the theory and the observations of 
the variations in speed during the progress of a reaction are passed over very 
lightly indeed. The prevalent theory of the action of mass is expressed by the 
equation 
Lar ieee 
dt 
where the differential coefficient expresses the rate of change in any substance ; 
u,v, . . . Yepresent the masses of the substances taking part in the change; and. 
k is aconstant. Some observations have been made upon the influence of viscosity, 
temperature, &c., upon the value of &; but these have been so meagre that Prof. 
Ostwald’s skilful determinations usually seem to contradict the theory in its 
present state. 
Accurate determinations of the speed of a reaction require the greatest care, 
not only for the measurement of time in addition to mass, but also to control the 
temperature and other conditions within very narrow limits. Many who have not 
the laboratory facilities or the natural taste for such researches may engage in the 
mathematical discussion of results already published. Many determinations of 
etherification, for various alcohols, acids, intervals, and temperatures, have been in 
print for tweuty years; and yet no summary of the deducible value of / has come: 
to my notice. The chemical section of the Ohio Mechanics’ Institute has recently 
undertaken some work in such computations; suggestions and co-operations from 
chemists and physicists elsewhere are cordially invited. This subject includes 
numerous mathematical problems that would afford valuable practice for college 
or university students, especially those who are candidates for honours. Professors 
of mathematics who will act upon this suggestion may render valuable aid to the 
cause of chemical research. The following subjects require special attention :— 
I. Fundamental Units.—The following provisional system is now suggested : 
for volume, one c.c. ; for mass, the chemical equivalent, expressed in m.g.; and for 
time, one hour. The unit of speed, as derived from these, would be the transfor- 
mation of unit of each active body per unit of volume and time. Thus in a 
normal solution of chloracetic acid (containing 94:5 m.g. in each c.c.) if wu and 
represent the quantities of acid and water respectively, we should have wu = 1 and 
» = 55'5, nearly. : 
If the reaction 
CH,Cl.CO.OH + H,0 = CH,(OH).CO.OH + HCl 
could continue for one hour at unit speed, the chloracetic acid would be entirely 
decomposed in that time, yielding a normal solution of both glycolic and chlor- 
hydric acid; but, according to the equation 
du 
the speed will vary with uw; if then the reaction degins with unit speed, kuv 
equals unity at that moment, or / = 0-018." 
The minute, hour, and day have all been used by chemists as units of time ; 
possibly one second or 1,000 seconds would be a better unit, for convenience in 
comparing the constants of speed or of chemical affinity with those of heat, 
electricity, &c. 
IL. Probable Errors.—A determination of speed requires at least two observa- 
tions of time and two of mass. A series of observations is generally made ; and 
the probable percentage error will vary greatly, according to the data selected or 
the method of combining them. The theory of least squares should be so applied 
in each case as to decide (approximately at least) the relative weights to be 
ae to the several determinations, and to calculate the probable error of the 
result, 
1 Dr. E. J. Mills proposes a different unit of chemical action in Phil. Mag. [5] I., 
1-16 (1876). 
