(33*.) In my paper on the Mechanical Action of Heat, published in the 1st Part of the 20th Volume of the Transactions of the Royal Society of Edinburgh, some of the numerical results depend upon the dynamical equivalent of a degree of temperature in liquid water. The value of that quantity which I then used, was calculated from the experiments of De la Roche and Bérard on the apparent specific heat of atmospheric air under constant pressure, as compared with liquid water.

The experiments of Mr Joule on the production of heat by friction, give, for the specific heat of liquid water, an equivalent about one-ninth part greater than that which is determined from those of De la Roche and Bérard. I was formerly disposed to ascribe this discrepancy in a great measure to the smallness of the differences of temperature measured by Mr Joule, and to unknown causes of loss of power in his apparatus, such as the production of sound and of electricity; but, subsequently to the publication of my paper, I have seen the detailed account of Mr Joule's last experiments in the Philosophical Transactions for 1850, which has convinced me, that the uncertainty arising from the smallness of the elevations of temperature, is removed by the multitude of experiments (being forty on water, fifty on mercury, and twenty on cast iron); that the agreement amongst the results from substances so different, shews that the error by unknown losses of power is insensible, or nearly so; and that the necessary conclusion is, that the dynamical value assigned by Mr Joule to the specific heat of liquid water, viz.:—772 feet per degree of Fahrenheit, does not err by more than two or at the utmost, three feet; and therefore, that the discrepancy originates chiefly in the experiments of De la Roche and Bérard.

(34.) The objects of this paper are twofold: First, To compare the results of the formulæ and tables relative to the power of the steam-engine, which have been deduced from the Dynamical Theory of Heat, with those of experiments on the actual duty of a large Cornish engine at various rates of expansion; and, Secondly, To investigate and explain the method of determining the rate of expansion, and, consequently, the dimensions and proportions of a Cornish engine, which, with a given maximum pressure of steam in the cylinder, at a given velocity, shall perform a given amount of work at the least possible pecuniary cost, taking into account the expense of fuel, and the interest of the capital required for the construction of the engine.

(39.) A machine working by expansive power consists essentially of a portion of some substance to which heat is communicated, so as to expand it, at a higher temperature, being abstracted from it, so as to condense it to its original volume, at a lower temperature. The quantity of heat given out by the substance is less than the quantity received; the difference disappearing as heat to appear in the form of expansive power.

The heat originally received by the working body may act in two ways: to raise its temperature, and to expand it. The heat given out may also act in two ways: to lower the temperature, and to contract the body. Now, as the conversion of heat into expansive power arises from changes of volume only, and not from changes of temperature, it is obvious, that the proportion of the heat received which is converted into expansive power will be the greatest possible, when the reception of heat, and its emission, each take place at a constant temperature.

The following remarks, being the result of a careful examination of a small district of country characteristic of the relations of the trap formations, are perhaps worthy of being recorded; although the general features of the county of Roxburgh have been very clearly stated in a paper by Mr Milne, published in the 15th volume of the Edinburgh Transactions.

The outburst of porphyritic trap forming the conspicuous small group of the Eildon Hills, may be stated to be surrounded by the characteristic greywacke of the south of Scotland. It forms an elongated patch on the map, extending from the west end of Bowden Muir in the direction of the town of Selkirk, and running from west-south-west to east-north-east (true) towards Bemerside Hill, on the north bank of the Tweed. The breadth is variable, probably less than is generally supposed; but it cannot be accurately ascertained, owing to the accumulated diluvium which covers the whole south-eastern slope of this elevated ridge. On this account, my observations on the contact of rocks have been almost entirely confined to the northern and western boundaries of the trap, although the other side was examined with equal care.

The following examination of capric acid and some of its salts, was made in the laboratory of Dr T. Anderson, to whom I am much indebted for his kindness in procuring for me the materials to work upon, and also for advice during the progress of this investigation. Capric acid has been found by Chevreul and Lerch in the butter of the cow and goat; by Redtenbacher, amongst the volatile oily acids he obtained by acting on oleic acid with nitric acid; by Gerhardt and Cahours, by the action of nitric acid on the oil of rue; and by Görgey in cocoa-nut oil;—from all these sources it has been obtained only in small quantities, and always along with other acids of the series to which capric acid belongs.

The study of the organic acids appears scarcely to have advanced of late years pari passu with the other branches of organic chemistry. It seems, indeed, as if the development of each of the different departments of the science had been, to a certain extent, periodical; each engrossing the labours of investigators to the temporary exclusion of the others, themselves to be renewed when some new experiments should reawaken an interest in them.

However this may be, the subject of the natural and artificial bases has proved so productive of interesting results as to have recently become the chosen and almost exclusive field of inquiry, notwithstanding several investigations which have thrown much light on one class of organic acids, namely, that represented by the general formula Cn Hn O4. With the exception of this section, the history of the organic acids remains very imperfect, and in many cases we have but a meagre account of a few of their salts.

I propose in the following pages to communicate to the Society the progress of my investigation of the products of the destructive distillation of animal substances, the first part of which was published in the 16th volume of the Transactions. Since that period, partly owing to my numerous avocations, and partly to the inherent difficulties of the subject, less progress has been made than I had hoped or expected, but still I have accumulated some facts of considerable interest, which I think deserving of the attention of the Society.

It may be remembered that, in the paper just referred to, I announced the discovery, among those products, of picoline, which I formerly obtained from coaltar, and of a new base, to which I gave the name of Petinine; and I entered pretty fully into the method adopted for the preparation of these substances, and of certain other bases, the existence of which I merely indicated, without at the time attempting to characterize them. On proceeding to the more minute investigation of these bases, I soon found that the quantity of material at my disposal was much too small to admit of satisfactory or complete results, although I had employed for their preparation above 300 pounds of bone-oil. I found it necessary, therefore, to begin ab initio with the preparation of the bases from another equally large quantity of the oil; and after going through the whole of the tedious processes described in my previous paper, with the expenditure of the labour of some months, I found my object again defeated by deficiency of material. After various experiments, which, though they led to no definite or conclusive results, served to familiarize me with the nature and relations of the products obtained, I made up my mind once more to begin again; and being resolved on this occasion not to be foiled in the same way as before, I used for my new preparation no less than 250 gallons of crude bone-oil, the weight of which was somewhat above a ton. The result of this process, though involving an immense amount of labour, has been satisfactory, not only in supplying me with a large amount of material, but has also enabled me to obtain many substances, some of them possessed of very remarkable properties, which had escaped my observation when operating on a smaller scale.

Sir Humphrey Davy, by his experiment of melting two pieces of ice by rubbing them together, established the following proposition:—“The phenomena of repulsion are not dependent on a peculiar elastic fluid for their existence, or caloric does not exist.” And he concludes that heat consists of a motion excited among the particles of bodies. “To distinguish this motion from others, and to signify the cause of our sensation of heat,” and of the expansion or expansive pressure produced in matter by heat, “the name repulsive motion has been adopted.”

1. The important researches of Joule on the thermal circumstances connected with the expansion and compression of air, and the admirable reasoning upon them, expressed in his paper “On the Changes of Temperature produced by the Rarefaction and Condensation of Air,” especially the way in which he takes into account any mechanical effect that may be externally produced, or internally lost, in fluid friction, have introduced an entirely new method of treating questions regarding the physical properties of fluids. The object of the present paper is to show how, by the use of this new method, in connection with the principles explained in my preceding paper, a complete theoretical view may be obtained of the phenomena experimented on by Joule; and to point out some of the objects to be attained by a continuation and extension of his experimental researches.

In the accompanying tables are contained the results of some experiments respecting the rate at which aqueous vapour condenses on a cold surface.

These results are not so consistent as could be desired, but having been obtained by a definite and carefully-conducted process, they may claim at least to be received as approximately true.

In planning the experiments, it was assumed that c = m (f“ − f“ʹ), where c is the weight of moisture which is condensed on a surface of given area in a given time; f“ the tension of vapour at the dew-point; f“ʹ its tension at the temperature of the condensing surface; m a coefficient varying with the velocity of the current of air.

The animals, either wholly new, or new to Britain, described in the following communication, were taken during a yachting cruise, with our indefatigable friend Mr Macandrew, among the Hebrides, in the month of August 1850. During this voyage, which lasted three weeks, a series of observations were conducted by means of the dredge and the towing-net. Not a single new form of testaceous mollusk was procured; our exertions were amply rewarded, however, by the discovery of several remarkable Ascidians and Radiata, some of them so curious in themselves, and so important in their zoological bearings, that we have thought it desirable to lay an account of their characters and anatomy before the Royal Society of Edinburgh.