[Extracted from a Letter addressed to Professor Kelland.]

My dear Sir,

In reading your paper in the Transactions of the Royal Society of Edinburgh, vol. xv., p. 315, some years ago, it occurred to me to try whether it would not be possible to give a general demonstration of the theorem, applying to apertures of all forms. I arrived at a proof, which I wrote out, but have never published. As I think it will interest you I will communicate it. You may make any use you please of it.

Case I. Aperture in front of a lens; light thrown on a screen at the focus, or received through an eye-piece, through which the luminous point is seen in focus.

The expression for the intensity is given in Airy's Tract, Prop. 20. If the intensity of the incident light at the distance of the aperture be taken for unity, and D be the quantity by which any element of the area of the aperture must be divided in forming the expression for the vibration, that expression becomes

the integration being extended over the whole aperture. If it should be necessary to suppose a change of phase to take place in the act of diffraction, such change may be included in the constant B.

A number of years ago I began to form and arrange in the Anatomical Museum of the University of Edinburgh a collection of the hair of the head to illustrate the varieties in colour and character which exist in the Races of Men. In a classification of the races based on the colour and characters of the hair, anthropologists have usually adopted the suggestion made by Bory de St Vincent, and have divided them into two groups: Leiotrichi, with straight, smooth hair; and Ulotrichi, with woolly or frizzly hair. Each of these again is capable of subdivision.

In this memoir I intend especially to examine the Ulotrichi, which comprise two well-marked subdivisions. In one the hair is very short, and is arranged in small spiral tufts, the individual hairs in which are twisted on each other, a mat-like arrangement of compact spiral locks closely set together being the result. In the other the hair is moderately long, the locks are slender, curled or spirally twisted in a part of their length and terminate at the free end in a frizzly bush-like arrangement. Ulotrichous hair is found in various African races, in the aborigines of Tasmania, New Guinea, the Melanesian Islands in the Pacific, in the Negritos of the Malay Peninsula and of some of the islands of the Asiatic Archipelago. The Leiotrichi are Australians, Polynesians, Mongols, Malays, Indians, Arabs, Esquimaux and Europeans.

A new rhynchonellide brachiopod has been collected from the Kahuitara Tuff (Campanian–Maastrichtian) of Pitt Island, Chatham Islands, New Zealand. Brachiopods are extremely rare in Cretaceous rocks from New Zealand, and this new genus and species is unlike any other rhynchonellide known from Australasia or elsewhere. Chathamirhynchia kahuitara is distinguished by its small size, strong ribbing, and well-developed sulciplicate folding, and internally by a large, robust cardinal process and raduliform crura. The shell structure of C. kahuitara is shown to be of typical fine fibrous ‘rhynchonellidine’ type. This brachiopod was probably strongly attached to volcanic rock or shells in a shallow-water, high-energy environment. Implications for the biogeography of brachiopods during the Late Cretaceous are briefly discussed.

From the results obtained by Berzelius in his experiments with tungsten, the number 189·28 is calculated as the atomic weight of that metal. Many later investigations have been made, in which uniformly a lower figure was arrived at, in the majority of cases very nearly 184, which has therefore been regarded as the atomic weight.

§ 1. The shielding effect which exists within hollow iron spheres and cylinders, when placed in a uniform magnetic field, has been previously investigated. Poisson, Stefan, Maxwell, and among others, and more recently, Professors Rücker and Du Bois, have contributed to the subject. If

and the ratio of n to R be the order 1 to 100, it appears that the following expressions may be taken as sufficiently correct:

Since Lord Kelvin showed that the resistance of the magnetic metals was influenced by the state of magnetisation of these substances, a good deal of work has been done in investigating more carefully the extent and nature of the relation. It does not appear, however, that any attempt has been made to discover how change of temperature affects this influence. Twelve years ago in Japan I set one of my Japanese students to the construction of an apparatus suitable for making this research. A few preliminary experiments were made; and leaving Japan shortly after, I brought the apparatus with me in the hope of continuing the work in this country. Not till this summer, however, did I find leisure to return to the problem. The results obtained I wish now to lay before the Society.

How convenient soever the wet bulb thermometer and the various organic hygrometers may be for giving indications, by simple inspection, regarding the relative states of dryness and humidity of the atmosphere, it is scarcely possible, in conducting meteorological observations, to dispense altogether with instruments calculated for affording more direct information respecting the amount of aqueous vapour present in the air at any particular time.

1. The late Mr Alexander Adie, optician, and Fellow of the Royal Society of Edinburgh, was so generally known to be a zealous and careful observer of meteorological instruments, that an attempt to combine the results deducible from his labours carried on (though with one long break) over more than forty years, cannot be otherwise than interesting.

2. The plan of superintending the careful reduction of the thermometrical part of Mr Adie's registers occurred to me a long time ago, but circumstances prevented the execution of it until two or three years since, when, through the kindness of Mr Adie and his family, the whole of the manuscript observations, commencing with 1795, were put into my hands, and the Council of the Royal Society of Edinburgh provided sufficient funds for the employment of computers for reducing them.

3. The work has proceeded with frequent interruptions, but is at length complete. Before I proceed to detail the particulars of the reductions and their results, I will give a short account of the earlier observations on the climate of Edinburgh which I have been able to trace, some of which perhaps have hitherto escaped notice.

The vertical movements of the earth's atmosphere from which the energy is derived which causes the horizontal movements of the air which we call winds, and by means of which the moisture evaporated from the surface of land and water is collected and carried to the higher regions of the atmosphere, where it is condensed to cloud and again distributed in the form of rain over the earth's surface, are of great interest, and a thorough knowledge of the laws governing these vertical movements is necessary to enable us to arrive at a correct forecast of the coming weather over any area.

The Character of Hamlet, has been variously judged of by critics, and what might be expected, it has been still more variously represented by performers upon the stage. Shakespeare himself seems to have apprehended that this would happen; and that injustice would be done to a hero, who probably, in his estimation, ranked higher than any other that he has brought into the drama.

In writing the life of a person who himself published nothing, it is extremely difficult to satisfy the expectation of his particular friends, without incurring the charge of adulation from the rest of the public. How far I have succeeded in doing justice to Mr Hamilton's merit, without insensibility or exaggeration, must be determined by those who knew him, and by those who can appreciate the worth of such professional remarks as I shall lay before them in the sequel. Mr William Hamilton was born in Glasgow July 31. 1758. Having finished the usual course at the Grammar School, he went to Glasgow College in 1770, and continued there studying with great diligence till 1775, when he became Master of Arts at the age of seventeen.

Changes in soil chemistry in response to varying climatic regimes can alter the equilibria of soil systems and result in different clay minerals. Variations in phyllosilicate clay composition can reflect temporal and spatial climatic changes, such as summer/winter monsoon cycles. The objective of this research was to investigate the mineralogy of the clay fractions as a proxy for determining variations in the East Asian monsoon climate, based on a section at Chaoyang in China spanning the last 0.423 Ma BP. The clay mineralogy record in the Chaoyang section was compared with other proxies as recorded in this section and with other palaeoclimatic indicators, including oxygen isotopes from oceanic sediments and loess–palaeosol sections on the Chinese Loess Plateau (CLP). The results from clay mineralogy and related climatic studies show that the summer monsoon has a trend of four increased stages and four decreased stages; whereas the winter monsoon displays the opposite trend. During the last 0.423 Ma BP, the strongest winter monsoon occurred around 0.243–0.311 Ma BP. During this period, which included an intense winter monsoon, the soil in the section had the least illite, one of the smallest kaolinite and illite/Chlorite (I/C) indices and an overall decreasing clay content. The period 0.225–0.243 Ma BP had the strongest summer monsoon over the last 0.423 Ma BP. This period had the greatest amount of illite, the highest I/C index, greater overall clay content and the strongest magnetic susceptibility signal. Additionally, this section contained the smallest mean grain size. The multi-monsoon climate cycles of alternating cold-dry and warm-moist conditions as recorded in the Chaoyang section corresponded well with multiple glaciation cycles based on deep sea sediments. This indicates that the Chaoyang section provides a record of palaeoclimate changes in northeast China that can be linked to mineralogical suites to assist in reconstructing the palaeoclimate over the Late Middle Pleistocene, and complements the global palaeoclimate records in the CLP.

Two large fossil plants are described from the Givetian (Middle Devonian) Eday Flags, South Ronaldsay, Orkney Isles, northern Scotland. Fossils with branches joined to stems of this age are rare. Each specimen comprises a robust and tapering main trunk from which numerous closely spaced branches arise distally. Although poorly preserved such that generic identifications are not possible, both specimens display the characteristic architecture of the plant order Pseudosporochnales (Cladoxylopsida). The newly discovered specimens demonstrate a variation in size and form that adds further data to the understanding of the ontogeny of these enigmatic plants, complementing recent morphological and anatomical findings. These specimens, in combination with many more fragmentary fossils of the same kind from the Orcadian sedimentary basin, add to our knowledge of the Givetian floras of Britain, and show that large plants with upright stems were present in the Middle Devonian landscape of Scotland.

Presented for the first time is a reconstruction of the skull of Diadectes (Diadectomorpha) based on several specimens of a single species Diadectes absitus from the early Permian of central Germany. Since its first discovery at the end of the 19th century the only reconstructions of the skull of Diadectes were without specific designation, despite a rich Permo-Carboniferous fossil record. The skull of D. absitus is reconstructed in dorsal, lateral, posterior, and ventral views and includes exocranial and endocranial elements. The reconstructions of Diadectes presented here are compared with those of all other authors, and the differences are analysed and discussed. The comparisons recognised three features not recorded in other species of Diadectes: (1) anterior and posterior margins of the transverse process of the pterygoid parallel one another; (2) the angle between the posterior margin of the transverse process and the lateral margin of the quadrate ramus of the pterygoid is sharply defined; and (3) the anterior ventral margin of the transverse process of the pterygoid bears a distinct sharp ridge. These characters are discussed in the context of the skull anatomy of Diadectes and inaccuracies in previous cranial reconstructions of the genus are rectified.

The chemical composition of soil from the Glasgow (UK) urban area was used to identify the controls on the availability of potentially harmful elements (PHEs) in soil to humans. Total and bioaccessible concentrations of arsenic (As), chromium (Cr) and lead (Pb) in 27 soil samples, collected from different land uses, were coupled to information on their solid-phase partitioning derived from sequential extraction data. The total element concentrations in the soils were in the range <0.1–135mgkg–1 for As; 65–3680mgkg–1 for Cr and 126–2160mgkg–1 for Pb, with bioaccessible concentrations averaging 27, 5 and 27% of the total values, respectively. Land use does not appear to be a predictor of contamination; however, the history of the contamination is critically important. The Chemometric Identification of Substrates and Element Distribution (CISED) sequential chemical extraction and associated self-modelling mixture resolution analysis identified three sample groupings and 16 geochemically distinct phases (substrates). These were related to iron (n=3), aluminium–silicon (Al–Si; n=2), calcium (n=3), phosphorus (n=1), magnesium (Mg; n=3), manganese (n=1) and easily extractable (n=3), which was predominantly made up of sodium and sulphur. As, Cr and Pb were respectively found in 9, 10 and 12 of the identified phases, with bioaccessible As predominantly associated with easily extractable phases, bioaccessible Cr with the Mg-dominated phases and bioaccessible Pb with both the Mg-dominated and Al–Si phases. Using a combination of the Unified Barge Method to measure the bioaccessibility of PHEs and CISED to identify the geochemical sources has allowed a much better understanding of the complexity of PHE mobility in the Glasgow urban environment. This approach can be applied to other urban environments and cases of soil contamination, and made part of land-use planning.

The presence of archaeocyath-bearing clasts from Cenozoic tills and Cambrian Mount Wegener Formation reveal erosion of a hidden Cambrian carbonate platform in Shackleton Range, Antarctica. We provide microfacies, paleontological, diagenetic and tectonically induced fabric data from carbonate clasts which, in addition to available geochemical and geochronological data from Shackleton Range, allow the paleoenvironmental reconstruction of a lost Cambrian Series 2 mixed siliciclastic–carbonate platform that was developed and eroded during the Ross orogeny. Carbonate production was dominated by non-skeletal grains in possibly restricted platform-interior and oolitic shoal complex settings, while open subtidal sub-environments (calcimicrobe carpets, calcimicrobe–archaeocyath patch reefs, muddy bottoms) were dominated by a diverse calcimicrobe assemblage and/or by secondary to accessory heterozoan assemblage (archaeocyaths and other sponges, chancelloriids, hyoliths, coralomorphs, trilobites, echinoderms). We describe a Botoman assemblage with 34 archaeocyathan species among 12 existing archaeocyathan genera. A new archaeocyath family Shackletoncyathidae is proposed. New species (Rotundocyathus glacius sp. nov., Buggischicyathus microporus gen. et sp. nov., Paragnaltacyathus hoeflei, Shackletoncyathus buggischi gen. et. sp. nov., Santelmocyathus santelmoi gen. et sp. nov., Wegenercyathus sexangulae gen. et sp. nov.) and Tabulaconus kordae coralomorph are reported from Antarctica for the first time. Archaeocyathan fauna share few species with contemporary fauna of South Australia (9) and even fewer with the Antarctic platforms of the Shackleton Limestone (2) or the Schneider Hills limestone (1). Similarity is greater with Antarctic allochthonous assemblages of Permo-Carboniferous tillites from Ellsworth Mountains (2), Cenozoic deposits from King George Island (4) or Weddell Sea (1). The Shackleton Range lost/hidden platform shows a distinct entity related with its tectonosedimentary evolution, in a possible back-arc basin on the Mozambique seaway during the E and W Gondwana amalgamation, which distinguishes it from those developed on the palaeo-Pacific margin of the E Antarctic craton.

Coal and hydrocarbons have been exploited from the Carboniferous rocks of the Midland Valley for over 200 years. This work characterises organic matter from the Mississippian black shales of the Midland Valley from Wardie, Scotland. Biomarker analysis allowed the estimation of the degree of microbial transformation of organic matter, type of kerogen and thermal maturity during hydrocarbon generation. Parameters based on the biomarker indicators confirm a generally mixed type II/III kerogen. However, some samples contain mostly terrestrial organic matter, whilst others contain predominantly marine organic matter, which shows that the sedimentary environment varied greatly throughout the basin. The presence of gammacerane suggests water column stratification and anoxic conditions. Organic matter was much better protected from post-depositional alteration within the concretions, where higher TOC (total organic carbon) and TS (total sulphur) contents occur, than in the surrounding sediments. This can be induced by very early diagenetic formation of these concretions which protected organic matter from late diagenetic degradation.

Estimated values of vitrinite reflectance (Rc, Rcs) show that the sedimentary rocks reached the catagenesis stage. Most samples exhibit maximum organic matter maturation temperatures of around c60–90°C. However, stable isomers of phenyldibenzo[b,d]thiophene detected in some samples indicate that in some cases post-depositional hydrothermal activity affected maturation of organic matter increasing temperatures to as high as c174°C.

The morphology of sterile and fertile structures (terminal strobili) of the Upper Devonian heterosporous lycopsid Kossoviella timanica Petrosjan 1984 from northern Russia (North Timan) is re-described: the axes are dichotomously branched; sterile leaves are narrow with smooth margins; the transition from sterile axes to strobili is gradual; the strobili are narrow and cylindrical, occasionally dichotomously branched; sporophylls are long, lanceolate, with crenulated margins; megasporangia with thin, mostly destroyed, sporangium walls contain one or two tetrads of large megaspores without a gula; numerous microspore tetrads are present in the microsporangia; both mega- and microspores are cavate, with a two-layered sporoderm; the outer layer of the sporoderm of both mega- and microspores consists of a net of intertwined cylindrical elements; the inner layer of the megaspore sporoderm is a basal lamina; and the inner homogeneous layer of the microspore sporoderm is split into multilamellate zones near the arms of the proximal scar. A comparison between abortive and fertile megaspores, some of which apparently were not completely mature, allows us to hypothesise that the enlargement and lateral stretching of structural units of the sporoderm, and the spaces between them, took place during the final stages of ontogenesis of megaspores along with the additional accumulation of amorphous sporopollenin. Both layers of the megaspore sporoderm, as well as the cavity between them, developed early in the ontogenesis. Although Kossoviella timanica was certainly a unique Late Devonian plant, it bears some resemblance to the Givetian heterosporous, bisporangiate lycopsid Yuguangia ordinata in having dichotomously branching axes, sporophylls with spiny margins and strobili with proximal megasporangia and distal microsporangia. Kossoviella timanica is also similar to the Famennian bisporangiate lycopsid Bisporangiostrobus harrisii in lacking a ligula and in having dichotomously branching strobili with proximal megasporangia and distal microsporangia.