Mr President,—It has been a practice from the foundation of the Royal Society of Edinburgh, to commemorate its deceased distinguished members by memoirs or biographical notices, read at the ordinary meetings of the Society. Some of these have been printed in the Transactions; and our published volumes are enriched by papers of Dugald Stewart, Professor Playfair, Sir John MacNeil, and Dr Traill, on the characters and writings of Adam Smith, Dr Hutton, Professor Robison, Sir Charles Bell, and Dr Hope. A biographical notice is now due to the memory of a distinguished countryman, late Vice-President of the Royal Society; and the following remarks will, in attempting that object, make a deviation from those more severe discussions with which the time of the Society is usually occupied, in connection either with pure mathematics, natural philosophy, or natural history.

There is an important geometrical problem which proposes to find a curve having a given relation to a series of curves described according to a given law. This is the problem of Trajectories in its general form.

The series of curves is obtained from the general equation to a curve by the variation of its parameters. In the general case, this variation may change the form of the curve, but, in the case which we are about to consider, the curve is changed only in position.

This change of position takes place partly by rotation, and partly by transference through space. The rolling of one curve on another is an example of this compound motion.

1. The presence of heat may be recognised in every natural object; and there is scarcely an operation in nature which is not more or less affected by its all-pervading influence. An evolution and subsequent absorption of heat generally give rise to a variety of effects; among which may be enumerated, chemical combinations or decompositions; the fusion of solid substances; the vaporisation of solids or liquids; alterations in the dimensions of bodies, or in the statical pressure by which their dimensions may be modified; mechanical resistance overcome; electrical currents generated. In many of the actual phenomena of nature, several or all of these effects are produced together; and their complication will, if we attempt to trace the agency of heat in producing any individual effect, give rise to much perplexity. It will, therefore, be desirable, in laying the foundation of a physical theory of any of the effects of heat, to discover or to imagine phenomena free from all such complication, and depending on a definite thermal agency; in which the relation between the cause and effect, traced through the medium of certain simple operations, may be clearly appreciated. Thus it is that Carnot, in accordance with the strictest principles of philosophy, enters upon the investigation of the theory of the motive power of heat.

Some time ago my brother, Professor William Thomson, pointed out to me a curious conclusion to which he had been Ied, by reasoning on principles similar to those developed by Carnot, with reference to the motive power of heat. It was, that water at the freezing point may be converted into ice by a process solely mechanical, and yet without the final expenditure of any mechanical work. This at first appeared to me to involve an impossibility, because water expands while freezing; and, therefore, it seemed to follow, that if a quantity of it were merely enclosed in a vessel with a moveable piston, and frozen, the motion of the piston, consequent on the expansion, being resisted by pressure, mechanical work would be given out without any corresponding expenditure; or, in other words, a perpetual source of mechanical work, commonly called a perpetual motion, would be possible. After farther consideration, however, the former conclusion appeared to be incontrovertible; but then, to avoid the absurdity of supposing that mechanical work could be got out of nothing, it occurred to me that it is necessary farther to conclude, that the freezing point becomes lower as the pressure to which the water is subjected is increased.

It is well known that a luminous object is seen for some time after its light has ceased to fall on the retina; but less attention seems to have been paid to the fact, that light requires a certain time to produce its full impression on the eye. Accordingly, while it is stated in most treatises on optics, that the sensation of vision continues after the action of light has ceased, only a few writers have mentioned that the total effect of light on the eye is not produced instantaneously, but that a certain time is required for its complete development.