Wa 
8 
430 SCIENCE. 
that Diplodus and Xenacanthus were generically 
identical. 
In 1883 Professor Cope (Proc. acad. nat. sc. Philad., 
p. 108) substituted the name Didymodus for Diplodus, 
because the latter name had been given in 1810 to 
Sargus by Rafinesque. ‘The distinguished naturalist 
was evidently unacquainted with the researches of 
his predecessors. 
There is much variation in the dentition of Pleura- 
canthus (as we shall now call Diplodus, or Didymo- 
dus), but it is rather a variation consequent on position 
in the jaws than specific or generic; and not only 
“the species,’ but one and the same species, may ‘ pos- 
sess two, three, or four denticles,’ but not teeth at all 
like Chlamydoselachus. However, somewhat analo- 
gous teeth are those of the type named Diplodus 
incurvus by Professors Newberry and Worthen (Pal. 
Ill., vol. ii. p. 62, pl. 4, f. 4). These were very dif- 
ferent from Diplodus, and belonged to a genus called 
Thrinacodus by St. John and Worthen (Pal. Ill., vol. 
iii. p. 289, pl. 5, f. 1,2). But whether the animals 
armed with such teeth resembled Chlamydoselachus 
may well be doubted. 
In fine, the order called Ichthyotomi by Profes- 
sor Cope appears to be demanded; but it has nothing 
whatever to do with the Pternodonta or Selachophich- 
thyoidi, and it may not even belong to the selachians 
(some of its characters are very peculiar, and resem- 
ble those of protodipnoans). Further, the order had 
already been recognized, defined, and named by Liut- 
ken. Didymodus, or Diplodus, and Triodus, can be 
co-ordinated with the spines, Pleuracanthus, Ortha- 
canthus (pt.), and Xenacanthus. All these names are 
referable to a single family (Pleuracanthidae) of the 
order Xenacanthini of Lutken. The proposed mem- 
oir of Professor Cope will, however, be a great boon 
to science; and to enable him to co-ordinate his data 
with those of the earlier paleichthyologists, and thus 
render it still more valuable, is the object of this com- 
munication. Apparently two genera, distinguished 
by their spines, exhibit the Didymodus, or Diplodus, 
dentition, —Pleuracanthus and Xenacanthus. In- 
formation is especially desirable respecting the char- 
acter of their branchial apertures. 
As to Chlamydoselachus, the anatomy will proba- 
bly reveal a structure most like that of the Opisthar- 
thri (Notidanidae), but of asomewhat more primitive 
type. Mr. Garman’s memoir will unquestionably 
be of great value, for probably no one is better ac- 
quainted with the selachians than that gentleman. 
THEO. GILL. 
The ‘unit of time’ controversy. 
¥ 
Upon reading your editorial comments in Science, 
No. 58, upon the ‘change in the unit of time’ con- 
troversy, which close with the words ‘‘ Unless, then, 
this matter admits of speedy and permanent decision, 
the one way or the other, with the entire agreement 
of all parties to the controversy, astronomy would 
appear to run the serious risk of forfeiting her claim 
to a place among the exact sciences,”’ it strikes me, 
that unless the whole thing is intended as a sarcastic 
criticism of Mr. Stone, of which there is no evidence, 
it is about time to call a halt upon some one for loose 
writing. 
_ if Mr. Stone maintains that a mean solar day, in- 
stead of depending upon the actual time of rotation 
of the earth on its axis and the actual time of its 
revolution round the sun (and hence capable of de- 
termination by actual observation), is an arbitrary 
interval of time fixed by the dictum (of Bessel, Le- 
verrier, or any other human being) that in that time 
the earth shall move so far in its journey round the 
[Vou. IIL, No. 62. 
sun (and that is exactly what his theory amounts 
to), and if he says,! ‘‘ Professor Adams’s argument, 
that ‘mean solar time is measured, not by the sun’s 
mean motion in longitude, as Mr. Stone’s theory 
supposes, but by the motion of the sun in hour-an- 
gle,’ is one that I do not profess to understand,’’ and 
if he persists in maintaining these absurd positions, 
then astronomers will simply leave him to himself, 
for argument in such a case is useless. 
As to the relation of astronomy to the exact sci- 
ences, let us see how much is the point in dispute. 
The increasing discrepancy between the formulae of 
Bessel and Leverrier for the annual mean motion ~ 
of the sun in longitude is 0”.0602 per year; that is, 
six-hundredths of a second of are while the sun 
moves 1,296,028 seconds. This amounts to eight- 
hundredths of a second of time (0.08) in twenty 
years. Expressed as a ratio to the whole constant, 
it is .000,000,046, or about 1 part in 21,500,000. 
The discrepancy between the two best modern de- 
terminations—those of Hansen and Leverrier —is 
only 0.0043 per year, or about one-fourteenth of 
the above; and perhaps it will be admitted by even the 
most enthusiastic devotees of the ‘exact sciences’ 
that this is a fairly well determined: astronomical 
constant. The proper theme for exciting astonish- 
ment should be, that Bessel, with the data available 
in his day, should have been able to determine this, 
and a dozen other constants, so wonderfully near 
their true values as modern observations show them 
to be. Only an intellectual giant of his wonderful 
skill and indomitable energy could have accomplished 
such results. H. M. PAUL. 
Washington. z 
[Caeteris paribus, loose writing is much less prob- 
able than loose reading. We counsel our correspond- 
ent to re-read, and with circumspection. Science 
hopes to present the views of all parties when so 
expressed as to merit a hearing, and, least of all, 
takes occasion to espouse the cause of a partisan. 
The controversy on ‘ the unit of time’ is regrettable; 
but foreign astronomers are abundantly competent 
to conduct the discussion, as they have done hereto- 
fore, without additions to the literature of the subject 
on the part of any one here. | 
The use of the method of limits in mathemati- 
cal teaching. 
Science for March 14 contains a letter by Professor 
Safford on methods of teaching the calculus, in which 
he refers to the ‘ new method of rates’ by the writers, 
in comparison with the method of limits. The 
phrase, ‘new method of rates,’ is quoted from a list 
of subjects for discussion by the M. P. club, Boston, 
and was probably intended as an abbreviation of the 
title of a pamphlet, ‘‘On a new method of obtaining 
the differentials of functions, with especial reference 
to the Newtonian conception of rates or velocities.”’ 
We have more recently published a treatise on the 
differential calculus, founded upon the method of 
rates or fluxions, in which the method published in 
the pamphlet is employed in obtaining the differen- 
tials of functions, but which has nothing in common 
with the methods used by Maclaurin, except the em- 
ployment of the conception of velocity in the funda- 
mental definitions. 
Professor Safford regards the doctrine of ‘ the sur- 
vival of the fittest’ as having pronounced against the - 
method of fluxions, and in favor of the method of — E 
limits. It seems to us that it is rather the geometrical 
methods of Maclaurin and the immediate followers 
of Newton that have thus been condemned, as com- — 
1 Monthly notices, January, 1884, p. 81. 
we J 
