The author, after noticing the proofs of Stigmaria being the root of Sigillaria, called attention to the external organs, known formerly as the leaves, and more recently as the rootlets of the former. He stated that in the many examples of stigmaria which he had examined, he had never observed these rootlets articulated to the stem by anything resembling a ball-and-socket joint, considering the appearance which had led to this notion as due to shrinkage and state of preservation.

The direction of the Magnetic Meridian, as indicated by that of a freely suspended magnetized needle will generally be erroneous, unless the magnetic axis of the needle is parallel to its axis of figure; and hence, in order to obtain an accurate value of the magnetic declination, it becomes necessary to take the mean of two observations of the needle, first suspended in its usual position and next inverted. If, however, the inversion of the needle is not accomplished with perfect accuracy, the correction, for want of parallelism between the magnetic axis of the needle, and its axis of figure, will not be complete; and the value of the magnetic declination obtained from the mean of two observations of the needle, first in its usual position, and then inverted, will be affected with a residual error due to imperfect inversion of the needle. The present investigation refers chiefly to that form of declinometer magnet, in which the magnet is converted into a collimator by attaching to it a lens and cross fibres or a divided glass scale, in the principal focus of the lens.

On opening any astronomical work of the present day, we are at first startled by, and then familiarized with, the excessive precision of the numbers set down. In our Nautical Almanac, for example, although referring to a period three or four years subsequent to the date of publication, the declinations of the stars and planets are set down to tenths of a second of arc, and their right ascensions to hundredths of a second of time.

This was a problem proposed some years ago by Professor Forbes, when discussing the question of the distribution of the stars. Simple as it is, no prior notice seems to have been taken of it, nor is the author aware that the full solution has yet been given. The problem is this:—“There are n dice, each of which has p faces, p being not less than n; it is required to find the number of arrangements which can be formed with them; 1st, “that no two shall show the same face; 2d, that no three shall show the same face, and so on.” The only part of this problem of which the solution has yet appeared is the first, and the result is p (p−1). … (p−n+1). The author supplies the solution of the remaining portions.

In this paper the author adduced, from contemporary chroniclers and diarists, all the visits of the Pest or Plague which occurred in Scotland after 1560; namely, in the years 1568, 1574, 1585, 1587, 1597, 1607, 1622, and 1645. He cited, from the same sources of information, the notable instances of scarcity and famine; namely, 1563, 1568, 1574, 1578, 1587, 1596, 1598, 1612, 1622, 1642–3. It thus appeared, that while there were several instances of famine not followed by the Pest, there was scarcely one instance of the Pest which was not immediately preceded by a famine. So far the opinion of modern medical writers, that deficient nutrition in the community is one of the predisposing causes of pestilential fevers, may be considered as borne out by facts.

Dr Hayes states that there is evidence establishing the fact that pure native iron exists abundantly in the country back from the central part of the colony of Liberia. Early travellers state that the natives of Africa find iron ore so pure, that they heat and hammer it into form. Explorations by the Liberians show that the inhabitants of towns are engaged in manufacturing iron, and an intelligent native has recently shown how it is done. Last year a mass was sent home by a working blacksmith, who cut it with a chisel from a mass of larger size connected with rock. This proved to be native iron, malleable and ductile, yet unequal in its molecular structure. The general arrangement of the particles is unlike that of any artificial iron known, and there are among the iron particles of crystalline and transparent quartz, octahedral crystals of magnetic oxide of iron, and one of the silicates of soda and lime. No traces of carbon exist in connection with it, and no piece of artificial iron has yet reached Dr Hayes which does not contain carbon.

The author described the succession of pleistocene beds at Gamrie, on the coast of Banffshire, as follows (ascending order):—1, boulder clay; 2, a thick bed of sand; 3, a thin bed of brick clay; 4, a thick bed of sand; 5, a thick bed of brick clay; 6, a bed of sand, containing shells of arctic character entire; 7, a moderately thick bed of pure clay; 8, a thick bed of sand; 9, a thin bed of ferruginous gravel (which Mr Chambers regards as the equivalent of the upper till, or coarse gravel, of other geologists); 10, a thick bed of soft blue clay; 11, a thick mass of sand rising to the top of an eminence on which is a vitrified fort.

The author endeavours to show that in the Old Red Sandstone period there extended across Scotland a branch of the sea or strait, whose northern shore was somewhere in the line of the mica schist rocks which extend from Aberdeen to the mouth of the Clyde, and its southern in the direction of the Greywacke rocks that run across from St Abb's Head to Wigtonshire. In this, at the earlier part of the period, there were considerable tidal currents; but when the upper beds were deposited, they were more or less completely absent, and there were present such as were chiefly due to the action of the wind.

Dr Anderson—It is a peculiar pleasure to me to be the organ of the Society this evening for presenting to you this token of the approbation of this Society and its Council.

As there must be many now present who are unacquainted with the origin, conditions, and mode of adjudication of the Keith Prize, I hope that others will bear with me for a moment till I state these very briefly. The prize was founded by the late Sir Alexander Keith of Dunottar and Ravelston, to be given to the author of the best paper read in this Society during each successive biennial period. The Council were appointed to administer the fund, and to adjudicate the prize. The adjudication is determined by advice of a committee of the Council specially nominated for the purpose.

After remarking that the perfect strictness of the demonstrations in Geometry is generally admitted, the author of the paper cited the almost universal belief in the soundness of Euclid's reasoning as a notable example of wide-spread credulity. He then enunciated the proposition that our knowledge of the truths of geometry is altogether derived from experience.

The question as to the arrangement by means of which the eye is adapted for distinct vision at different distances has for two centuries strongly attracted the attention of physiologists. The numerous hypotheses, and untenable theories which have been advanced on this subject are all, however, more or less unsatisfactory.

In this paper a short account was given of the comparison of the oka with the imperial grain weight, and of the arsheen with the inch.

The oka was stated to be 19,807 grains, so that 18 cantar of 44 oka each make one ton one pound.

The length of the arsheen was determined by comparison with the ebony standard of Sultan Selim.

The extreme length, as obtained by contact, was 29·890 inches, but the ends had evidently been tampered with; on that account the divisions of the rod were referred to; these gave results varying from 29·944 to 29·949, and therefore the mean, 29,946 inches, may be taken as the true length of the Turkish arsheen.

This paper is intended to meet the objections taken by Mr D. Sharpe, in a paper published in the Quarterly Journal of the Geological Society for February 1855, to the views of the present writer, and those of several eminent geologists, on the structure of the chain of Mont Blane.

De Saussure first described the singular superposition of gneiss to limestone which occurs on the south-east side of the valley of Chamouni, a testimony the more clear from its obvious opposition to the Wernerian views of the period.

Polyommatus Artaxerxes, or the Scotch Argus, is an insect not only of great local interest, but has attracted, and continues to attract, the notice of entomologists all over the world. Among the English, and still more among the foreign students, who annually throng our University, there are always a considerable number who arrive in Edinburgh anxious to see “the rare butterfly from Arthur's Seat,” or who are commissioned by entomological friends to obtain it. Besides, there are the still more destructive emissaries from the London and provincial dealers in insects, who infest the hill during the season in which it is found. But although the situation in which this insect is principally taken is extremely circumscribed, I am not aware that its numbers are materially diminished by this continuous drain upon them.

The first part of this communication was occupied with a detail of some observations, made in the course of last summer, on the quantity and intensity of Solar light, as compared with familiar sources of artificial flame. The instrument employed for these observations was a simple monochromatic photometer, whose construction was minutely described.

The object of this paper was to ascertain, by a geometrical construction, the optical appearance presented by the binocular vision of a straight line and a circle, or of two straight lines. The problem discussed was, accordingly, the geometric one of the intersection of a cone with a plane, or of two cones with each other: and the conclusion arrived at was that the apparent image is always a conic section. The author took no account of the perspective of the presented combination of images, nor of the union or disunion of the extremities of the respective images when their lengths are different.

The author, after referring to his former paper on this subject, stated that he had continued the investigation, and that the number of undescribed forms besides those formerly figured had proved so large, that the present paper does not conclude the subject, but that a good many forms remain for a future communication. He added, that even now, after he had explored 600 slides of it, new forms were still occasionally found.

The first part of this paper was occupied with the discussion of the validity of Newton's Theory of the Propagation of Sound. In order to discover the velocity of sound, Newton supposes a series of particles ranged in a straight line to be set to vibrate all equally and isochronously, but the epoch of vibration to vary gradually along the line; and he then investigates the circumstances under which such a vibration is possible. The true result of the investigation is this,—that if the two extreme particles be kept vibrating by some external influence, and if all the intermediate particles be fairly started with the velocities appropriate to their positions in the series, the constrained vibrations of the two extreme particles, aided by the elasticities of the intermediate parts, are sufficient to maintain the vibrations of those parts.