May 30, 1884.] 
known by their true scientificnames. This is the case 
with Eschscholtzia, Romneya, Clematis, Isomeris, 
Silena, Malva, Ceanothus, Hosackia, Ribes, Phacelia, 
Gilia, and many others for which the generic name 
has become a popular name. 
This is owing to various causes, one being the dif- 
ficulty of applying the old familiar garden names; 
which are used, however, when any resemblance can 
be traced, as is the case with larkspur, honeysuckle, 
columbine, etc. Many of the settlers have also be- 
come familiar with the true names of these flowers 
by having received them from parties that have in- 
troduced them to cultivation, for which the greatest 
credit is due to the late James Vick. 
Many visitors, as well as settlers, seek to learn the 
names of the many strange and beautiful flowers, 
that, by massing, become such a feature in the scenery, 
and find the ‘dry’ scientific names as easy to learn, 
and as sensible, as the old Spanish names, but few of 
which survive in the popular mind. Thanks to the 
little botany of Volney Rattan, largely supplemented 
by visiting and amateur botanists, all are enabled 
to learn the more common species with comparative 
ease. C. R. ORcUTT. 
The use of the method of rates in mathe- 
matical teaching. 
In the case of the question, ‘‘ Does change in the 
rate of motion take place at an instant, or during an 
interval? ’’ I am surprised to find that Professor Wood 
(Science, May 16) regards my amendment as only 
increasing the difficulty. It may be that I have been 
misunderstood: permit me, therefore, to answer the 
questions which the professor goes on to ask in illus- 
tration of this difficulty. Assuming (of course, cor- 
rectly) that my answer to the question is, that it takes 
time to produce a change in the rate of motion, he 
asks, ‘‘ How long is this interval?”’ I answer, ‘‘As 
long as you please usually: of course, the longer the 
interval, the greater the change.’’ — ‘‘ If everso small, 
is the rate variable during the interval ?’’ — ‘‘ Certain- 
ly.” — ‘‘ If variable, the original question arises, and 
we wish to know if change involves a part of the in- 
terval.”’ — ‘‘ Of course, a part of the change takes 
place in a part of the interval, and the rest of the 
change takes place in the rest of the interval.’’ — 
** Does change in the rate take place at ‘a point’ in 
the path, or during ‘aspace’ of the path? ’”? — ‘‘ Dur- 
ing ‘a space’ of the path; that is, while the point is 
passing over a space of the path.’”’ — “‘ If at ‘a point,’ 
is it not equivalent to asserting that a change takes 
place in no time? [Most certainly it would be, but 
we do not assert this at all.] And if an interval is 
necessary, must it not be conceived as infinitesimal? ”’ 
—‘*By no means: if you want a finite change, and 
that is what is usually meant by a change, you must 
take a finite interval of time; but, if you insist on 
introducing the conception of an infinitesimal change, 
you must admit also an infinitesimal interval of time.’’ 
Let us put precisely parallel questions with respect 
to the position of a moving point. Does change of 
position take place at an instant, or during an inter- 
val? During an interval. How long is this interval? 
That depends upon the amount of change of position 
you desireto produce. If everso small, is the position 
of the point variable during the interval? Certainly, 
if the point moves. Does change of position take 
place at a point in the path? Certainly not: a point 
has position, but no magnitude. 
If there is any difficulty in conceiving the velocity 
of a point to be continuously variable, there is pre- 
cisely the same difficulty in conceiving the abscissa of 
a point moving on the axis of x to be continuously 
SCIENCE. 
645 
variable; in other words, in conceiving the possibility 
of motion itself. It should be remembered that the 
definition of the measure of a variable velocity, pre- 
supposed in this discussion, is simply that which we 
find in such treatises as Tait and Steel’s Dynamics of 
a particle: ‘‘ Velocity is said to be variable when the 
moving point does not describe equal spaces in equal 
times. The velocity at any instant is then measured 
by the space which would have been described in a unit 
of time, if the point had moved on uniformly for that 
- interval with the velocity which it. had at the instant 
contemplated.’ Wma. WooLsey JOHNSON. 
Annapolis, May 19. 
Pleuracanthus and Didymodus. 
In your issue of April 11, my friend Professor Gill 
communicates his views on the relationships of Pleu- 
racanthus and Chlamydoselachus, and endeavors to 
correct some of my opinions and statements. On 
some points I stand corrected, thanks to Professor 
Gill’s superior knowledge of the literature of the 
subject. However, as Professor Gill has not seen my 
material, nor the paper which I read before the Phil- 
osophical society upon it, I may, in turn, enlighten 
him on some important aspects of the case. 
Professor Gill objects to the identification of the 
genera Didymodus and Chlamydoselachus on the 
sole ground of the diversity in the form of the teeth. 
He probably has other reasons for objecting; but, with 
his usual magnanimity, he has not used his most 
effective weapons. He doubts the pertinence of the 
recent and extinct genera to the same order. He 
points out that the oldest name of the genus called 
Diplodus is Pleuracanthus, and that my order Ich- 
thyotomi has been already defined and named by 
Lutken as the Xenacanthini. 
On these positions, I make the following com- 
ments : — 
1. There is no generic difference to be detected, in 
my opinion, between the teeth which are typical of 
Diplodus Agass. and Thrinacodus St. J. and W. and 
the recent Chlamydoselachus. Differences there are, 
but apparently not of generic value. The identifica- 
tion of the recent and extinct genera rests, as far as 
this point goes, on the same basis as that of the recent 
and extinct Ceratodus. 
2. At the time of my proposal of the name Didy- 
modus, I was not convinced that fishes of this type 
bore the spines referred to the genus Pleuracanthus 
Agass. None of the authors cited figure any specimens 
which present both tricuspidate teeth and a nuchal 
spine. None of my ten specimens possess a spine. 
However, Kner describes two specimens as exhibit- 
ing both tricuspidate teeth and a spine, and Sir P. 
Egerton’s statements (/.c.) on this point are positive. 
So we must regard Pleuracanthus as the name of this 
genus, with Diplodus as a synonyme. 
3. Diplodus being regarded as a synonyme of Pleu- 
racanthus, it follows that Chlamydoselachus Garm. is 
distinct on account of the different structure of the 
dorsal fin, which is single and elongate in Pleuracan- 
thus, according to Geinitz and Kner. The presence 
of the nuchal spine in Pleuracanthus is also, probably, 
a character of distinction, although we do not yet 
know whether such a spine is concealed in Chlamy- 
doselachus or not. 
4. The identity of Didymodus (type, Diplodus com- 
pressus Newberry) and Pleuracanthus may now be 
questioned. None of the specimens are figured and 
described by the authors above cited, as displaying an 
occipital condyle, or posterior frontal cornua. My 
specimens of Didymodus compressus do not exhibit 
