JUNE 138, 1884.] 
A third point made by Professor Tait against force 
is, that its numerical expression is that of two ratios, 
— the ‘space-rate of the transformation of energy,’ 
and the ‘ time-rate of the generation of momentum.’ 
These results are obtained by simple division, in an 
equation which expresses the fact that the work 
done by a body in falling the distance h is just that 
required to lift it through h against gravity. The 
fallacy involved in treating the numerical expression 
for force as force itself has been well exposed by 
Mr. W. R. Browne, in a criticism of this encyclo- 
paedia article (Phil. mag., November, 1883); and the 
assumption that ratios are necessarily non-existent 
is even more fallacious. Were it trustworthy, Pro- 
fessor Tait’s equations would lead quite as conclu- 
sively to proofs of the non-objectivity of space and 
time (the former becoming the rate of work-units, 
the latter of motion-units, per unit of force), and so 
to a confirmation of the celebrated German view 
that whatever is universal and necessary in thought 
belongs to the subject, as to what he deduces from 
them; or they might even give mass in the form of a 
ratio, and hence suggest the non-objectivity of mat- 
ter. 
Not the least of the professor’s objections against 
force, it would appear, is thatit is ‘ sense-suggested.’ 
It is a mere truism to say that no other suggestor is 
possible within the domain of science. It is, per- 
haps, better worth while to call attention to the indu- 
bitable fact that the real ground of the objection 
against ‘action at a distance,’ entertained by many 
physicists, is exactly that such action is not directly 
suggested by sense-impressions: for this is what they 
must really mean by calling it ‘ occult’ ; actions as our 
consciousness knows them, and as we can produce 
them, being generally characterized by proximity 
undistinguishable from actual contact. Further, if 
there is any reproach in this epithet, energy is quite 
as open to it as any function of energy can be: in 
fact, our senses directly report work in the form of 
nerve-disturbance, and nothing else. Force is no 
more truly an inference from nerve-reports testifying 
of energy exerted, than is matter: in fact, the infer- 
ence of the independent existence of matter is the 
less direct and more questionable of the two. The 
view advocated by Mr. Browne, following Bosco- 
vitch, that matter is but ‘an assemblage of central 
forces, which vary with distance, and not with time,’ 
or with direction, is one of great simplicity, as well as 
suitability to analytic treatment, and one of which 
no disproof is possible. 
It is not too much to claim, therefore, that, in the 
very difficult task of proving or disproving objective 
reality, Professor Tait has not here been successful. 
HENRY FARQUHAR. 
Worth-eastern and north-western Indian im- 
plements. 
I do not see that it necessarily follows, because 
such implements as I have described as ‘club-heads’ 
were or are in use among the Ojibwas as ‘ bone- 
breakers,’ that the Lenni Lenape used these pebbles 
for such a purpose, and not in the manner I have 
suggested. It would naturally be inferred from Miss 
Babbitt’s remarks, that the Dakota puk-gah-mah-gun 
never varied in its size or shape. If so, then prob- 
ably no weapons of this pattern have occurred in 
New Jersey; but this is not, true of any form of 
weapon, agricultural or household implement, ever 
made by the Indians. They vary indefinitely in size, 
shape, and degree of finish; and the many forms 
merge imperceptibly one into the other, as axes into 
hammers, knives into spears, and these again into 
SCIENCE. 
701 
arrow-heads. Miss Babbitt herself distinctly states 
that the two forms of ‘ club-head’ and ‘ bone-breaker’ 
are essentially the same. If the specimen I figured 
(fig. 212) in my ‘ Ancient stone implements of eastern 
North America’ be not a club-head, it does not follow 
that the more nearly globular fig. 211 was not; and 
I am glad to be able to state that I have seen just 
such grooved, globular stones mounted in wooden and 
hide handles, that were, until very recently, in use by 
Sioux Indians. 
I am very glad that Miss Babbitt has pointed out 
the use of a large number of these oval, grooved 
pebbles as ‘bone-breakers:’ it is a most desirable 
addition to our knowledge of the archeology of the 
Atlantic-coast states; and it is now possible to grade 
and classify this simple pattern of stone implements 
much more satisfactorily. Of such found in New 
Jersey, I would say, then, that they are, first, grooved 
hammers, or mauls; second, club-heads (Dakota, 
puk-gah-mah-gun); third, ‘bone-breakers;’ fourth, 
net-weights. 
I suggest this division as based upon the size, the 
degree of finish, the evidence of use (as in the ‘ bone- 
breakers’), and, lastly, the conditions under which 
many are found. If the flat, discoidal pebbles with 
side-notches are net-weights, and of this there can 
scarcely be a doubt, then the smallest of the groove 
pebbles, which we usually found associated with 
them, were doubtless put to the same use. 
CHARLES (©. ABBOTT. 
May 18. 
Atmospheric waves from Krakatoa. 
Mr. H. M. Paul is, doubtless, perfectly correct in 
insisting (Science, iii. 581) that the atmospheric waves 
following the Krakatoa explosion should not be con- 
founded with the elastic waves producing sounds: 
in fact, these latter are so brief that it is very ques- 
tionable whether they would show themselves at all 
on barometric traces. There would not be time enough 
for the mercurial barometric column to respond to the 
momentary compressions and rarefactions: much less 
would they be indicated by fluctuations extending 
over thirty minutes ormore. ‘The atmospheric waves 
which encircled the earth, and disturbed the self- 
registering barometric traces on the 27th of August, - 
1883, must therefore have been huge aerial gravity- 
waves, due to the enormous displacement of air 
produced by the ejection of vast volumes of gaseous 
products into the atmosphere at the time of this 
volcanic explosion: they were analogous to the great 
earthquake water-waves that are sometimes trans- 
mitted thousands of miles across oceans. 
The point in this connection which needs eluci- 
dation is the fact, established by the observations of 
Gen. Strachey, Professor Forster, and others, that 
the velocity of these waves was approximately the 
same._as that of an elastic sound-wave in air. It is 
the near coincidence of these velocities which has 
led to the confounding of these gravity-waves with 
elastic sound-waves. The approximate identity of 
the velocities in these two cases may be traced to the 
relation existing between the elasticity or resilience 
of the air, on which the velocity of sound depends, 
and the height of a homogeneous atmosphere, on 
which the velocity of long aerial gravity-waves 
depends. 
It is well known that the mathematical investiga- 
tions of Sir G. B. Airy and others, confirmed by the 
experimental results of Scott Russell, show, that, in 
the class of water-waves in which the wave-length 
bears a large ratio to the mean depth of the water, 
the velocity of propagation of the wave is sensibly 
