error of the specific gravity s according to Table II. (A.), on which the calculation of the contractions of the volume is founded.

Under all circumstances, according to the formulas (1.) and (3.), it may be taken as a general rule, that when to sulphuric acid of different degrees of dilution so much water is added that the volume of the mixture reaches its maximum of contraction, then the value of this contraction can be represented by the length of the ordinates of an equilateral hyperbola (the asymptotes being parallel to the axes of the co-ordinates), when the number of atoms of water, which in the acid employed are combined with 1 atom of dry acid, is taken as the abscissæ.

As it must constantly be taken as a rule that heat is evolved by a diminution or contraction of volume of a body, and it is known that by mixing an already much diluted sulphuric acid with more water a sensible quantity of heat is evolved, it was natural to believe that the heat so produced stood in some relation to the decrease of the volume. Such a relation in the meantime has not been proved, and chemists have denied the possibility of any such direct relation between the contraction and the heat evolved, for the reason that there are other bodies, for instance, alcohol of certain degrees of dilution, which by mixing with water increase in volume instead of decreasing, and yet produce heat. But it appears to me that this objection is not decisive. It cannot well be said that the production of heat is a direct or immediate effect of the change of the volume, as it would certainly be a paradox that an extension and a contraction of volume should have just the same effect; but more correctly it may be supposed that the change of the volume as well as the production of heat are both the effects of a higher cause, namely, the endeavours of the chemical or molecular forces to obtain a new state of equilibrium; and as the value of both these effects must be in proportion to the intensity of the acting force, it is not improbable that the increase of volume as well as the contraction may be expressed as a function of the heat evolved, or the contrary.

The consideration that the molecules of the fluid, when the volume of the mixture has reached its minimum, must be supposed to be most symmetrically arranged, and to have obtained a stable equilibrium, which they even with a certain inertia try to retain, because the volume in the neighbourhood of its minimum is subject only to excessively slow change upon the addition of more water, in its proportion to the sum of the volumes of the mixed parts, this consideration, in combination with the following experiment of Parkes, induced me several years since to endeavour to find a path to discover the relation between the change of the volume and the heat evolved, which at length, at least so far as sulphuric acid is concerned, appears to have led to a satisfactory answer to the question.

Parkes has tried several experiments of the temperature which is produced when concentrated sulphuric acid and water are mixed in several proportions. He found that when to a great quantity of water greater and greater quantities of acid were added by degrees, the temperature of the mixture increased to a certain maximum, and decreased again with the further addition of acid. This maximum temperature (216° F.) took place when the quantity of water and acid was in the proportion of 10:25, consequently when the mixture contained I equivalent dry acid and 3 equivalents water, or it occurred with the same degree of dilution as the maximum of

contraction.

By his important thermo-chemical experiments Hess has endeavoured to show, that when the several hydrates of sulphuric acid SO, H2O, SO, 2H,O, SO, 3H,0, &c. are mixed with an excess of water, then the quantities of heat

evolved by the combination of acid and water (when this heat is not increased by a new addition of water) are in the same proportion to each other as the numbers 10:6:4:3:2; or, with the exception of the first hydrate, which has the relative number 10 instead of 12, the heat produced is in inverse proportion to the number of atoms of water in the acid employed. But this is precisely the same rule which we have discovered for the value of the maximum of contraction for the corresponding hydrates. In order to make a comparison between the value of the contraction and the quantity of heat observed by Hess, I have chosen that series of experiments which he himself seems to regard as the most complete and most accurate. The determination of the heat evolved seems yet to be embarrassed with so great difficulties, that the several series of experiments, as well by one and the same as by different observers, at least as regards the absolute quantity of heat, have given very different results.

Hess has thus found*, that when to an acid, of the composition stated below, an addition of water is given to that extent that the heat evolved is not further increased, then the heat produced by one atom of dry sulphuric acid is equal to the numbers in the 3rd column of the following table.

From these observations I have calculated the most probable value of what Hess calls one portion of heat, viz. the heat evolved by the acid SO, + 6H2O with an excess of water, and found it equal to

46-4020-262=46·402 (1 ± 0·01128),

* Poggendorff's Annalen der Physik und Chemie, lvi. p. 467.

The number 132-2, l. c. is probably a misprint for 134.2, as the mean value of Nos. 8

and 9 is given equal to 134·2 (page 468).

The mean error in this series of experiments is consequently equal to 4.676, and the most probable error of a single observation = 3.154.

Regarding the heat evolved by one atom of concentrated acid (SO3 + H2O), for which Hess in another series of experiments has found the value to be 229-41, this acid should, if it followed the same law as the other hydrates, produce six portions of heat or 278-41, and the difference between the observed and calculated value would be equal to -590. Hess supposes therefore that it only produces 5 portions of heat, or 232-01, and the same difference will only be 2.50.

-

If now we suppose that the diffused heat is proportionate to the maximum of contraction of an acid, which in one atom SO, contains n atoms water, or if we put

Wm C,.....

(11.)

where W is the quantity of heat evolved by the acid employed, and C the maximum of contraction calculated before (Table V.), we obtain for the determination of m the following equations::

and the probable error of a single observation = 371.

A like result will be obtained, if for W is taken the values of the maxima of contraction directly found in Table IV., which give the equations

from which we obtain m' = 4034·14 +86-49, and the probable error of a

single observation 4.01.

As the probable error in these two cases is very slightly different from the uncertainty of the values of the quantities of heat calculated according to the hypothesis of Hess, it may be supposed with the same degree of probability, that the heat evolved by a certain hydrate of sulphuric acid on the addition of an excess of water is proportionate to the maximum of contraction of the same hydrates; or that both are inversely proportionate to the number of atoms of water which the acid employed contains combined with one atom of pure acid.

This law at least appears to hold good for the larger degrees of dilution. Regarding the acid SO, H2O, Hess supposes, as previously stated, that it

with an excess of water diffuses only five portions of heat instead of, as in the above law, six. We have previously seen that the maximum of contraction for the more concentrated acid is also greater than, according to that law, it should be.

For such a discontinuity in the law which determines the quantity of heat it is difficult to see any grounds, and, as we previously have shown (Table V.), it does not exist in the maxima of contractions, as these with sufficient accuracy can be calculated by formula (5.). If now the quantity of heat in Table VIII. is calculated according to the same formula

b

W =
a + n'

(13.)

it will be seen that these values, even for the concentrated sulphuric acid, only slightly differ from the observed. The values of a and b, which best agree with all the observations in Table VIII., are the following:

The probable error of a single observation according to this formula will only be 2-109, whilst according to the hypothesis of Hess it is equal

to 3.154.

It is worthy of observation, that the constants b and ẞ in the formulæ (13.) and (5.) are determined with the same accuracy by the observations of contractions as by those of the heat evolved, whilst the constants a and a are much more accurately determined by the latter than by the former. This is seen by comparing the equations (14.) and (6.).

If therefore it is considered as proved that the maximum of contraction as well as the production of heat by the addition of an excess of water can be expressed as functions of the atomistic constitution of the acid em

ployed by help of the formulæ (5.) or (13.), that consequently C =

b

W=
a + n

B

a + n

C, then the quantity of heat produced can be represented as

function of the heat evolved by the equation

W =

b. C
B-(a-a) C'

..(15.)

where b, ẞ, a and a have the values given in the equations (6.) and (14.). If in this formula the values for C are substituted from Table V., the same values for the quantity of heat W will be accurately reproduced, which are calculated in Table XII. above.

Researches on the Influence of the Solar Rays on the Growth of Plants. By ROBERT HUNT.

THE experiments connected with this investigation have been extended over a period of seven years; they have been made at every season of the year; and the locality in which they have been carried on has been changed from the south-western extremity of the kingdom to the neighbourhood of the metropolis.

Although there are many important points which remain open for investigation, and others, which although examined, require, from the complexity of their phænomena, still more minute research, I believe I am enabled to lay before this meeting of the British Association a series of important facts connected with the processes of germination and vegetable growth, as affected by solar radiations.

The title heading each of my former reports has been the "Influence of Light, &c." I have now changed that form of expression and adopted the above. My reasons for this are, that much confusion has arisen from our habit of referring all the effects observed in the processes of vegetation to the agency of light, whereas it appears that some agencies which are not luminous materially influence the phænomena of vegetable vitality.

Without entering into any discussion in this place on the probable existence, or otherwise, of a principle distinct from light and heat in the sun's rays, to which to refer the curious chemical changes produced by solar influence, it will be sufficient to admit the existence of three distinct classes of phænomena, which cannot, I think, be disputed.

These are luminous influence, calorific power, and chemical excitation. The problem which these researches were directed to solve, was the proportion and kind of influence exerted by light, heat and actinism-as the principle supposed to be active in producing the chemical phænomena of the solar rays has been called-in the various stages of vegetable growth.

The means we have of separating these phænomena from each other are not very perfect; indeed, in the present state of our knowledge, it is impossible to have evidence of the operations of either light, heat or actinism absolutely separated from each other. If we use the prismatic spectrum, we have over every portion of it a mixture of effects. Even in the mean yellow, or most luminous ray, we have a considerable amount of thermic action, and, under some circumstances, evidence of chemical power. In the violet rays, which have been particularly distinguished as chemical rays, we have light and heat; and in the calorific rays we have decided proof of both luminous and actinic power. In the experiments which have been made with the prismatic spectrum, we have in fact no certainty that the results stated to be due to a particular ray-that ray being regarded as the representative of a particular phænomenon-are not the combined effect of the three forces.

The same objections apply to absorbent media, but the amount of each influence is readily determined; and we are therefore enabled to refer any particular result to a tolerably well-defined agency.

All the experiments recorded in this report have been made under the action of those radiations which have permeated variously coloured media, such as tinted glass and coloured transparent fluids. It is not sufficient to state that a yellow, red, or blue glass or fluid was employed, as it by no means follows that these media are permeated only by the rays corresponding in colour, or by the influences due to a given order of refrangibility.

The difficulties which oppose themselves to experiments made with coloured media have been strongly felt by other observers. Dr. Daubeny says in his 1847.

C