the same process as that which gave us the maximum temperature to which the current of hot gas brought the caloriineter. We made vapour pass through the tube, D E, (fig. 5) without any current of gas, and observed the rate at which the calorimeter heated. We stopped the experiment when the increase of heat in the calorimeter was become exceedingly slow. Then we raised the heat of the calorimeter artificially about 2 degrees, thus raising it above the maximum point, and continued the experiment till it had almost ceased to sink. We took the mean between these two terms as the effect produced by the vapour tube. This experiment was made twice with great care. In the first experiment the ascending series conducted us to 51.8° (the air being at 46-778°), and the descending series to 53'042° (the air being at 46·634°). If we take the mean between these two numbers, we get 5.58° for the maximum effect produced by the vapour tube on the calorimeter. second experiment gave us exactly the same number.

The

It may be asked, if the steam tube will communicate as much heat to the calorimeter when the steam of gas is passing as when it is absent. It is easy to see that it will not, since the temperature of the tube, D E, remaining the same, the calorimeter is hotter in the one case than in the other; and it is a well-known principle, that when one body communicates heat to another, the quantity communicated is the more the greater the difference of temperature

between the two bodies.

It is very difficult in the present case to determine how much the heat communicated by the steam tube will be diminished by the increase of temperature of the calorimeter. Fortunately, the quantity is so small that it is of little importance. We may suppose, without risking any error of importance, that the quantity of heat yielded is as the difference between the temperature of the calorimeter and of the tube, D E. This difference being 144° in the experiments which we have related, and producing an elevation of temperature amounting to 5.58° in the calorimeter, this elevation ought to be 4.5°, when the difference between the temperature of the steam tube, D E, and of the calorimeter, is only 129.6°, as was the case in the experiments which we made on the different gases,

NOTE 2d.

We determined in the following manner at what degree the current of hot air maintained the calorimeter stationary.

In consequence of data furnished by a preliminary experiment, we raised the temperature of the calorimeter to 76 359°. The thermometer, indicating the temperature of the air of the room, stood at 44 83°.

The calorimeter was then wiped with care, that no unknown cause might accelerate its cooling, and the current of hot gas was made to pass through it. The experiment was continued till the thermometer of the calorimeter, observed every ten minutes, almost ceased to rise. The observations were as follows:

From this table we see that the current of hot air was capable of heating the calorimeter only about 0017° the last ten minutes. The calorimeter was then raised to the temperature of 78.073°. The current of hot air was continued, and the thermometer observed every ten minutes. The results were as follows::

The calorimeter during the last ten minutes sunk only 0.02°. We obtain the maximum effect by taking the mean of the results furnished by these two sets of observations.

The result is, that the current of hot atmospherical air rendered the calorimeter stationary at the temperature of 77.333°, that of the ambient air being 45.172°.

NOTE 3d.

We may compare the cooling of a hot body placed in air whose temperature is constant to the motion of a body, M, which goes in a direct line towards a fixed point, D, with a velocity always pro

M

C

D

portional to the space, M D, which remains to be passed over. The fixed point, D, is the temperature of the surrounding air, and the space, M D, is the variable excess of the temperature of the hot body above that of the surrounding air. Hence we will apply to the motion of such a body the reasoning on which is founded the formula cited in the paper.

This formula is an expression for the space, S, which the body setting out from C, the distance of which from D is known, will pass over in the time, T; supposing it to preserve during the whole motion the initial velocity, V, which it had in C. Nothing would be simpler than the determination of this space, if V were known for

we should have SV T: but it is not given immediately by experiment. We must therefore endeavour to determine it by joining, to the data which we have already, that which we obtain by the knowledge of the space which the body setting out from the point, C, passes over with a variable velocity, v, which at first is equal to V. This space is given us by experiment. We shall express it by A. B: A being the known distance, C D, and B the that space remains to be passed over at the end of the time, T. For the greater convenience, let us suppose for a moment that it is the space A B that we have to determine, B being unknown, and V being known. Its expression will be d (Ax), or — dx = dt, x being the general expression of the space which remains to be passed over each instant, that of the velocity at the same time, and t that of the time elapsed. But since at each instant the velocity is proportional to the space that remains to be passed over, we may make v=kx, k being a constant quantity which may be determined by making k A = V. We shall have then - d x =

dx

kxdt, and - kdt. Integrating the sides of this equation, we obtain log. hyp. x + C = kt. To determine the constant quantity, C, make x = A, which suppose the time, t, to be nothing. We get - log. A + C = o, and C = log. hyp. A. Substituting this value of C in the preceding equation, we shall have log. + log. A, or log. x

A

A

= kt,

ekt (e being the

=

ekt

A, and A

number whose hyperbolic logarithm is unity ;) x

Α

Applying this equation to the time given, T, ≈

A

will become B, and we shall have B = and A

A

ekt

Let us suppose, now, that B and A B are given by experi

ment, and that V, or, which comes to the same thing, k, is unknown. To discover its value, it is sufficient to make use of the equation, which on the preceding hypothesis gave the value of A — B, supposing B known; or still more simply to employ the equation log. kt, to which we came by putting for x and t their values B

= A log. We have seen above that S was the space passed over by the body with a uniform velocity, V, during the time, T. To apply this formula to the cooling of a hot body, we must denote by A the excess of its temperature above that of the air at the beginning of the experiment; and by B, the same excess at the end of the time, T.

ARTICLE VII.

Essay on the Cause of Chemical Proportions, and on some Circumstances relating to them: together with a short and easy Method of expressing them. By Jacob Berzelius, M.D. F.R. S. Professor of Chemistry at Stockholm.

I. On the Relation between Berthollet's Theory of Affinities and the Laws of Chemical Proportions.

SOME chemists have affirmed that the existence of chemical proportions is contrary to the principles of the theory of affinities with which the illustrious Berthollet has enriched chemistry. On that account they have refused to adopt it. But if, on the one hand, the knowledge of chemical proportions, which we at present possess, does not accord with all the applications made by Berthollet, and by other chemists, of his theory; on the other hand, it is incontestable, that these principles have never been refuted, but are more and more confirmed, the more they are examined. Chemists, before Berthollet, were misled by considering the weakest of the two chemical forces, or affinities, opposing each other as null. Berthollet pointed out that error, and showed the effect which the chemical mass produces.

Berthollet himself, far from denying the possibility of chemical proportions, has contributed a good deal to prove their existence, although the numbers resulting from his analytical experiments be not always very accurate. He has proved that when the elements cease to oppose each other, in consequence of their chemical mass, their combinations always take place in definite and invariable proportions. The doubts entertained by some chemists of the truth of Berthollet's principles originate certainly from the conduct of some of his zealous supporters, who have extended his doctrine to cases to which it does not apply, and have maintained the existence of indefinite combinations even when the action of the chemical mass cannot interfere. opinion no doubt occasioned the fine experiments of Proust, whose object was to show that, when the metallic oxides absorb more oxygen, they pass at once from one degree of oxidation to another, without passing through the intermediate steps; and that what had been considered as an intermediate step was merely a mixture of a perfect oxide with an imperfect one.

This

The effects of the chemical mass are produced when, for example, three bodies, A, B, and C, exist together in the same solution; that is to say, in mutual contact; and when both A and B have an affinity for C, and endeavour to form the new combinations, A C and B C, which still remain in solution, and of course preserve their contact with the surplus of A and

B, which exists in the solution. If it has the strongest affinities, it combines with a greater proportion of C than B does: but though the attractions between A and C be greater than those between B and C, A is not able to draw to itself the whole of C, to the exclusion of B. In such a case, the portion of C combined with A to that combined with B will be determined by the strength of the affinity, and by the proportion of each present in the solution. Any person may satisfy himself of the reality of this division of C, by pouring concentrated muriatic acid into a solution of sulphate of copper. The solution, which was formerly blue, acquires a green colour by the addition of the muriatic acid (for muriate of copper is green); and this colour becomes stronger the more muriatic acid is added. The cause of this phenomenon is, that the affinity of the muriatic acid, though the weaker, still continues to act, and acts with more intensity the greater the quantity of that acid present. If, for example, 100 parts of sulphuric acid, and 100 parts of muriatic acid, divide 100 parts of oxide of copper between them, so that the sulphuric acid takes 80 parts, and the muriatic 20 parts, it is clear that the force with which 100 of sulphuric acid remain in combination with 80 of oxide is equal to the force with which 100 muriatic acid remain in combination with 20 of oxide; that is to say, that the two opposite forces are in equilibrio. If any one of these combinations should separate from the solution-if the sulphate of copper, for example, should begin to crystallize; the phenomena would change. A new force, crystallization, would be added. This force does not act merely by abstracting a part of the chemical mass, but likewise as a positive force, capable of counterbalancing and of being counterbalanced.

It is obvious that in all this there is nothing inconsistent with the laws of chemical proportions. But it will be said that the 100 parts of sulphuric acid combined with the 80 parts of oxide of copper, and the 100 of muriatic acid with the 20, are not combined according to the laws of chemical proportions. It is obvious that the surplus of each of these acids is employed in counterbalancing the surplus of its antagonist, and cannot be considered as combined with the oxide of copper. Of consequence, the part of each acid really combined with the oxide is neutralized according to the laws of chemical proportions. I conceive that this single example is sufficient to show that the principles of Berthollet's theory are not inconsistent with the laws of chemical proportions.

II. On the Cause of Chemical Proportions.

The fact that bodies combine in definite proportions when other forces do not oppose their re-union, added to the observa