LAND AND WATER 
February lo, 1916. 
some particular duty needs to bu uf a definite mininuun 
weight, appropriate to the load it may have to bear. 
Thus if for some purpose it is deemed that a giant bomb, 
weighing say one ton, is necessary, the aeroplane to carry 
it must weigh in the region of four tons. To exceptional 
cases such as this the present discussion does not of 
course apply. 
In all cases where no such condition exists there is 
one very strong argument in favour of employing units 
as small as conveniently possible in great numerical 
strength. This reason is tliat of fire concentration. In 
my " Aircraft in Warfare " I have shown that this is 
determined by a law which I have termed the " N* " Law ; 
this law, which rests ultimately on mathematical de- 
monstration, but which is independently supported 
(quantitatively) by an analysis of Nelson's dispositions 
prior to tlic battle of Trafalgar, informs us that if a fleet, 
m the present application our air fleet, meets an enemy 
fleet in battle, its fighting strength or value is propor- 
tional to the square of its number of units, and directly 
i:)roportional to the unit \'alue or power. 
Relative Strengths. 
In the simplest case if the units of both fleets are'of the 
same value, the relative strengths of two opposed fleets is 
proportional to the squares of their numbers respectively ; 
thus a fleet 50 strong could meet and destroy a fleet of 40 
and the residue could meet ua equal terms a fleet jo strong, 
because so''' ^ 30'' plus 40-. 
In practice the chances would be very much in 
favour of the single fleet of 50, for, flesh and blood being 
what it is, some remnant of the first fleet to be engaged 
would assinedly quit the scene when it becomes evident 
that the alternative is anihilation. 
In the case of machines of different individual 
fighting value, the advantage of seeking strength by 
number rather than by individually powerful units 
becomes immediately demonstrable. Thus let the one 
belligerent be assumed to place his reliince on machines 
of great individual gun power, and build a fleet of 
" battle planes " mounting three machine guns apiece ; 
let the enemy on the other hand send into action a fleet 
of the same tonnage of single gun machines — we may 
fairly assume of three times the numerical strength — thus 
if the numerical strength of the first fleet be .m, by the 
N-square law that of the second will be 3«, the fighting 
value of the first fleet wfll therefore be «- by 3 and that 
of the second will be (3») "^ by i = 9?t- or three times the 
value of the other. That is to say for a given expenditure 
on the creation of a fleet, and for the same number of 
men and guns, the policy of the small one-man machine 
gives a superiority over the large three man machine 
in the ratio of three to one in effective fighting strength, 
an advantage which can only be described as overwhelm- 
ing. 
It is always to be admitted that there is the personal 
factor which cannot be taken into account by any mathe- 
matical comparison. Also there are such questions as 
the direction of light and the other unforeseen conditions 
which in any actual engagement contribute to a potent 
degree to the ifltimate result. All and any of these, 
however, are as likely to favour one belligerent as the other 
and the arithmetical computation of relative strength as 
a generalisation is in no wise invalidated by these con- 
siderations. 
The N-Square Law. 
It is not without interest to follow out the working of 
the N-square law in detail in the example above given. 
Let it be first assumed that the large machine offers as 
good a target, but no better than the small machine. 
Now we will suppose one large machine which we will call 
the Battle Plane with its three guns to be attacked by 
three of the single-man craft of the enemy, whicii we 
wiUcall Fokkers, to fix our ideas; let it be supposed tliat 
each of the three guns of the Battle Plane are dirc'clcd at 
one of the Fokkers, then, under the return fire of one of 
the Fokkers the Battle Plane will be hit just as often as 
it itself " gets one home," and if \vc count only hits which 
are deemed mortal, the Battle Plane will be mortally 
hit three times over (once by each of its assailants) whilst 
each of the said assailants are hit once each. Hence where 
large numbers are concerned a given onnage of sin;^le gun 
machines would destroy three successive fleets of equal 
tonnage of three gun machines before its own power is 
completely broken.* 
Now as to the assumption. The actual target pre- 
sented by the three gun machine is considerably greater 
than the one gun machine ; this, so far is it a vulnerable 
target in respect of which one hit is mortal, is stifl further 
against the three gun type. In this category we may in- 
clude engine, petrol tank, and such- like. The three 
gunners, although presenting three times the vulnerable 
target of one, will commonly require three hits for their 
destruction, and this may be taken as neutralising the 
larger target they present since with equally good gunnery 
they will coflectively receive three hits to one given. 
Thus the net result is to place the three gun machine at 
a disadvantage beyond that which the N-square law 
indicates. 
As a mode of defence against counter aircraft artillery 
also the importance of numerical strength is paramount, 
though perhaps not so decisive as in aerial combat. Thus 
one well directed shell of large calibre is sufficient to put 
an end to an aeroplane large or small, in fact the large 
machine presenting a greater vulnerable target is at a 
disadvantage. The destruction of a fleet of raiders, 
therefore is the more difilcult as the number of aeroplanes 
is the greater. Conversely llu' injury inflicted in " loss 
of tonnage " per unit time will be inversely as the number 
of machines employed. From this j)oint of view there- 
fore the smaller the individual machines the more effi- 
ciently and economically will their duties hr. jxTlormed. 
In the present article the case has been fully presented 
for numerical strength as against the individually powerful 
unit. In a second article the arguments will be given 
on the other side, and, so far as it is possible, conclusions 
will be formulated as to the general lines which in my 
opinion should be followed in our constructive pro- 
gramme. 
Our Pre-ent State of Knowledge. 
I will say, however, here that in my opinion there are 
no satisfactory arguments which can be fornmlatedin the 
present state of knowledge in support of the large machine 
for conducting aerial w'arfare, the " Battle Plane " as if 
has been popularly termed. I am fairly convinced that 
in any case the numerically strong fleet of one-man one- 
gun macliines represents the best line of policy both for 
the time being and for the more immediate futmx. 
A dav may come when the size of air fleets will be so 
unwieldy that the only possibility of increasing fighting 
strength will be by augumentation of the power of the 
unit, but this is so far distant that it cannot legitimately 
be allowed to influence our present policy. Above 
everything in the fighting machine for defensive purposes, 
whether for anihilating the reconnaissance service of the 
enemy, or for defeating his aerial raids, the big three or 
four-man aeroplane is radically out of jjlace. Such 
heavy type will never be able to give a good account of 
itself in comparison with an equal tonnage of the smaller 
machine. 
We have heard in the daily press much talk about 
the German " Fokker," the supposed wonderful qualities 
of which machine have been lavishly praised. It is not 
the technical excellence of the Fokker which we have to 
fear or watch, it is — if I may say so— the Fokker policy. 
In ^foll Davis, bv Bernard Capss (Gco-ge Allen and Unwin) 
f)S., a pretty conTJcly of Kestoratiou days, more depends 
on manner than on nuitter ; the author has evidently a horror 
of solecisms, wliicli, i)erliaps, is the reason why he spares us 
the entry of Charles himself, although the scene is mainly 
at Whitehall, and stops short at tlie Duke of York as a figure 
in the play. Moll Davis, gay and heartless, is set by George ' 
Hamilton to complete the estrangement between Lord 
Cliesterlield and his wife, (leorgC having designs on the wife 
after the cu.stom of the times. Since Cliesterlield and his lady 
are not on speaking terms, Moll enters their house as guest, 
letting each suppose that the x)tlier had invited her ; the 
result is comedy, never degenerating to farce, but with many 
wittv touches ititersi)ersed among the incidents of the story. 
The author has been cariful to avoid exaggeration of the 
manners of the period, and his book serves to pass a pleasant 
hour or two— as a well-told story ought. 
• A tarcful c.xiimination of the argument as here given shows that 
it is not exact ; it imis,t be taken as a jjopulariscd version of that 
wliicli is proved more rigidly in my ' .Aircraft in Warfare " (CouiiaWe. 
Loudou) in whicli many examples and appUcatious are given. 
