a. 
eo 
} 
Aprit 11, 1884.] 
pared with the analytical methods and more flexible 
notation adopted by the followers of Leibnitz. 
The Leibnitzian notation, although originally con- 
nected with the doctrine of infinitesimals, has now 
been universally accepted; so that we must inevitably 
denote an absolute velocity by and a relative 
velocity by om The question which is still, as it 
seems to us, debatable, is whether these symbols shall 
be defined (1°) by the conception of a velocity, (2°) as 
limits of finite differences, or (3°) as the ratios of in- 
finitesimal differences. ‘The second course arose as 
a protest against the logical difficulties involved in 
the conception of infinitesimals: it labors under the 
disadvantage of attaching no separate meanings to 
the symbols dz, dy, and dt, and thereby loses much 
of the advantage of the Leibnitzian notation. This 
method is best exemplified in the excellent treatise 
of the late Dr. Todhunter. On the other hand, the 
employment of the notion of rates in the fundamental 
definitions enables us to give to the detached symbols 
dz, dy, and dt, definite meanings which are not of 
necessity infinitesimal. 
It appears to us that this method of presenting 
the subject is better adapted than that of limits to the 
purposes of elementary instruction. We do not at- 
tempt or desire to dispense with the use of limits, 
a the following quotation from our preface will 
show: — 
“ The distinction between the view of the differential calculus 
here presented, and that found in most of the standard works on 
the subject hitherto published, may be stated thus: the deriv- 
ative = is usually defined as the limit which the ratio of the 
finite quantities Ay and Az approaches when these quantities 
are indefinitely diminished. When this definition is employed, 
it is necessary, before proceeding to kinematical applications, to 
prove that this limit is the measure of the relative rates of x and 
y. Inthbis work the order is reversed; that is, dz and dy are so 
defined that their ratio is equal to the ratio of the relative rates 
of x and y: and in chapter xi., by applying the usual method of 
evaluating indeterminate forms, it is shown that the limit of 
AZ - Seen - . < 5 
when Az is diminished indefinitely, is equal to the ratio 
dy 
dx 
prepared to show that the limit has a definite value, capable of 
expression in a language already familiar to the student.” 
Our experience has been, that the student trained 
by this method finds no difficulty in passing to the 
employment of infinitesimals, in obtaining the differ- 
entials which are required in the mechanical appli- 
cations of the integral calculus; for example, those 
required in the determination of moments of inertia, 
resultant attractions, etc. 
5 Fe) a a9 (0) OF 
W. W. JOHNSON. 
U.S. naval academy. 
Silk-culture in the colonies. 
In your review of my census report on silk-manu- 
facture in the United States, your critic takes issue 
with me as to the amount of silk raised in the colo- 
nies. He declares that there is a tendency on my 
part “‘to depreciate the quantity and quality of silk 
produced, —a tendency which is natural, and doubt- 
less unconscious in an agent of manufacturers.”? In 
support of this grave imputation, your critic adduces 
two points on which he disputes my proof that cer- 
tain estimates, hitherto accepted as relating to raw 
silk, really refer to cocoons, and probably to fresh 
cocoons. _ He says, first, that I by no means make it 
SCIENCE. 
Thus the employment of limits is put off until we are 
4351 
clear that the term ‘raw silk balls’ really meant co- 
coons, ‘*as it might apply to the twisted hanks of reeled 
silk, and the term ‘ cocoons’ was in use at that time.’’ 
To this it need only be said, that, in the literature of 
the colonial period, cocoons are frequently designated 
by the term ‘balls,’ or ‘silk balls.’ For instance: — 
“Removing your branches from the tables, and your silke- 
balls or bottomes from the branches 5 dayes after the worke is 
perfected, the balls are then to be made election of for such seed 
as you will preserve for the year following. Bonoeill and De 
Serres do both agree that there should be proportioned 200 balls 
for one ounce of seed, the balls male and female.” 
On the other hand, in a widely extended reading 
on the subject, I have never met with the term ‘ balls ’ 
as signifying reeled silk in any form; and I have no 
reason to believe that reeled silk was made into balls. 
Your critic remarks, secondly, ‘‘ It is certainly not 
justifiable to assume that the cocoons were necessari- 
ly fresh, as they are not thus handled and marketed.’’ 
They are so handled and marketed at the present day. 
Statistics of production in European countries and 
districts are compiled, based on the weight of fresh 
cocoons. Thecommerce in them is very large. Quota- 
tions of their market-prices appear, during the season, 
in trade reports and journals. For instance: in the 
Moniteur des soies of June 30, 1883, under the head- 
ings ‘Prix des cocons Frang¢ais ’ and ‘ Marchés des 
cocons Italiens,’ there are pages of this sort of infor- 
mation; and it is so well understood as referring to 
fresh cocoons, that no special designation is used for 
them: they are simply ‘cocons.’ Indeed, I am as- 
sured, on good authority, that it is only fresh cocoons 
that go from the producers to the filatures: even if 
‘choked,’ they are accounted fresh. 
Is it not justifiable to believe that estimates of the 
weight of cocoons produced in Georgia, and of what 
was sent to the filature there, were similarly made: 
that is, that they referred to fresh cocoons? This 
view of the case came to me only after months of 
research and final good fortune in tracing the origin 
of an historical error. Until then, I had accepted 
without question the current histories in their ac- 
counts of silk production in the colonies. My expla- 
nation reconciles their strange discrepancies: before 
refusing it, should not some other solution be offered? 
While differing wholly from the conclusions of your 
article as to the causes of failure and cessation of silk- 
culture in this country, I should not have troubled 
you with a reply to criticisms on my work, had they 
not contained the imputation to which, with great 
regret, I have deemed it necessary to refer. 
Wm. C. WYCKOFF. 
Rainfall at Amherst, Mass. 
The month of February, 1884, stands alone upon 
the meteorological record of Amherst college in show- 
ing an average cloudiness of seventy-seven per cent 
of the sky. During the forty-two years which this 
record covers, in no previous case has the cloudiness 
of a month averaged more than seventy-four per 
cent; in only five cases has it reached seventy; the 
range generally being between forty and sixty, and 
the mean almost exactly fifty. 
The fact that clouds and fog gather only in air con- 
taining particles of dust, which has been scientifically 
demonstrated, suggests the question, whether the vol- 
canie dust from Krakatoa, which in higher air gave 
to us the brilliant evening skies of December last, 
may not, in its gradual descent toward the earth, have 
reached in February the lower level, in which our 
clouds are formed, and have been the cause of this 
unprecedented accumulation of them. 
S. C. SNELL. 
Amherst, Mass. 
