APRIL 18, 1884.] 
come on the stage at a comparatively late 
period in the world’s activity, and that it 
would be well to inquire, before bounding with 
joy at his new possession, whether it may not 
be an old one in the world’s stock of knowl- 
edge, or even valueless; but for the old boy, 
the incorrigible old boy, who is constantly pop- 
ping up with his theory of comets, his theory 
of the gyroscope, or his very important meas- 
urements of the thickness of a mercury-drop, 
what can be done? His questions and talk 
may show evidences of an active mind, but of a 
mind working within a Chinese wall of self-suf- 
ficiency. He feels intensely indignant when 
told to examine the records, and compare his 
work with that of others. He is only working 
as every philosopher formerly worked, within 
himself; but at this age he is —a bore. 
LETTERS: TO THE EDITOR. 
¥,* Correspondents are requested to be as brief as possible. 
The writers name is in all cases required as proof of good faith. 
The use of the method of rates in mathemat- 
ical teaching. 
In Science for March 28, Professor Wood, referring 
to the method of rates, says, ‘‘ There is the same diffi- 
culty in the fundamental conception as in the infin- 
itesimal method;” and he represents a student as 
asking the questions, ‘‘ ‘In a mathematically perfect 
engine, does the piston stop at the end of the stroke?’ 
‘Does it remain at rest at any time 2?’ ‘ How can it 
reverse its motion, if it does not stop?’ ‘How can 
it cease going in one direction, and move in the 
opposite direction, without stopping between the two 
motions ?’”’ ‘This difficulty, if it exists, must be met 
in the teaching of mechanics, and may therefore be 
discussed apart from the question whether it be ad- 
visable to found the differential calculus upon the 
conception of velocity. The form of the questions 
which Professor Wood puts into the mouth of the 
student somewhat puzzles me. I can but suppose 
that Professor Wood answers ‘ Yes’ to the first ques- 
tion ; but, in that case, how can the student ask the 
third or fourth question ? The difficulty must lie in 
the answer to the second question, ‘ Does it remain 
at rest at any time?’ It would not be safe to an- 
swer this question at all in this form, because it 
indicates a confusion of mind in the use of the word 
‘time.’ ‘At any time’ might mean ‘at any instant;’ 
but the use of the word ‘remain’ shows that the 
student probably meant ‘remain at rest for any time;’ 
that is, for any interval of time. To the question 
thus amended, we can safely answer, ‘No.’ But 
having already admitted that the piston does stop at 
@ certain instant, namely, ‘the end of the stroke,’ 
the student has no occasion to ask the third or fourth 
question. Of course, a student may be easily puzzled 
by the metaphysical subtleties and sophistries by 
which a certain school of philosophy persuaded itself 
that motion was impossible; but, left to himself, he 
has no more difficulty in appreciating the difference 
SCIENCE. 
475 
between an ‘instant’ and an ‘interval’ of time 
than he has in distinguishing between a point and a 
line in geometry. 
Farther on in his letter, Professor Wood asks, 
‘Does change in the rate of motion take place at an 
instant, or during an instant?’ It seems to me that 
if he will dispense with the colloquial use of the 
word ‘instant ’ for a small interval of time, and sub- 
stitute ‘during an interval,’ the so-called difficulty 
will disappear. Do his students ever ask whether the 
positive and negative parts of the axis of z are sepa- 
rated by a point, or by a space ? 
Wm. Woo.sey JOHNSON. 
Annapolis, April 5. 
Paleozoic high tides. 
Your reviewer of the Geographisches jahrbuch, re- 
ferred to by Professor Newberry in Science (No. 61, 
p. 402), was led, by the evidence given in brief below, 
to the conclusion that tides higher than those now 
observed, produced in the way explained by G. H. 
Darwin and illustrated by Ball, had occurred within 
paleozoic time. It was not, however, his intention 
to accept the gigantic tides described by Ball, but 
simply tides significantly stronger than those of the 
present time; for these seem not only warranted, but 
required, by the spread of paleozoic strata. 
Soundings and dredgings, as summarized, for exam- 
ple, in the Lithologie du fond des mers, by Delesse, 
prove that the coarser land-derived sediments, such 
as form conglomerates and sandstones, are deposited 
within a moderate distance of their origin, excepting 
in narrow tide-ways, such as the English Channel, 
where they stretch out farther; elsewhere, pebbles 
especially fall within a very narrow fringe along shore. 
The paleozoic strata of the eastern United States give 
ample evidence of submarine transportation of land- 
derived sediments certainly three hundred miles from 
their source, of sands at least half this distance, and 
of clean sands with pebbles certainly a hundred 
miles; and this when measuring only from the pres- 
ent south-western margin of the Cambrian strata. 
In this regard, the Medina, Oriskany, and carbonif- 
erous sandstones and conglomerates, which overlie 
calcareous or shaly strata, from which their siliceous 
elements could not have been derived, give very much 
stronger evidence than that obtained from the Pots- 
dam sandstone, which was formed during the advance 
of the sea over an old land-surface, whose local waste 
may have formed this basal deposit close along shore. 
I must consequently persist in believing that the 
spread of pebbles and sand over the old sea-floor dur- 
ing the above-named epochs implies a greater trans- 
porting-force than is now known in the modern 
oceans. 
The Jurassic sandstones of the Colorado plateau 
were, according to Capt. Dutton, deposited with very 
little shaly admixture over an area of thirty-five thou- 
sand square miles. A liberal estimate of the Bay of 
Fundy gives it under four thousand square miles, and 
its deposits are rather muddy than sandy; that is, 
muds such as were washed out of the old Jurassic 
basin are allowed to accumulate in the Bay of Fundy. 
Whether the tides were much stronger in Jurassic 
time than now, is perhaps an open question; but that 
marine transportation was then stronger seems, at 
least from this example, very probable. 
In looking for a cause of former greater activity in 
the ocean, we find it only in the possible variation of 
the tides and currents, unless recourse be had to the 
older cataclysmic theories. Increase in the velocity 
of currents needs stronger differences between polar 
and equatorial temperatures, or an advantageous con- 
