176 
NATURE 
[Dec. 29, 1870 

special balloon to allow for this, but the lower part of the balloon 
is left unfilled. 
The Géant had a special balloon for this purpose attached to 
the bottom of the large one by a kind of short connecting tube 
of a very large diameter, and this balloon was called the comfpen- 
sator, The arrangement can be seen by the engravings showing 
the Géant in aerial travels, 
If we suppose that we have at our disposal a balloon of india- 
rubber susceptible of any distension, we are in a position to assimi- 
late the motion of our aérostat to the elevation of an Atwood’s 
Machine moving upwards with a certain moving weight, without 
any other friction than that of the air. All the calculations and 
formula worked for that philosophical instrument can be used. 
=the weight of the air replaced; 4 =the weight of the 
a—b will be the motive 
a 
balloon including gas and everything ; 
power; the motion will take place according to the rule for 
accelerating powers ina medivm where the pressure is diminishing, 
as is the case with the atmosphere when the balloon is ascend- 
ing. If we pay no attention to the friction on the air, which is very 
small indeed when motion is slow, we have anacceleration of motion 
varying as ¢, and a height obtained varying as 7%, as is well known. 
If g’ is the new motive power and g the motive power of the 
A a A 4 a—b_ a—déb 
ordinary specific gravity, then g'= ¢ x —— ; 
a 

remaining 
constant under the assumption we have given. 
The best way to realise this assumption is to suppose that the 
balloon is partially empty when leaving the surface of the earth, 
and the assumption holds good as long as the balloon is not filled 
up by dilatation. The time taken by the dilatation to fill up the 
space allowed to it, regulates the level where the balloon can 
ascend without losing any of its motive power. This friction 
must be considerable in cases where the balloon is to be sent to 
a great distance from the earth. The chamber of dilatation must 
be chosen in proportion to that distance. At all events it must 
be calculated thus: 7 being the radius of the sphere = aR is the 
3 
maximum volume which the gas is able to take without escaping 
into the atmosphere, C being the weight of gas and A its 
gravity for each cubic metre ( Angas 
7 A 
cubic metres which can be afforded for dilatation, Sy) Hp) 
being the actual pressure on the earth. The pressure can be 
C 
diminishel in the proportion 4 
is the number of 
without the gas beginning to 
4 R38 
3 
If we call //, the altitude where this escape is to begin, 
C 
we can write the equation //,=//, A 
4nk3 
value of the corresponding altitude, it is necessary to look at 
the empirical tables inserted in the Annuaire du Bureau des 
Longitudes of each year, and calculated for reckoning the altitude 
from actual barometric pressure, These tables were calculated by 
M. Mathieu on the assumption of the truthfulness of Laplace’s 
equations given in his A/dcanigue céleste ; but I suspect_these 
assumptions are not sound, and may possibly mislead French 
aéronauts, while Prussians are watching them below ready to 
shell their balloon if it comes within range. But having instituted 
no direct measures for ascertaining the value of this law, aéronauts 
are obliged to make use of it. The calculations of M. Dupuy 
de Lome for carrying his intended balloon out of range suppose 
the truthfulness of the numbers of the Bureau des Longitudes, 
If in doing so aéronauts are not sure of escaping hostile bullets, 
they can at all events get rid of every analytical obstruction, 
which is certainly something. 
When the escape begins, the motive power is not destroyed 
at once. It certainly diminishes at a very quick rate if the 
appendix is wide enough to give free issue to the gas, and the 
vertical motion is also rapid. If not there is some danger 
of explosion, as can easily be imagined. Generally aéronauts 
are very anxious to get rid of this danger, which can be 
done yery easily by opening the escape valve, But this 
escape, 
To ascertain the actual | 

operation involves the aéronaut in a ‘‘sea of troubles,” as the 
valve for discharging the gas is rendered gas-tight only by the 
application of a proper plaster. The only way of dealing 
rationally with that excess of gas is to have a proper vertical 
motion when the discharge begins. That condition is very 
easy to obtain if you start with a very small ascensional power 
indeed. 
Meta j : 
In the fraction —— is very small, and moreover if the fraction 
a 
E 
A is large enough, you can conduct your balloon very 
tri 
safely at any distance if you do not meet with dark clouds, 
or burning sun. You can get rid very easily of these conditions 
by disposing cleverly of your ballast, as will be very easily 
understood by everybody after some explanation, There is 
however a circumstance which is very annoying in our military 
ascents, and on which it may not be useless to say a few words : 
the necessity of going at a certain level before reaching the 
meridian of the enemy’s lines. The aéronaut is therefore obliged 
to know that distance and the quickness of the motion of the 
; URL : : 
wind, so that the fraction— gives the number of minutes at his 
disposal to reach the level required above that dangerous 
meridian. 7 = medium velocity of the wind, as obtained 
by balloons sent free into the air, = elevation which 
the enemy’s bullets cannot reach, I suppose it to be 6000 
yards. Having no proper experiments at my disposal, I beg 
leave to make that gratuitous assumption. M. Dupuy de Lome, 
in his contribution, speaks only of 3000 metres, but Krupp’s 
cannon was not in operation when he was writing. Z=distance 
of enemy’s lines from the workshop. It is of great importance 
to increase that distance as far as possible, and I advised the 
Government to take two starting stations, one from the northern 
bank to be used when the wind was blowing southerly, and one 
from the southern when the wind was blowing northerly, so that 
in every case aéronauts might cross the whole of our city. But 
the suggestion was disregarded. The solution adopted was to 
start in the night time! It is a singular mode, very unscientific, 
to solve an analytical problem by the sending of the aéronauts 
either to the great ocean to be drowned, or to Norway to be 
frozen. The subject is far from being exhausted, as to the re- 
bounding of the balloon according to the law of oscillatory 
motions. But fearing to extend my remarks to a length beyond the 
patience of my readers, I beg leave to end my contribution at 
this point, thanking the editor of NaTuRE for the hospitality 
exhibited towards a French aéronaut, and hoping to be more 
fully acquainted with the English scientific public on some future 
occasion. W. DE FONVIELLE 


SOCIETIES AND ACADEMIES 
LONDON 
Royal Society, Dec. 22.—‘‘On the Constitution of the Solid 
Crust of the Earth.” By the Ven. Archdeacon Pratt, M.A., 
F.R.S. In this paper the author applies the data furnished by 
the pendulum-observations recently made in India, to test the 
truth of the following hypothesis regarding the Constitution of 
the Earth’s Crust, which he propounded in 1864, viz. that the 
variety we see in the elevation and depression of the earth’s 
surface in mountains and plains and ocean-beds has arisen from 
the mass haying contracted unequally in becoming solid from a 
fluid state ; and that below the sea-level, under mountains and 
plains, there is a deficiency of matter, approximately equal in 
amount to the mass above the sea-level ; and that below ocean- 
beds there is an excess of matter approximately equal to the 
deficiency in the ocean when compared with rock; so that the 
amount of matter in any vertical column drawn from the surface 
to a level surface below the crust is now, and ever has been, 
approximately the same in every part of the earth. In 
order to make this hypothesis the subject of calculation, the 
author takes the case of the attenuation of matter in the 
crust below mountains and plains, and the excess of matter 
below ocean-beds, to be w/orm, to a depth m times the height 
above the sea-level or the depth of the ocean, as the case may 
be. The results are shown in the following Table, in which 
the numbers are the last figures in the ratio of the differences 
