1. The symbol is called an impossible or imaginary quantity, because, in analogy with the received laws of algebraic symbolism, it must mean such a quantity as, being multiplied into itself, gives for a product –1. Assuming, then, that every quantity must be either plus or minus, it follows that the square of every real quantity must be plus; and hence , which gives its square minus, is called an imaginary or impossible quantity.

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.

The portion of Berwickshire, of which the object of this paper is to describe the more remarkable geological features, comprises, within a very limited space, an assemblage of phenomena of the highest interest, in relation to the wonderful changes which this part of our island has undergone in the earlier periods of the earth's history. Its situation is immediately to the north of Dunse, and its area is about 16 square miles, within which are comprehended the junctions of the greywacke rocks of the Lammermuirs, with the strata of the old red sandstone formation, and of the latter with the lower members of the coal measures. The chief eminences within the district are Cockburnlaw, which attains a height of 912 feet above the level of the sea; Dunselaw, 630 feet; the Knock, Borthwick, and Castlemains Hills; and the Staneshiel, a hill of the same formation as Cockburnlaw, from which it is separated by a ravine of 300 or 400 feet deep, in which the Whiteadder flows. The general topographical features of the district will be best understood by reference to the accompanying map.

The following results are deduced from the observations of the balance or vertical force magnetometer, which consists of a magnetic needle, balanced horizontally, and resting, by a knife-edged axle, on agate planes. Much doubt has been entertained as to this instrument's capability of shewing changes of moderate nicety, and it has been considered altogether unavailable for changes of long period: it has been shewn (Vol. XVI., p. 67), that there are several difficulties in the way of an accurate interpretation of the observations, independent of the instrumental capacity. If it be added, that disturbances seem to affect the daily means of the vertical component, in a more serious way than they do those of the horizontal component, it will be seen that there are a series of difficulties, which tend to render good and consistent results from the balance magnetometer nearly unattainable. It will be judged afterwards how far these difficulties have been overcome in the present instance.

In April 1846, I communicated to the Royal Society a paper on a new organic base, to which I gave the name of Picoline, and which occurs in coal-tar, associated with the Pyrrol, Kyanol, and Leukol of Runge. In that paper I pointed out that the properties of picoline resembled, in many respects, those of a base which Unverdorben had previously extracted from Dippel's animal oil, and described under the name of Odorine; and more especially mentioned their solubility in water, and property of forming crystallisable salts with chloride of gold, as characters in which these substances approximated very closely to one another. And further, I detailed a few experiments on the odorine of Unverdorben extracted from Dippel's oil, with the view of ascertaining whether or not they were actually identical, but on too small a scale to admit of a definite solution of the question.

The usual methods of obtaining pure phosphoric acid by the oxidation, with nitric acid, or by combustion, of pure phosphorus, are well known; but, although they yield a pure product, yet, as the phosphorus must be prepared from phosphoric acid, it is obvious that we shall derive a great advantage from any method of purifying easily and cheaply the phosphoric acid from bones, instead of first reducing it to phosphorus, and then re-oxidizing it. In practice, phosphorus is made from the superphosphate of lime, and it is from the same salt that phosphoric acid may be most economically prepared.

In a former communication to the Society, I noticed a reaction presented by all spring, well, and river waters which I had examined, that, even after being boiled, they yielded, with acetate of lead, a precipitate readily soluble, in whole or in great part, in acetic acid. This easy solubility in acetic acid shewed that the precipitate was neither a sulphate nor a phosphate, and the comparatively slight action of nitrate of silver proved that it was not a chloride. There seemed, therefore, to remain only the conclusion that it was either a carbonate, or was due to organic matter. The former alternative, of course, depended on whether the solution in acetic acid was attended with effervescence or not; and as this seemed usually not to be the case, and as, on decomposing some of the precipitate by sulphuretted hydrogen, some organic matter in solution was obtained, the conclusion seemed to be, that the appearance was caused by organic matter, probably of the nature of the crenic and apocrenic acids of Berzelius. I have since, however, found that by very careful observation, effervescence may be noticed during the solution of the precipitate more frequently than I at first supposed. It is not so easy as might be imagined to determine this point.

The investigation I am about to bring before the Royal Society, was undertaken in consequence of a discussion which took place in the Zoological Society of London in 1843, in reference to the chemical composition of the bones of the gigantic bird the Dinornis, discovered some time previously in New Zealand. At the meeting in question, the distinguished palæontologist Dr Falconer drew attention to the frequent, if not constant, occurrence of fluoride of calcium in fossil bones, and, as he stated, also in those of mummies; and threw out the suggestion, that the fluoride might shew itself in these animal remains, not as an original ingredient of the bones, or as derived from the matrix in which they were found, but as a product of the transmutation of their phosphate of lime. The idea of such a conversion taking place, is as old at least as the days of Klaproth, who suggested the possibility of phosphoric acid becoming changed into fluoric. It is commented upon by Fourcroy and Vauquelin, as well as by Gay Lussac, as a thing possible but not probable, and which their ignorance of the nature of fluoric acid prevented them from discussing satisfactorily.

The remarkable power which chlorine possesses, of destroying all colours of organic origin, has long been an object alike of speculative and practical interest. The theory of bleaching, however, has hitherto remained imperfect, in consequence chiefly of the observation of Sir H. Davy, that chlorine loses the power of decolorising when deprived of water. So striking is the difference, in this respect, between wet and dry chlorine, that it led the distinguished chemist mentioned, to deny to this gas the character of being essentially, or per se, a bleacher. He regarded as the true decolorising agent the oxygen of the water, which must be associated with chlorine before the latter can bleach. The late Dr Turner has stated Davy's view so shortly and clearly, that I quote his abstract in preference to any statement of my own. “Davy,” says he, “proved that chlorine cannot bleach, unless water is present. Thus dry litmus suffers no change in dry chlorine; when water is admitted the colour speedily disappears. It is well known also, that hydrochloric acid is always generated when chlorine bleaches. From these facts, it is inferred that water is decomposed during the process; that its hydrogen unites with the chlorine, and that decomposition of the colouring matter is occasioned by the oxygen which is liberated. The bleaching property of binoxide of hydrogen, and of chromic and permanganic acids, of which oxygen is certainly the decolorising principle, leaves little doubt of the accuracy of the foregoing explanation.”

The most important steps in a science are those which lead most directly to the establishment of principles or laws peculiar to that science itself, and which constitute its claim to be regarded as a distinct branch of human knowledge. It has been long acknowledged that such is the character of many of those phenomena of living bodies which depend on mechanical movements, or changes of position in their particles, and therefore that the laws of vital contractions are to be regarded as equally elementary and distinctive principles in physiology, as the laws of motion or of gravitation in natural philosophy. But a diificulty has been long felt, as to whether a similar claim to peculiarity of the principle on which they depend, can be urged for the chemical phenomena of living bodies.

The condition of the alkali in the blood—of that portion on which its alkaline reaction depends—has been the subject of much speculation, and of many experiments. Enderling is one of the latest inquirers who has given it his attention. After having made an analysis of the ashes of the blood, he has come to the conclusion, that the alkali in it is in combination with phosphoric acid, the former predominating in the form of the tribasic phosphate of soda.

Numerous researches have established as a general rule that the products of the decomposition of organic substances vary with the circumstances of the experiment, and the nature of the agents under the influence of which it is performed. If, for instance, we examine the action of heat alone, we find it causing a set of decompositions specially characterised by the evolution of carbonic acid, formed by the union of part of the carbon of the substance with the whole or part of its oxygen; and this action is rendered more definite, and the number of the products circumscribed by all circumstances facilitating the formation of carbonic acid, such as the presence of a base, which will even cause its evolution when heat alone is incapable of producing decomposition. Acids, on the other hand, have a precisely opposite effect, they, in some instances, altogether prevent the formation of carbonic acid, and cause the oxygen to exert its action on the hydrogen of the compound, and to eliminate one or more atoms of water which do not generally exist ready formed in it.

It has frequently occurred to me that the difficulty experienced by instrument-makers, in obtaining for sextants and other similar instruments, reflecting mirrors perfectly parallel in their polished surfaces, and also the greater difficulty of procuring glass perfectly homogeneous in its structure, might be overcome by the use of metallic reflectors.

It is well known, that, from the want of perfect parallelism in glass mirrors there arises an error in the reading of such instruments, inasmuch as the emergent ray does not pass out of the glass at the same angle as the incident falls upon it, and that from the want of homogeneousness in the substance, and the unequal refractions caused by the veined structure of the glass.

According to the theory devised by Huygens, to explain the phenomenon of double refraction in Iceland spar, a pencil of light transmitted through that substance is divided into two pencils; the index of refraction for the one being constant, while for the other it varies with the inclination of the transmitted light to the optical axis of the crystal.

Dr Wollaston, in 1802, verified the spheroidal form of the wave of light, which Huygens had assumed to account for the refraction of the extraordinary pencil, by a careful experimental investigation, conducted by means of his elegant instrument for “examining refractive and dispersive powers by prismatic reflection.” In 1810, Malus, in his Théorie de la Double Réfraction, also demonstrated experimentally the accuracy of the Huygenian law for the extraordinary pencil. I have not had an opportunity of consulting the memoir of Malus, so as to know the precise nature of his experiments, with reference to the refraction of the ordinary ray; but the object of Dr Wollaston's researches was simply to prove the law of extraordinary refraction, and the constancy of the index of refraction for the ordinary ray, is therefore tacitly assumed by him.

The proper temperature of our globe is a question which, formerly abandoned to speculation and hypothesis, has only lately been made the subject of direct experiment. Preliminary to it, and intimately connected with it, is another inquiry of great interest, namely, What is the thermometric effect of the whole solar heat which falls in a year on the surface of the globe ? How much is transmitted to the interior? How much dissipated at the surface? To what depth does the influence of the seasons extend, and in what manner is that influence modified at different depths? It is impossible to say to how many curious and important inquiries a solution of these preliminary questions may lead the way; and it is to them that our attention is at present to be confined. We shall not speak, except incidentally, of the absolute heat of the interior of the globe; we shall only discuss the modifications of the solar heating influence near its surface.

The Balance Magnetometer was imagined by Dr H. Lloyd, of Dublin, for the purpose of observing the variations of the vertical component of the earth's magnetic intensity. It consists simply of a balanced magnetic needle, with a knife-edged axle, resting on agate planes, at right angles to the plane of the magnetic meridian. In the instrument from which the results in this paper are deduced, the position of the needle is observed by means of micrometer microscopes.