the fundamental distinction between atom and molecule is clearly grasped, it will at once be seen that Berthelot's statement is too general to be of much service in elucidating the mechanism of chemical change.

Berthelot's law is simply a crude application of the principle of the degradation of energy; the principle, namely, that energy always tends to run down from a more available to a less available form. Inasmuch as the production of a chemical compound, with evolution of heat, is an instance of such running down of energy, from the form of chemical affinity to that of heat, it follows that the reversal of this process will require the expenditure of work. But the law of maximum work does not attempt to analyse the expression chemical affinity. Under this term Berthelot includes actions and reactions of different kinds. This is at once apparent from the statement in the Essai, that the first fundamental principle of thermal chemistry, viz." the quantity of heat evolved in a reaction measures the sum of the physical and chemical changes which occur in that reaction"-furnishes the measure of chemical affinities".

Berthelot's work is saturated with the conceptions of the molecular theory: but, by some fatal perverseness, he refuses to apply this theory to chemical phenomena. While recognising the existence of molecules, and building his generalisaa molecular foundation, he refuses to accept the conception of atom, or rather he hopelessly confuses it with that of equivalent. The molecule is for him a definite and definable portion of matter, the parts of the molecule are only numbers.

If by chemical affinity is meant an action and reaction between atoms, then the principle already quoted certainly does not afford a measure of this affinity.

Berthelot's law, then, appears to be a definite statement applicable to chemical reactions; but inore precise investigation shews that the application is only possible when 'chemical' is used in a vague way as including much that is usually called 'physical.'

1 Introduction, p. xxviii.

2Ce principe fournit la mesure des affinités chimiques.'

The principle of the degradation of energy is a highly generalised statement applicable to certain cycles of change; Berthelot attempts to apply it to parts of such cycles, forgetting that what is true of the whole is not necessarily true of the parts.

Thirty years ago Thomsen' generalised the relations between chemical action and thermal change in the statement, "Every simple or complex reaction of a purely chemical kind. is accompanied by evolution of heat."

If by a reaction of a purely chemical kind' is meant the combination of atoms to form molecules, no objection can be made to this statement; we recognise its importance and universality, as we recognise the same qualities in such statements as all men are mortal,' or 'no white men are black.' But we may doubt its utility. Thomsen explains that 'reactions of a purely chemical kind' are those, which proceed without addition of energy from sources external to the system, and consist only of the strivings of atoms towards some stable equilibrium. On the other hand a chemical system may be raised to a temperature such that its constituents are no longer stable, and reactions may then occur with expenditure of external energy; but these changes do not depend solely on mutual atomic attractions. But actions of a purely chemical kind' never occur, except as parts of cycles of reactions, which include changes that do not consist 'solely of the strivings of atoms towards more stable equilibrium.' Hydrogen and oxygen do not combine to form water, neither do chlorine and hydrogen combine to form hydrochloric acid, without the addition of energy from external sources. Y

Statements such as those quoted from Thomsen or Berthelot are true, only when an arbitrary separation is made of chemical changes into two parts, and one of these parts is

1 See Thermochemische Untersuchungen, 1. 12—16.

2 loc. cit. 1. 16.

3 "Der chemische Process ist rein chemischer Natur, wenn er ohne Aufwand fremder Energie verlaüft, und nur durch das Streben der Atome nach mehr stabilen Gleichgewichtslagen zu Stande kommt."

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alone called chemical. Every chemical change, however simple, consists of at least two parts, the first of which is the necessary antecedent of the second; the law of maximum work ignores this duality, or, it might be more accurate to say, the law assumes that the second part of a chemical process can occur without the first. Every process of chemical change may be compared to the flight of a stone from, and its return to the surface of the earth. During the first part of this process there is a continual transference of kinetic energy from the moving stone to the surrounding medium, and during the second part, a continual transference from the medium to the stone, until the stone comes to rest, when its energy becomes a part of the total energy of the system, earth + stone. If the final resting-place of the stone is nearer the centre of the earth than the spot from which it was projected on its upward flight, then the stone contains less energy, relatively to surrounding systems, at the close of the transaction than at the beginning. On the other hand, if the starting-point is nearer the earth's centre than the final point of rest, then the transaction has resulted in gain of energy to the stone. In both cases the second part of the transaction, that which occurs between the turning-point and the final resting-point of the stone, is attended with loss of energy; but this second part does not represent the complete transaction. The law of maximum work is applicable only to the second part. And moreover this law ignores the fact that the stone (or chemical system) does not leave its initial point of rest of its own accord; the law assumes that no work need be done, no energy expended, in the passage of the (stone or system) from its original position to that at which the energy-relations between it and surrounding systems come within the cognisance of the law.

134. An attempt has been made by Thomsen to measure the thermal values of the first parts, i.e. separation of molecules into atoms, of certain changes which result in the production of hydrocarbons. Attention has already been drawn to this investigation.

1 See ante, chapter II. section IV. par. 84.

Thomsen's results are obtained by the aid of many hypotheses, some of which appear to be quite unjustified by facts'. Among such hypotheses I would place ;

(1) The assumption that the molecule of carbon is diatomic:

(2) The assumptions on which the reasoning is based. whereby the thermal value of the process resulting in the formation of this diatomic molecule from amorphous carbon is calculated.

Thus, comparing the reactions

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(a) C2H2+H2=С2H4, (b) C2H1+H2=C2H ̧ (c) C2H2+ H2=2CH1, it is found (assuming 2CH, to be equal to C2H ̧) that the mean thermal value for the addition of H2 = 14570 gram-units.

But, at the same time

the value of the reaction [CH, H2] is found to be equal to [C2H2, H2] + (2 × 14,570),

and the value of the reaction [C'H', H2] is found to be equal to [C2, H2] + (3 × 14,570).

Hence, if we assume that

the value of the reaction [C2, H2] is equal to [C, C]+(4× 14,570), it follows from the known value of the reaction [C2, H2], that

[C, C]= 106,630 units2.

But this value [C, C] represents the sum of two thermal changes, (a) the heat absorbed in gasifying amorphous carbon and separating the molecule into its pair of constituent atoms, and (b) the heat evolved in the falling together of a pair of atoms to form the (hypothetical) diatomic gaseous molecule C Thomsen attempts to determine the value of (a); but in doing this he makes another startling assumption vis.

that because

therefore

[C, O2]=96,960, and [CO, O]=68,080,

[C, O]=[C, O2]-[CO, O]=28,880.

1 Thomsen's papers will be found in Ber. 13. 1321 and 1388; and 15. 318 (also Journal für prakt. Chemie. 131. 157). A much condensed account is given in Thomsen's Thermochemische Untersuchungen, 2. 96-113. A clear and full account of Thomsen's investigation, by J. P. Cooke, appeared in Amer. Journal of Science and Arts [3], 21. 87—98.

2 Thomsen uses this value to calculate the reaction [C2, H2], [C2H2, H2] &c., but of course the results agree with those actually found by experiment.

Thomsen apparently forgets that the reaction [C, O3] represents the production of 44 grams of gaseous carbonic anhydride from 32 grams of gaseous oxygen and 12 grams of solid carbon; whereas the reaction [CO, O] represents the addition of 16 grams of gaseous oxygen to 28 grams of gaseous carbon monoxide1.

Some very strange results are obtained by Thomsen: e.g. he thinks it very probable that [O,C,O] = 2 [C,O], but the numbers on which his own hypothesis is based shew that [O,C,O] 2 [C,O] = 39,200 +; in fact this value is constantly used throughout the investigation. Again the calculated probable value of the heat absorbed in separating two carbon atoms from amorphous carbon is 77,800 units, but to do this, and also to form the diatomic molecule C, from these separated atoms, requires an absorption of 106,630 units, therefore the falling together of two carbon atoms to form a molecule is attended with the absorption of 28,830 units of heat.

Later on we find that the strange behaviour of the atoms of carbon is to be traced to the vagaries of their 'bonds.' Two atoms of carbon may unite, on the bond hypothesis, in four ways:

(1) One bond of each atom is satisfied by one bond of the other atom: heat evolution = about 14,500 units.

(2) Two bonds of each atom are satisfied by two bonds of the other atom: heat evolution = 14,500 units.

(3) Three bonds of each atom are satisfied by three bonds of the other atom: heat evolution=0.

(4) Four bonds of each atom are satisfied by four bonds of the other atom heat absorption= about 28,000 units.

It also follows from Thomsen's numbers that [C,C]<[C,H], and that [C,O]> [C, C] (when C+C forms C-C).

As might be expected, the application by Thomsen of his hypothetically determined values leads to somewhat anomalous results. The calculated heats of formation of hydrocarbons sometimes agree fairly well with the observed numbers, sometimes there are marked differences between the two

1 See also ante, this section, par. 130.