DECEMBER 10, 1896] 
NATURE 
125 
taught, and I shall gain advancement in the profession to which 
I have reason to believe that I was ‘‘ heaven-born.” 
Prof. Perry seems in a parlous state, between ‘‘ friends’? who 
** worship a German soul-destroying fetish,” and foes, ‘‘ academic 
enemies,” who object to the use of the term centrifugal force ! 
Now, I wonder who they are, and why they object to this 
term. There was once a type of text-book wherein kinetic 
problems were treated statically, and the centrifugal force 
exerted by the revolving body was depicted in the diagram 
and reasoned about as if exerted zon the body ; does Prof. 
Perry count among his enemies those who fought against this 
misleading practice? Again, there appear to be other foes who 
will not let him use the pound-weight as a unit of force in peace ; 
but is he not a victim of some delusion? A pound-weight or an 
ounce-weight or a ton-weight are extremely handy force units for 
actual application, or for calculations dealing with heavy bodies 
at rest ; and an engineer is largely concerned with the statfts of 
heavy bodies, as Prof. Perry truly says, why then should he not 
use the appropriate unit? Again, when he is pumping water 
or lifting weights he finds the foot-pound or the kilogram-metre 
a handy conventional abbreviation for an energy unit: it must | 
be some churl who objects, not a physicist. Was the foot-pound 
repugnant to Joule? All that a physicist is anxious about in 
connection with units is that they shall be used accurately and 
intelligibly, he knows that they are mere agreed-upon convyen- 
tions, of which some are more generally convenient than others, 
and he tries to define them conveniently for the practical man’s 
use, and to retain visibly all essential factors ; but he is careful 
not to identify the number of units, or any other mere measure 
of the thing, with the thing itself. 
This last is a point on which some, I fear, are still not clear. 
Nobody makes this mistake with regard to matter. It can be 
filed and twisted and heated, &c., it never runs the risk of being 
thought of as a number of units. Energy is less tangible, and 
runs more risk of being so maltreated; while as to force, a 
few philosophers can now be found who teach that force is a 
mere measure of the time-rate of change of momentum. I 
wonder if they would say that to a man on the rack ! 
As to units, I have no objection on principle to hogsheads or 
kilderkins, but I should seriously object to a student who held 
that while a pound was a force, a kilogramme was a mass, and | 
at the same time was willing to believe that a kilogramme 
equalled 2°2 pounds. 
To identify weight and mass is barbarous, to denote their 
units by the same name is unwise, to lose sight of the 
dimensions of g, and treat it as merely equivalent to 32°18, is 
illiterate. The whole matter can be put in a nutshell by saying, 
w and g are both vectors, parallel vectors, and 7 is their (scalar) 
ratio, 
There are, in fact, three distinct things, all capable of being 
denoted by such a word as ‘‘ ton” in common parlance. There 
is the mass or quantity of material, which concerns us in dealing 
with markets ; there is the inertia or reaction to force, which is 
important when we are dealing with acceleration ; and there is 
the etherial stress, due to the neighbourhood of the earth, which 
<lrives the two pieces of matter together unless they are propped 
apart. 
The last-mentioned curious and ill-understood deportment of 
two bodies is interesting in itself, and appeals directly to the 
engineer whenever he has to increase the distance between the 
earth and another body ; it has, indeed, laid such hold of his 
imagination that he has begun to think it the most fundamental | 
property of matter, and is willing to identify it with the actual 
substance of the smaller of the two bodies : he is even willing to 
identify it with its inertia-reaction, especially after division by 
some arbitrary number suited to himself, his parish, and his 
work. 
May I tell Prof. Perry what is at the root of the perennial 
debate between engineers and teachers of mechanics ? 
It is the subject of acceleration. An engineer's bodies are 
nearly always either at rest or in uniform motion, their ac- 
celerative stages he is usually able to ignore. The portion of 
mechanics which serves his need is, therefore, simple enough, 
and he rebels against more. But the teacher perceives the 
treatment of acceleration to be the key to mechanics in its higher 
sense—viz. as an introduction to physics, and as the foundation 
science of the material universe. He emphasises the idea of 
inertia, therefore, and sets problems in the accelerative stages of 
motion, because he knows that there lurk the difficulties and 
there the soul of the science. He hopes that an engineering 
NO. 1415, VOL. 55 | 
student, in these days of a wider application of physics than 
was common half a century ago, may be willing to learn some- 
thing more than the mutilated fragment of science which serves 
for commercial purposes. Sometimes he hopes, but at present 
he hopes in vain, that the student’s own more immediate superiors 
will refrain from encouraging him in half-knowledge and casual 
omissions, and the testing of everything by immediate pecuniary 
results. He hopes that the Engineer, although very busy in his 
proper domain, may have a sympathetic faith in a larger train- 
ing, and not inadvertently snuff out any nascent clearness of ideas 
by ranging himself alongside our true and only natural foes, the 
powerful obstacles of ignorance, idleness, and prejudice. 
Vast improvements in school teaching are possible, and 
should be strenuously urged. Prof. Perry is now, I suppose, 
head of the Government teaching of mechanics in this country, 
and his educational views are no individual concern ; but let 
him discriminate. There is plenty of scope for his warning 
voice and vigorous sense of the need for contact with realities 
at every stage. Let him inveigh against wasting time over the fifth 
book of Euclid, for instance, (if any body now does) and other 
extravagantly refined conceptions too subtle for the majority of 
people who have so much to learn of which their teachers are 
ignorant, let him urge teachers to express common things easily 
and not only in a scholastic jargon misunderstanded of the 
people; but, maxzma debetur pueris reverentia, let him urge 
clearness of idea and accuracy of speech on all who deal with 
the junior student. These should not call different things by 
the same name; these should not be satisfied with lazy and 
incomplete specifications with essential factors omitted ; these 
should grasp the real and the essential and distinguish from the 
arbitrary and the conventional, emphasising the one and treating 
lightly the other, and not considering either themselves or their 
pupils heaven-born geniuses because unable to grasp fundamental 
principles. 
Above all I ask Prof. Perry to believe that the physicist 
means something solid when he asserts that formule need not 
| all be of the engineering pocket-book type, the type where the 
units must be stated before an equation is intelligible or useful. 
Such formule are in truth a mere mixture of arithmetic and 
convention, very useful in their place but not really applied 
mathematics at all. 
Misapprehension on this point is at the bottom of the need- 
less and hampering introduction of units by engineers into 
every equation ; and at the risk of being tiresome, I must once 
more illustrate the difference between an arithmetical formula 
of the engineering pocket-book type, and a real mathematical 
equation, by some simple example. The following may or may 
not be a sailor’s rule, but it is an approximately true and 
handy one :— 
Your height above the sea-level expressed in feet, if square- 
rooted and multiplied by 3, gives the distance of the visible 
horizon in miles. 
A handy rule I call it, and no more. Your ship’s captain 
who knows that alone is in the position of your engineering 
student who, whether taught at college at not, has been taught 
badly, and has not brains enough in himself to supply the 
deficiency. 
The equation, ot which the above rule is a convenient but 
specialised and mutilated version, is 2. RZ=d*. My readers 
must pardon the triviality of the illustration, and the fact that it 
is not accurate to the second order of minutice, because none of 
these things matter to my present purpose. The principle I am 
urging is illustrated well enough by the two points, (1) that the 
size of the earth, which was omitted from the rule, makes its 
appearance in the equation, and it is obviously a vital element in 
the problem ; (2) that the equation requires no specification of 
units, but is complete in itself, and is independent of 
every system of units that ever were devised; /% is not the 
number of feet, or of metres, or anything else, it is the actual 
height ; @ is not the number of miles or of inches to the horizon, 
but it is the distance itself; and similarly 2 R is the diameter of 
the earth, and not any numerical specification of that diameter. 
The thing, so far as it is true at all, is true from the bottom 
upwards and entirely true, number and dimensions and every- 
thing, with no factor omitted, or slurred over, or suppressed ; 
that, and not the C.G.S. or any other trivial convention, 1s 
what is meant by absolute measure. 2x uno disce onines. 
Using this trivial example as a type or fable, I say that the 
college-taught student who knew 2 R / = @?, or its equivalent 
Euc. III. 36, but could not apply his knowledge to estimate 
