Marcu 24, 1923] 
com) to the various melanic sports which occur 
in other species of mammal, such as the black leopard. 
I have seen a black individual among a litter of the 
common Canadian squirrel. 
On the other hand, a melanic local race implies a 
new regulatory balance. As an example of the rela- 
tion of racial character to the environment, I may 
mention the common red grouse of Scotland, supposed 
to be the only species of bird peculiar to Britain. In 
Europe there is the allied species of willow grouse, 
differing in having the tips of the primaries white 
and in turning white in winter. When a Scotch 
landowner imported the willow grouse he found that 
in two or three generations they became indistinguish- 
able from the red grouse ; and when red grouse were 
introduced into Norway, they reverted in a few 
generations to a form indistinguishable from the 
willow grouse. E. W. MacBripe. 
Zoological Department, 
Imperial College of Science, 
March 5. 

Definitions and Laws of Motion in the 
*« Principia.’’ 
In his recent interesting article (NATURE, February 
17) on the Definitions and Laws of Motion in the 
“ Principia,”’ Sir George Greenhill reopens a very old 
discussion (NATURE, vol. 39, 1888-9). It might have 
been expected that the lapse of one-third of a century 
would have been sufficient for reconciliation of the 
engineer and the physicist. Every scientifically 
trained engineer knows, as Sir George Greenhill 
knows, that no confusion is introduced by the employ- 
ment of a given multiplier or divisor in every term of 
an equation. 
The only new feature now given in the mathematical 
discussion lies in his equation (1), 
Wu/g= Fz, 
in which it is insisted that the g as a divisor must be 
attached to the v and not to the W. But, in the 
weight problem, this merely makes the equation an 
identity with W=F ; and, if we introduce F as a non- 
gravitational force, say by the use of a spring-balance, 
or a column of compressed air, etc., still giving ¢ its 
old value, we find a different average F, and therefore 
a different W, at different localities. It is this local 
variation of W which reveals to the physicist an 
absence of that aspect of invariance, the existence of 
which he, as a scientific man, feels compelled to search 
for. And his search is not in vain ; for he finds that, 
with v, ¢, and average or actual F (non-gravitational) 
all constant, W is proportional to g, and therefore 
the attachment of g to W is justified, in his belief, by 
Nature. In fact, he has come into contact with the 
materiae vis insita. 
I have never known any student of engineering 
who, having first had a normal training in physics, 
felt compelled, in his engineering studies, to alter his 
ideas. e knows that his “ factor of safety ’’ in 
constructional details is large enough to cover such 
variations of g as he meets with in practice. The real 
quarrel (if it still exists) is only one regarding the use 
of the word “ pound,”’ and the context in the engineér’s 
or the pee statement usually prevents confusion, 
even if it were not the case, as I have always found it 
to be, that the student of engineering is quite willing 
to speak, when clearness requires it, of the mass of a 
pound and the weight of a pound. 
I do not agree with Sir George Greenhill that Mach 
was right in saying that Newton’s Def. I. is only a 
definition of density. I regard it as presuming that 
- the meaning of density is known, so that the definition 
is really one of the guantitas materiae, to which the 
materiae vis insita or inertia massae is proportional. 
No. 2786, voL. 111] 
NATURE 
395 
It then implies the physical law that inertia is inde- 
pendent of the form of aggregation, and depends, for 
a specific material, only on the extent of the aggrega- 
tion. Nor do I agree with him that Newton’s use of 
many different words for the name of the same thing 
was undesirable. We must remember that Newton 
was the pioneer, introducing new ideas, and requiring 
therefore to use every form of phraseology or nomen- 
clature that might help to make them understandable. 
Sir George Greenhill disagrees with Tait, and credits 
him with the honour of introducing innovations. Now 
Tait was a modest man, and a loyalist towards 
Newton. He gives the honour to Newton, whose 
interpreter only he was. The further statements on 
this point made in Sir George Greenhill’s second 
article do not alter the position. 
Tait’s wise words (/.c.) of a third of a century ago 
are well worth attending to to-day, apart from 
electrons. He said . mass is the personal 
property of a body, one of the invariable things in 
nature :—and not an accidental property dependent, 
for its amount and even its very existence, on the 
momentary surroundings. The letter M has hitherto 
been used by Newtonians in this sense. If anyone 
has since attached to it another and different sense, he 
is responsible for the consequent confusion. Would 
it not be well if Prof. Greenhill, and the School to 
which he has attached himself, would kindly leave to 
Newtonians their M, as defined for them by their 
Master; and (with severely logical consistency) turn 
it upside down (thus, W) when they wish to embody 
their own revolutionary definition ? No Newtonian 
will refuse to recognise Wv?/2g as a correct expression 
for so much energy :—though he will probably think 
it both clumsy and complex, and will prefer to write 
as usual his Mv?/2.” W. PEDDIE. 
University College, Dundee. 

In his article under the above title in Nature of 
February 17, Sir George Greenhill expresses the 
opinion that it would be worth while to examine the 
previous state of the theory of dynamics to see what 
laws were current before the statement as given by 
Newton. The evidence of Newton on this point is 
often overlooked, though it is noted by Tait. In the 
scholium to Corollary VI. on the Third Law of Motion, 
Newton freely acknowledges the work of his pre- 
clecessors. 
““ Hactenus principia tradidi a mathematicis recepta 
et experientia multiplici confirmata. Per leges duas 
primas et corollaria duo prima Galilaeus invenit 
descensum gravium esse in duplicata ratione temporis 
et motum projectilium fieri in parabola; conspirante 
experientia, nisi quatenus motus illi per aeris resisten- 
tiam aliquantulum retardantur.” 
In these days of the Fletcher trolley and Atwood’s 
machine it would be interesting to know what were 
the experiments Newton had in mind as confirming 
dynamical principles. Mach has pointed out the great 
achievement of Galileo in arriving at the First Law of 
Motion, but he does not assign him credit for a 
knowledge of the Second Law. It is quite apparent 
from the above quotation that in the time of Newton 
there existed a tradition that Galileo’s teaching of 
dynamics embodied the Second Law as enunciated in 
the “‘ Principia.’’ This is borne out by Lagrange in his 
introduction to the second part of his ‘‘ Mécanique 
Analytique,”’ in which he states that the Second 
Law is contained in the note added by Viviani at the 
suggestion of Galileo to the ‘‘ Dialogues of Two New 
Sciences ’’ (Eng. Trans. Crew and De Salvio, p. 184), de- 
ducing that the speeds falling down planes of different 
inclinations but of the same height are equal, In 
this note it is assumed as self-evident that the 
