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[Vol. XX. No. 509
fluid when sent, and that evening sections were cut and mounted
after short treatment with picro-carmine. Without examination
two slides were sent to Sir Robert (we were busy on small-pox),
who returned them with the remark, "Only muscular fibre.''
Dr. Bookey looked at me and I gazed upon him, we then sub-
jected the slide to examination with T \ water-immersion Powell
and Leland and No. 3 eye-piece, all apparatus being Powell and
Leland. I have seen reticulation since, but in a tumor purely
epitheleomatous; it was simply wonderful. The cells were per-
fectly differentiated, and the reticulation was so regular that
we at once forgave Sir Eobert for his hasty conclusion.
We hope to continue our investigations on amoeboid organisms;
but, as the process is so long, my colleague persuaded me to send
you these remarks. A. Cowley Malley.
The Fundamental Hypotheses of Abstract Dynamics.
I have been prevented from making earlier reference to Mr.
Dixon's letter in Science of Sept. 9, p. 149, criticising my address
on the above topic. Science, Aug. 5, p. 71. The letter was espe-
cially interesting to me as I had not seen his paper, " On the
Logical Foundations of Applied Mathematical Sciences," com-
municated to the Mathematical Society of London some few
Mr. Dixon, taking the relativity of direction into account,
seems to me to have proved that the Laws of Motion may be re-
garded as forming a definition of force. My argument to show
that if they be so regarded, they are not in general consistent with
one another, involved the specification of accelerations by refer-
ence to a single point, and thus assumed the possibility of deter-
mining directions absolutely. While valid, therefore, as against
the writers to whom I referred, who make the same assumption,
it has not the more general validity which I supposed.
That 1 have regarded force as a non-relative conception, while
Mr. Dixon has thus shown that it may be regarded as relative,
would seem at first sight to place us in antagonism. It does not,
however; for I have merely discussed certain points in connec-
tion with the laws of motion, employing the ordinary conception
of force, and making no inquiry as to the assumptions involved
in it, while Mr. Dixon proves that this conception must involve
certain assumptions, and seeks to determine what they are.
Mr. Dixon points out that it is the law of the conservation of
mechanical energy only which is deducible from the assumption
that stresses are functions of the distance between the particles
on which they act, and that this law would not include the gen-
eral law of the conservation of energy until all energy was shown
to be mechanical. That is quite true; but it does not seem to af-
fect my contention, that, since we are now so sure of the conser-
vation of all forms of energy that the law of the conservation of
mechanical energy is frequently assumed as itself axiomatic, the
laws of motion, if they are to be retained as dynamical axioms,
should be supplemented in such a way that this law would be de-
ducible from them. Nor does the fact that the law of the con-
servation of energy is usually expressed at present in a form
which is probably temporary seem to me to make this any the
less desirable. The conception of potential energy may lose its
utility as we gain clearer insight into dynamical phenomena.
When that time comes we may have to modify our fundamental
hypotheses to suit the clearer views which will have been gained ;
but in the meantime it seems none the less desirable that we
should have axioms sufficient for the deduction of the law of
c uservation in its present form.
There is, as Mr. Dixon supposes, an omission in the sentence of
my paper which he found unintelligible. If commas be inserted
after the words sum and masses, it will be found to state that, if
m 1 and w s be the masses of two particles, and a the relative ac-
celeration produced by a stress between them, this stress may be
shown to be proportional to
a m x w a -f- (Wj -f m 2 ).
It follows that, if one of the particles be of infinite mass, the
stress is proportional to the mass of the other multiplied by the
relative acceleration. When I conclude from this that "if, in
applying the second law of motion, a particle of infinite mass be
chosen as point of reference, all the forces acting on a system of
particles, may be regarded as exerted upon them by the particle
of infinite mass," these forces are supposed to be exerted in ac-
cordance with the third law of motion, which asserts action and
reaction to be equal and opposite, but not to be in the line joining
the particles acting on one another. I do not myself regard this
fiction as of any importance. I mentioned it in passing because
I wished to refer subsequently to Newcomb's assertion that the
law of the conservation of energy assumes it.
Mr. Dixon considers it inconvenient to include in one law of
stress two statements resting on such very different evidence as
that forces may be considered to be attractions or repulsions and
that their magnitudes depend solely on the distances between the
particles on which they act. I need hardly say, however, that I
see no objection to enunciating the two statements in separate
sentences. For educational purposes, indeed, it would certainly
be well to enunciate what I have called the law of stress, piece-
meal, as is invariably done in the case of what I have called the
law of force. J. G. MacGregor.
Dalhousle College, Halifax, N. S., Oct. 4.
The Libyan Alphabet.
I gladly accept Dr. Brinton's offer (Science, Sept. 80) ; only, if
his object is truth rather than the scoring of a point, he will
place in the editor's hands, not the Grammaire tamachek, which
would be useless for the purpose, but the Grammaire Icabyle,
which alone contains the full forms of the three Berber alpha-
bets, but which Dr. Brinton appears never to have seen. Even
the Grammaire tamachek, now that he has got hold of it, he
seems incapable of understanding. The other day he mistook
diacritical marks for accents, and now he tells us that Hanoteau
connects the Libyan and Semitic systems " solely" because both
are read from right to left, even charging me with disingenuous-
ness for suppressing this fact. The charge might stand, had I
made the assertion, which is as wide of the mark as is Dr. Brin-
ton's appeal to Hanoteau, on the question of accent. The very
Berber name asekkil (pi. isekkilen) of the letters is equated by
Hanoteau (p. 5) with the Arabic shakl and the Hebrew sakal,
"forme, figure, dont les Grecs ont fait aiyXal,'' hence the French
sigle. I am not defending these equations, but merely give them
to show how ignorant Dr. Brinton still is of the contents of the
Grammaire tamachek, which he had the temerity to insinuate I
had never seen (Science, Aug. 19). May I ask Dr. Brinton who
are the " French scholars " that regard the initial t as radical in
the word M/mar, and that accent the word differently from Barth,
for this also appears to be again insinuated ? The recent death
of M. E. Renan reminds me that that illustrious " French
scholar " is also arrayed against Dr. Brinton, holding that the
Punic origin of the Libyan alphabet is an established fact (His-
toire des langues semitiques, 2d ed., p. 194. et seq.). Dr. Brin-
ton is to be envied his possession of " plenty of documents in tift-
nar." Such documents are excessively rare in Europe, and even
amongst the Tuaregs themselves, who, apart from rock inscrip-
tions, have never made any extensive use of this old and defec-
tive script. Considering the weakness of his position, Dr. Brin-
ton shows as much want of tact as of bad taste in charging his
opponent with lack of candor. A. H. Keane.
79 Broadhurst Gardens, Soulh Hampstead, N. W.
Is There a Sense of Direction ?
IK his article on the "Sense of Direction," in Science of Oct. 7,
Dr. Work says, "It is very well known that an unguided horse
returning to familiar haunts will do so over the same route by
which he left them, rather than in a direct line by sense of direc-
tion." An incident which came under my observation some six
years ago directly contradicts this theory. My father had pur-
chased a very intelligent mare about a month before, and on this
occasion I hitched her single to a carriage, and drove to a town
about fourteen miles distant. As the direction was almost due
north-west, the road ran alternately west and north, there being
about eight corners to turn. Although the mare might have been