172 
seum of Natural History, but a use was also 
made of type material in other collections. 
Osborn’s idea in presenting the matter in 
this form is that “the permanent data of sys- 
tematic paleontology are the type specimens, 
determinate or indeterminate, the type local- 
ity, the type geologic level. Descriptions, 
figures, opinions, inferences, phylogenetic and 
other speculations are subject always to the 
fallibility of human observation and interpre- 
tation.” These ideas of course are funda- 
mental and apply to other phases of paleon- 
tology than the systematic portion. 
A full discussion of the “Genesis and 
Evolution of Single Dental Characters” is 
given with abundant illustrations. This is fol- 
lowed by a review of “ Geologic Horizons and 
Life Zones” appropriately illustrated with 
maps and tables. 
The systematic portion discusses one hun- 
dred and forty-six species distributed among 
ten genera. Hach species is carefully dis- 
cussed and the type material illustrated. On 
turning the pages one is struck by the frag- 
mentary nature of many of the species—but 
this is the condition throughout all fossil 
vertebrate groups. To some of the species 
more information has been added since their 
description but many of them stand to-day 
as they were originally described. Many spe- 
cies are known from very complete material. 
_ The contribution is one of which American 
paleontologists may well be proud. Its per- 
manent character is the careful collection and 
assembling of data on all species of fossil 
horses known from the Oligocene to. the 
Pliocene of North America. The magnitude 
of the task is almost appalling in the amount 
of detailed work involved. The author tells 
us that this is a portion of the work done in 
connection with his “Monograph of the 
Equide” on which he has been working for 
the last eighteen years. A portion of the 
present work is due to the collaboration of Dr. 
W. D. Matthew to whom the author gives full 
credit. 
The high standard assumed by the publica- 
tions of the American Museum of Natural 
History twenty-five years ago is maintained 
SCIENCE 
[N. 8. Vou. XLVIIT. No. 1233 
in the present memoir. The typography and 
illustrations are excellent. Roy L. Moonie 
CoLLEGE or MEDICINE, 
UNIVERSITY OF ILLINOIS 
SPECIAL ARTICLES 
NOTE ON MEASURING THE RELATIVE RATES 
OF LIFE PROCESSES 
THE development of quantitative methods 
in biology depends: largely on finding means of 
measuring the speed of life processes. In 
most cases the absolute rate is of less im- 
portance than the relative rate (e. g., the nor- 
mal velocity compared with that observed 
under the influence of a reagent). Exami- 
nation of the literature shows that the deter- 
mination of relative rates is frequently made 
in a faulty manner, which could easily be 
avoided by a slight change of method. 
We may illustrate this by supposing that 
the life process in question is a chemical one. 
The rate of a chemical reaction is expressed 
by its velocity constant. The simplest case is 
that in which a single substance, A, decom- 
poses. The usual equation is? 
K- qlee lige x | 
in which K is the velocity constant, J’ is time 
and A—X is the amount remaining at any 
given time, T. 
When the reaction is half completed the 
value of A — (A — X) is always 2, no matter 
what the original concentration of A. The 
time required to reach this stage of the re- 
action is inversely proportional to the value 
of K: for it is evident that if we double the 
value of K we must halve the value of 7’, pro- 
vided the value of A =(A—W2X) remains 2, 
or any other constant value. Hence we see 
that no matter what stage of the reaction we 
choose (half completed, one fourth completed, 
ete.) the velocity constants are inversely pro- 
1 Natural logarithms give the true value of k, 
but common logarithms are frequently used: these 
multiply the value of & by .4343. For illustrations 
of the application of this equation to life processes 
see Osterhout, W. J. V., Science, N. S., 39: 544, 
1914; Jour. of Biol. Chem., 21: 585, 1917; Proc. 
Nat. Acad. Sciences, 4: 85, 1918. 
