SUPERIORITY IN AN AIR-SHIP—RENARD. 151 
strength in a large balloon than a small one, which will increase the 
weight of a square meter of the envelope and accordingly result in 
a double cause of increase in the total weight. This will also be 
true with regard to the suspension cords and all the material con- 
stituting the dead weight. 
It can be demonstrated that in balloons of different volumes this 
dead weight increases nearly as the fourth power of the linear 
dimensions; that is, more rapidly than the volume. Thusin a balloon 
of twice the volume the dead weight will not be multiplied by 2 
but by 2.52, and with triple the volume the dead weight will be 
multiplied not by 3 but by 4.33 and so on. In spite of this unfavor- 
able circumstance, however, we may say in the limits of practice, 
that the carrying capacity increases with the volume. It increases 
also with the lightening of the motors, for if the motor is lighter for 
a given power the economy in weight so realized can be used to 
increase the weight carried; in general, however, it is preferred to 
profit by this hghtening by increasing the motive power and conse- 
quently the speed. 
In a dirigible the total ascensional force is the product of the vol- 
ume of the balloon by the lifting power of a cubic meter of gas. 
This latter quantity depends entirely on the specific gravity of the air 
and of the gas employed. As long as no gas lighter than hydrogen 
can be found there can be no hope of a change in the present condi- 
tions, and even if such a gas should be discovered, we should always 
be limited by the weight of a cubic meter of air, 1.293 kilograms. 
This figure represents the extreme limit of weight that a cubic meter 
of the gas could lift, if it weighed nothing. However, a cubic meter 
of pure hydrogen weighs only 0.090 kilogram; a cubic meter of this 
gas therefore raises a weight of 1.203 kilograms, and even if there 
existed a gas of zero density only 90 grams per cubic meter would 
be gained over the lifting power of hydrogen. 
Consequently, it is true at the present day and always will be, 
that the total lifting power of a balloon can be increased only by 
an enlargement of its volume. 
In an apparatus heavier than air this total ascensional force is 
again equal to the product of two factors; in this case, however, it is 
the surface of the sustaining planes, and the supporting power per 
square meter. ‘To increase this total ascensional force it thus becomes 
nece.sary to increase one or the other of these factors. 
Theoretically, the dimensions of the sustaining planes can be in- 
creased, but in practice it is difficult, for these surfaces become much 
heavier as they increase in size and thus absorb a large part of the 
increase of ascensional power attained thereby. If this is carried 
still further the weight of the sustaining surfaces can be increased 
to such an extent that all the benefit of the increase in size is lost, 
45745°—sm 1909——11 
