Marca 28, 1884.] 
relative order of the sub-faunas, the record agrees, 
in general, with that of the series exposed along the 
same meridian, farther north, in New-York state. 
The principal difference which strikes one familiar 
with the New-York section is the appearance: of S. 
disjuncta and O. Tioga lower down in the faunas in 
the southern sections. 
But although heretofore S. disjuncta has been 
met with in America only in the middle and upper 
parts of the upper Devonian, in Devonshire we find 
_ it reported from the middle Devonian, with corals and 
trilobites in abundance; and in northern Europe it 
begins at least as early as the base of the upper 
Devonian. 
While it is beyond doubt that even in New-York 
state the three spirifers mentioned appear mingled 
-at various zones in the upper Devonian, we do not 
question the fact that the periods of abundance for 
each species are in separate zones, and assume a reg- 
ular sequence relative to each other. ; 
HENRY S. WILLIAMS. 
Cornell university. 
’ 
The use of the method of limits in mathemati- 
cal teaching. 
Rice and Johnson’s ‘ Method of rates’ is especially 
to be commended for the scholarly manner in which 
they developed the subject; but there is the same 
difficulty in the fundamental conception as in the in- 
finitesimal method. One may assume to understand 
an expression with which he is familiar until closely 
questioned. A student learns to repeat with ease, 
‘Velocity is rate of motion,’ and thinks he un- 
derstands it; but I have had many such ask, ‘In a 
mathematically perfect engine, does the piston stop 
at the end of the stroke?’ ‘ Does it remain at rest at 
any time?’ ‘ Howcan it reverse its motion, if it does 
not stop?’ ‘ How canit cease going in one direction, 
and move in the opposite direction, without stopping 
between the two motions?’ These are critical ques- 
tions, lying at the very foundation of all change of 
motion. Does change in the rate of motion take 
place at an instant, or during an instant ? 
The method of limits leads the mind towards a 
result the conclusions of which it is impossible to 
escape: hence, as a system of philosophy, it retains 
its strong hold. DE VoLson Woop. 
Hoboken, March 16. 
Ropes of ice. 
On Saturday, March 8, while traversing several 
counties of southern Ohio by railroad, I observed an 
illustration of the viscosity of ice, that seems deserv- 
ing of mention. ; 
For a number of hours, rain had been falling, much 
of it freezing as it fell; but through the day the tem- 
perature rose slightly, remaining, however, close to 
the freezing-point. All exposed objects were coated 
with ice. In particular, telegraph-wires and the 
strands of wire fences were heavily loaded. In the 
afternoon the ice broke loose from the wires at in- 
numerable points, hanging from them in depending 
curves, the fixed points of which were sometimes as 
much as six or eight feet apart, and the lowest points 
of the curves from two to twelve inches below the 
wires. Occasionally the curves would break, and the 
ends of the ice rope, two or three feet in length, 
would project downwards from the wires at an angle 
of forty-five degrees or more. 
The best examples were passed without opportunity 
SCIENCE. 
375 
to make examination, but all of the facts were illus- 
trated at the stations where the train stopped. 
E. O. 
Tllusive memory. 
I merely intended, in my letter of March 7, to pre- 
sent two of the most prevalent theories which have 
been advanced for these illusions. The ‘race mem- 
ory’ theory, kindly brought out by W. B. T., should 
perhaps have been mentioned, as well as the theory 
of Lewes and Ribot, that these deceptions arise from 
the retrojection or false location of a present mental 
image as a recollection. The inheritance of the 
actual cerebral impressions of a former generation 
rests upon no scientific basis. We do inherit the 
brain structure, and, in so far as brain functions are 
dependent upon structure, we may be said to inherit 
certain functional disposition and powers; but this 
structure, and the impressions made upon it by sense- 
perception, are essentially different facts. 
The correspondence invited should be addressed 
to Princeton, NV.J., instead of Princeton, N.Y., as 
as wrongly given in Science, No. 57. 
HENRY F. OSBORN. 
Princeton, N.J., March 21. 
Ripple-marks. 
Professor Wooster’s note in No. 457, on ripple- 
marked limestones in Kansas, recalls an observation 
of my own in Utah. In the south part of that terri- 
tory the Jurassic formation includes a sectile lime- 
stone fifteen to twenty-five feet in thickness, contain- 
ing remains of Camptonectes and Pentacrinus. Some 
of the surfaces of the layers exhibit coarse ripple- 
marks, the wave-lengths ranging from six inches to 
one foot. The associated fossils cannot be regarded 
in this case as indicative of quiet conditions, for in 
neighboring districts the same forms are found in 
argillaceous sandstones. In the sandstones the shells 
and crinoid segments exhibit wear from rolling, but 
in the limestone their angles are unimpaired. While, 
however, there is no evidence in the limestone of 
violence, there is evidence of motion. The crinoids 
have not been found entire, and all their segments 
are usually detached. Moreover, the structure of 
some of the limestone layers is odlitic. 
I conceive that the association of ripple-marks with 
shallow water, while usual, is not invariable. The 
most important condition for the formation of ripple- 
marks is motion; and any thing competent to produce 
motion at the bottom of deep water may form them. 
Wind-waves on the Atlantic are said to have brought 
sand to the surface from a depth of five hundred feet, 
and they must be supposed to produce at a still greater 
depth the gentler agitation necessary for the forma- 
tion of ripple-marks. 
The association of the Kansas ripple-marks with 
fine argillaceous rocks is perhaps unprecedented, but 
there seems no theoretic reason to regard it with won- 
der. Fine sediment does not usually come to rest in 
spots where the water is subject to agitation, but ex- 
ceptionally it does; and the centre of every shallow 
pond with a muddy bottom affords an illustration. 
Some years ago I observed ripple-marks on a surface 
of fine river-sill at the bottom of a pool which had 
communication with a rushing river. The pulsation 
of the torrent communicated agitation to the pool, 
but no current; and I inferred that the pulsatory agi- 
tation caused the rippling. ‘The pool shared to some 
extent the muddiness of the river, and the silt on its 
bottom was evidently a forming deposit. Not far 
away the bank of the same river exhibited in section 
