found when, by the aid of the preceding principles, the values of c, Q and v, are known. Among the results which are thus obtained, we must notice that which relates to the complete dissociation of the products of combustion.

In this case, according to the values of c and v, (41) and (44), the formula reduces to

and, as the constants h and Kare independent of the nature of the substance, we are led to the following consequence: The force of an explosive substance when entirely dissociated, is proportional to its heat of combustion.

We have, also, h11.15, and K 2.443; inserting these values in (47), and putting p. 1, we have for the expression of the force in atmospheres,

This is evidently a limit superior to that actually reached.

15. Intermediate states-Equivalent combustions.-There is reason to suppose, as has already been stated, that the chemical state of the products at the instant of maximum tension is not generally that of complete dissociation; the actual state is less simple and varies with the conditions of combustion.

Among the different reactions which these conditions may cause, we note those which present the same initial and the same final states. To these reactions the following principle, laid down by Berthelot, in his thermo-chemical researches, under the name of the "principle of the calorific equivalence of chemical transformations," applies:

Having given a system of simple or compound bodies in a determined state; if this system undergoes any physical changes bringing it to a second state, the quantity of heat absorbed or given out depends solely upon the initial and final states of the system. It is the same, whatever may be the nature or sequence of the intermediate states.

Let us call, for brevity, those reactions which have the same initial and final states, calorifically equivalent, or simply equivalent reactions. Observing that:

1st. Equivalent reactions have the same heat of combustion Q;

2d. The specific heat of differing equivalent reactions is the same, since, according to the hypothesis of No. 3, it depends only upon the nature and proportions of the simple elements present in the reactions.

Thus the force varies only as the specific volume v,; and we have this consequence:

The force developed by the same explosive substance, in varying equivalent reactions or combustions, is proportional to the specific volume of the products formed at the instant of maximum tension.

By the different values of this element, variable with the state of dissociation of the products, may be explained the considerable variations of the force; even though chemical analysis of the final products and calorimetric determinations remain the same.

16. Theoretical calculation of the force of the final products when vaporized. The lower limit of the force of an explosive is obtained by the aid of the value of v., corresponding to the final state of the products, supposed entirely gasified, but not decomposed, at the instant of maximum tension.

Making the calculation for the substances whose specific volume has already been found (No. 12), and comparing them with those which are obtained by the formula for total dissociation, we have the following table:

The linear unit adopted being the meter, the table gives, in atmospheres, the pressure developed by a kilogram of the substance detonating in a cubic meter.

17. Approximate expression for the force of an explosive substance. We may obtain another expression for the force of an explosive substance. It is only approximate, but is extremely simple, and has the advantage of containing only quantities which may be determined by direct experiment, without its being necessary to have recourse to the determination by chemical analysis; which, as the foregoing considerations show, depends upon the theoretical and somewhat unreliable values of the specific volumes.

Take the general expression for the force,

From equation (14), which is between the heat and specific volume of a gas, we find

The ratio n is equal to 1.40 about for hydrogen, nitrogen, oxygen, carbonic oxide, etc. We have, consequently,

if these gases, or others approaching nearly the state of a perfect gas, were the only products of combustion. But, in a great many cases, these products comprise besides vapor of water and other even more complex vapors, which are liquefied or solidified after the cooling. For these compounds, n is less than 1.40, and approaches unity, in consequence of the progressive formation of the final state.

If, then, we call ɛ the weight of permanent gas due to the combustion of a kilogram of the explosive substance, the quantity n- I may, in a first approximation, be considered as a function of e, which, vanish

2

5

ing with, becomes for €1. We have then, nearly, n and consequently,

This formula shows that, similarly to a law of Berthelot, the force of explosive substances is nearly proportional to the product of the heat of combustion by the weight of the permanent gases produced by the explosion.

If the conditions of the explosion are such that the substance is entirely, or even partially, dissociated, so as to produce compound gases for which we would have n=1.40, as would be the case for carbonic oxide, we must take 1, and the force would be given by (50). The latter agrees, as may easily be shown, with the value (47) already obtained.

18. By means of experiments made at the central depot, has been determined for some substances. These together with the heats of combustion, and the corresponding forces, expressed in atmospheres, are tabulated below:

19. Relative force of the explosive substances. It is remarkable that the five powders should have about the same force, notwithstanding differences of fabrication. This result has been confirmed by experiment, which shows that the bursting charges of the five different powders for the same shell varies only 15 to 17 grams.

The mean of the forces of powders is 5.29. This corresponds to a force of 5290 atmospheres for a kilogram of powder, detonating in a liter, that is to say, in its own volume; these results are thus in accord with those made by Captain Noble upon powder exploded in its own volume. The pressure measured by him under these conditions by means of a gauge, was 37 tons on the square inch, or 5600 atmospheres, for the F. G. powder, and about 32 tons for the R. L. G. The following table shows the relative force of the different explosives:

Name of explosive.

Relative force.

I.

1.08

4.55

3.06

1.98

1.49

55 parts picrate of potassium and 45 of saltpetre,
Equal parts picrate and chlorate of potassium,

1.82

20. The figures of this table appear to agree sufficiently well with the real effects of explosives, fired in a manner to produce what, in the experiments undertaken with M. Roux, we have called explosions

of the second order, that is to say, explosions produced by any other agency than a strong fulminating primer.

For example, the relative force of gun-cotton is about equal to that found by the French commission on gun-cotton (3.20), derived from the comparison of the charges just necessary to burst a shell.

Other similar experiments confirm the result for nitro-glycerine. The mean charge of powder required to rupture shell was 16 grams. In the same shells, the effect of dynamite which contained 50 per cent. of nitro-glycerine, fired by a small quantity of powder, was such that I part of nitro-glycerine was equal to 2 parts of powder, under these circumstances. But, as Berthelot has remarked, the heat disengaged by firing dynamite is divided between the products of the explosion of the nitro-glycerine and the inert vehicle, which latter has about the same specific heat. It results that, in such dynamite, the temperature, and consequently the force, must be lowered one half. The force of pure nitro-glycerine should then be doubled, and be estimated at about 4. The difference between this value and that given in the table is not great. We will add that, for a mixture of picrate and nitrate of potassium, the bursting charge was found to be about 11 grams, which corresponds to a relative force of which differs little from the theoretical value, 1.49.

1.45;

21. On the relative force of some substances, when dissociated.-In applying formula (51) to nitro-glycerine and gun-cotton, we suppose that those of the products which are not permanent gases after the cooling, are vaporized, but not dissociated, at the instant of maximum tension. If they are, on the other hand, decomposed into gas so that the value of n is 1.40, we must use formula (50). In comparing, as before, the new values with the mean force of powder, we obtain the following relative forces:

Nitro-glycerine,
Gun-cotton,

5.68

3.58

In these new conditions, then, the force of gun-cotton becomes almost four times that of powder.

As to the figure for nitro-glycerine, it appears to have been almost reached in an experiment made by M. Roux, where about 2.7 grams of pure nitro-glycerine were fired by 1 gram of powder in an ordinary shell. In this experiment, 2.7 grams of nitro-glycerine equalled 15 grams of powder; whence the value of the relative force is 5.55, which differs little from its theoretical value, 5.68.

22. Explosions of the first order.-But, however great the power