54 
JUNE 30, 1923] 
NATURE 
887 

proposed for it from the time of Lanchester’s phugoid 
system down to the systems of Brodetsky and the 
present writer. These last systems reduce the study of 
the perfect aeroplane to the solution of a system of 
assumed and stated equations, in fact a problem in 
pure mathematics only. 
If the conditions necessary for steady motion (under 
forces in equilibrium) and inherent stability are satisfied, 
an aeroplane will tend to assume a state of steady 
motion provided that the initial conditions represent a 
sufficiently small displacement from the steady state. 
But under widely different initial conditions it may 
tend to assume an altogether different motion, and, for 
example, it may sooner or later lose headway or crash 
to the ground, pitching over and over. We are thus led 
to considerations of superstability, an inherently super- 
stable aeroplane being defined as one which, like a non- 
capsizing lifeboat, will tend to assume a state of steady 
motion whatever be the initial conditions of projec- 
tion ; failing that, to investigate the limits of super- 
stability ; in other words, the limiting initial conditions 
under which the machine tends towards instead of 
away from steady motion. It is clear that such an 
investigation will involve the search for periodic solu- 
tions of the equations of motion which, though difficult, 
should not be harder than many problems on which pure 
mathematicians have set their faces. In condition 
with lateral displacements a spiral gliding motion 
would represent one limit of superstability, but there 
are probably others which may or may not occur in 
practical applications. At present Dr. Brodetsky 
appears to be the only applied mathematician who 
has really made substantial advances tending in this 
direction. 
It seems rather probable that further developments 
will involve the solution of integral equations. 
Possible future applications to the location of air- 
craft are suggested by a paper by Dr. A. B. Wood and 
Capt. H. E. Brown on “ A Radio-acoustic Method of 
locating Positions at Sea,” read before the Physical 
Society on March 9g, and the discussion thereon, in 
which Capt. Fowler, Major Tucker, and others took part. 
In this method a wireless signal is made at the same 
instant that a charge is fired into the sea, and the times 
of arrival of both signals are recorded at land stations, 
thus determining the distance of the ships from them. 
The method is obviously applicable to the sound ranging 
of aircraft in commercial aviation, but, as Mr. Smith 
remarked in the discussion, the captain of a vessel 
would certainly need to make the observations himself, 
and, up to the present, experiments on detection of 
acoustic signals, and especially echoes of sound signals, 
by means of apparatus carried on aircraft, have not 
been so successful as could have been wished. It is to 
be hoped, however, that experimental work on this 
subject will be continued, as the means hitherto at our 
disposal for location of aircraft leave much to be 
desired, especially if cross-country flights are to be 
effected at any considerable distances from the main 
air routes. 
The possibilities of employing helium in airships are 
discussed by Capt. G. Arthur Crocco in the Alti dei 
Lincei, xxxii. (1) 2, 3. It is estimated that from the 
natural gas wells in the United States a supply of three 
million cubic metres per annum is obtainable, and 
NO. 2800, VOL. 111] 
taking twenty years as the life of a well, the cost works 
out at two dollars per cubic metre. This supply would 
not be sufficient to replenish the consumption of more 
than one airship in active continuous service on long- 
distance traffic under existing conditions, and Crocco 
considers in detail the different causes of loss and the 
means of reducing them within practicable limits. The 
author separates the consumption of gas into three 
categories, which he describes as “consumption of 
navigation,” “‘ osmotic diffusion,” and “ washing of the 
gas ” necessitated by loss of purity, and due to endos- 
motic entry of air into the envelope accompanying the 
exosmotic diffusion of the helium. The annual losses 
of gas due to these three causes are in the ratio of 100, 
10, 1, and it is estimated that if the first could be 
eliminated the annual loss of gas by an airship could be 
reduced to 20 per cent. of the total volume, and that a 
large fleet of commercial airships could be maintained 
in continuous working at a reasonable cost. 
The “consumption of navigation” represents the 
amount of gas let out to compensate for the loss of 
weight of the fuel, and, as pointed out, this assumes 
serious dimensions in long-distance journeys where 
excessive buoyancy cannot be overcome by lowering the 
elevators. The necessity for this discharge of gas can 
be obviated in two ways, namely, by condensing the 
water in the products of combustion and by “ thermic 
sustentation,” and in his second paper Crocco examines 
the former method. It is estimated that 1000 grams 
of fuel contain 150 grams of hydrogen, which, combining 
with the oxygen of the air, give 1350 grams of water, so 
that by condensing this the gain of oxygen can be 
made to compensate for losses in other directions. The 
necessary superpressure to effect this condensation can 
be secured by means either of causing a back pressure 
in the motor or by separate compression. The paper 
contains formulz and calculations of the amount of the 
superpressure required to effect the necessary conden- 
‘sation, and this of course is a function of the degree of 
saturation of the atmosphere. It is found that this 
only reaches a serious amount in the case of very hot 
and dry weather, such as in average climates only 
occurs on a few days in the year. Remembering that 
only 1000 grams out of 1350 have to be condensed, the 
author finds that the loss of power required for the 
purpose is not sufficient to interfere with the practical 
application of the method when the effects occurring 
exceptionally are reduced to annual percentages. 
In a paper communicated through Prof. Levi Civita 
to the Alti det Lincei, xxxi. (2) 1-2, Dr. E. Pistolesi 
employs moving axes to formulate the differential 
equations of motion of a fluid in the field of velocity 
produced by a screw propeller. In this way the prob- 
lem is reduced to one of steady motion. The method 
is closely similar to one adopted many years ago in 
connexion with problems on the small oscillations of 
gravitating rotating fluids, with the difference that 
in applications of approximate methods the velocity 
components relative to the airscrew will not be small, 
but in certain cases it may be possible to regard as 
small the components relative to fixed axes set up by 
the motion of the screw. ) a 
Another hydrodynamical line of investigation which 
has recently come into prominence in connexion with 
the effects of skin friction on the resistances of aircraft 
