Fresruary 4, 1897 | 
NATURE 
Sh /) 
Symbols of Applied Algebra, 
UxrortunaTeELy Mr. C. S. Jackson (p. 293) does not appear 
to believe that I mean what I say, nor does he definitely appre- 
hend what I mean. It is possible, however, that he represents 
some other teachers, and, therefore, I must regretfully occupy 
your space with the elementary statements: (1) that absolute 
measure has nothing to do with ‘‘standard substances”’; 
directly a standard substance is introduced the ‘ measure ” 
becomes relative ; (2) that specific gravities are expressible in 
tons per cubic yard (weight or mass being understood in accord- 
ance with context and subject-matter), or in grammes per cubic 
inch, or even in dynes or poundals per cubic metre ; and (3) 
that to consider a density as a mere number is erroneous. 
January 31. OLIVER J. LODGE. 
On Mass. 
DEesPire the extraordinary letter of Mr. C. S. Jackson, which | 
appears in your issue of December 31, 1896, I must say that if 
there is a term which teachers of rational mechanics should retain 
and emphasise, it is the term ass. Mass denotes the quantity 
of matter, or the amount of stuff, in a given body. It is a 
definite and invariable quantity, whether you have the body at 
latitude o° or at latitude 90°; whether you conceive it trans- 
ferred to the surface of Jupiter, or to the outermost ring of 
Saturn. 
On the other hand, the weight of the said body is a variable 
quantity, being measurably greater in a high than in a low 
latitude. At the earth’s centre, it vanishes; on the moon, it 
would be less than here in New York; whilst on Jupiter, it 
would be considerably greater. 
The inevitable conclusion is that scientifically the ass of 
a given body is of more importance than sucha variable quantity 
as its weight. 
This holds even commercially, for when we buy a pound of 
sugar we are more concerned with the quantity of the saccharine 
material that we get than with its weight. The weight is 
taken, in any given place, as a convenient measure of the 
mass. 
Mr. Jackson’s equation 
P/Q = fla 
is misleading ; it is true only when the forces P and Q act 
on egzai’ masses. To write such an equation without the above 
statement, is merely begging the whole question at issue. 
It is to be hoped that teachers of rational mechanics will 
ever insist on the different ideas connoted by the terms J/ass 
and Wezght. M. F. O'REILLY. 
Manhattan College, New York City, January 13. 
Dynamical Units. 
Ir Prof. Perry's reply to my letter (on p. 126) is summed up 
in the charge that I think of ‘‘stuff’’ when I ought to be 
thinking of inertia, then the issue between us should reduce to 
very minute dimensions. It is, perhaps, unfortunate that in 
English the term mass may signify either ‘‘ quantity of matter” 
or the inertia of that matter, but hardly so unfortunate as the 
fact that weight may denote either a quantity of matter or a 
force, an ambiguity to which we are all prone, though 
Prof. Perry makes light of it ; for a definite amount of matter 
implies, at least, a definite amount of inertia, but not 
a definite weight, in the sense of force If Prof. Perry thinks 
that with himself the word mass means simply inertia, then, 
substituting at the bottom of p. 49 in the current volume, I find 
that he says: “* My unit of inertia is the zvev¢za [the italics are 
mine] to which unit force gives an acceleration of 1 foot per 
second per second.” I am free to confess that I cannot 
dissociate the conception of inertia from the idea of matter ; 
but here we have abstraction indeed. 
The main points to which I confined my remarks were the 
observation that with British standards the poundal is unique 
among units of force, and the showing that the alternative 
system of units advocated by Prof. Perry is artificial and incon- 
venient. 
as may suit his craving for rigorous expression, the objections to 
his proposals will still hold. But I do not know for certain what 
alterations he demands. In the case of a student who is com- 
mencing the study of dynamics by observing the effect of forces 
applied to bodies moving smoothly on the flat, would he tell 
him at the outset that it is not a number of pounds of iron or 
NO. 1423, VOL. 55] 
Even if he makes such verbal alterations in my letter | 
other stuff that he is moving about, though he may think so, 
but an amount 72 of inertia? Surely he would not. Or is it 
that he objects to my statement that his system involves the 
| conception of one piece of matter (the standard pound) whose 
weight (under conditions) is the unit of force, and also of 
another lump of matter of 32°18 Ibs. whose inertia is the unit 
of inertia? Well, if he says that no such conception presents 
itself to him I will not insist. I am not familiar with his 
psychological processes, but such images arose in my mind on 
reading his exposition of the system, and I think the same 
would (and ought to) oceur in the case of a student on first 
trying to understand it. And it is for the beginner that Prof. 
Perry is so solicitous: an advanced student may be left to 
choose his own system, and will get on in spite of all 
| systems. 
In seeking to justify his preference, Prof. Perry, dexterously 
using the figure paraleipsis, extracts such support as he can get 
from existing legal definitions of the pound. We have had our 
law-abiding instincts appealed to in this connection before ; but 
the law is a broken reed to rely on. The legal standard pound 
was originally established almost entirely with a view to facilitate 
the accurate weighing of Prof. Perry’s conventional or meta- 
physical ideas—in other words, quantities of stuff of various 
kinds. Its environment did not signify, as its weight, in the 
sense for which modern physicists try to reserve the term, was 
quite a secondary matter. The standard pound was adopted for 
the sake of something which it and all its true copies, of what- 
ever material they may be made, possess, or appear to possess, 
| in themselves ; and this thing they possess, or are associated 
with to the same extent wherever they may exist in the known 
universe : and it is not their weight, in the modern sense. It is 
their mass, in the sense of, or as measured by, their quantity of 
inertia. Prof. Perry is welcome to whatever comfort he can 
obtain from the wording of Weights and Measures Acts. 
However, we have the thing—the standard pound. No one 
denies that its weight, when it is placed in vacuo near London, 
furnishes us with an excellent practical unit of force. But this 
is not good enough to secure the banishment of the poundal and 
the dynamical system associated with it. I do not quite gather 
where Prof. Perry himself considers the ‘‘ huggermugger ” comes 
in with regard to this unit ; but if I understand his letter aright, 
something perilously near to this appears to have crept in among 
his observations on the subject. ‘ 
In his letter (NATURE, vol. lv. p. 176) he affects to ignore 
the fact that the standard pound really furnishes us with a 
standard something that is constant—its inertia. He uses such 
phrases as ‘‘ Assuming . . . that the weight and inertia of a 
| certain body measured under the same circumstances at the same 
place are always the same” ; and again: ‘‘ Now here are your 
standards ” (ze. of weight and inertia) ‘tin one piece of metal 
and its environment, and in yourinstruments.” How ingenious 
is the suggestion that its inertia suffers from the same incurable 
disease that afflicts its weight, viz. that it is a function not of 
the body only, but also of its more or less unknown and uncon- 
trollable environment. If it should ever be shown, as he seems 
to think may occur, that for a given body its inertia—the ratio 
of force to acceleration produced—is not to be regarded as an 
absolute constant, then not only the poundal, but a good many 
more of our dynamical ideas will have to be thoroughly over- 
hauled. 
Furthermore, he cannot mean what he appears to say, that he 
really considers the weight of a body, its attraction by and for 
the earth, to be the most fundamental property of matter, though 
from the stress he lays on the importance of his system one 
might almost suppose that it is so, and, moreover, that it is the 
weight at London which possesses this distinction. If he means 
that he regards the gravitational field of force associated with 
every particle of matter (ether-stress, if you will) as the most 
fundamental property of matter, I understand him, while not 
quite agreeing with him. Still, he can found a mechanical 
system on that basis, free from the objections applying to his 
present system ; but it will have no 32°18, and I am afraid 
practical men will not receive it with gratitude. : 
As emphatically pointed out by Prof. Lodge, the interest of 
the question is pre-eminently educational. Prof. Perry agrees 
that to an expert, so far as his own personal work is concerned, 
the units he works in are generally of no great consequence. 
Such a one can use, say, the Birmingham wire-gauge or the 
Baumé hydrometer with much more facility than an ordinary 
person could use more rational devices. And so far as actual 
