Several attempts have already been made to interpret the well-established results of biometry in accordance with the Mendelian scheme of inheritance. It is here attempted to ascertain the biometrical properties of a population of a more general type than has hitherto been examined, inheritance in which follows this scheme. It is hoped that in this way it will be possible to make a more exact analysis of the causes of human variability. The great body of available statistics show us that the deviations of a human measurement from its mean follow very closely the Normal Law of Errors, and, therefore, that the variability may be uniformly measured by the standard deviation corresponding to the square root of the mean square error. When there are two independent causes of variability capable of producing in an otherwise uniform population distributions with standard deviations σ1 and σ2, it is found that the distribution, when both causes act together, has a standard deviation . It is therefore desirable in analysing the causes of variability to deal with the square of the standard deviation as the measure of variability. We shall term this quantity the Variance of the normal population to which it refers, and we may now ascribe to the constituent causes fractions or percentages of the total variance which they together produce. It is desirable on the one hand that the elementary ideas at the basis of the calculus of correlations should be clearly understood, and easily expressed in ordinary language, and on the other that loose phrases about the “percentage of causation,” which obscure the essential distinction between the individual and the population, should be carefully avoided.

Ocean Drilling Program (ODP) Site 677 provided excellent material for high resolution stable isotope analysis of both benthonic and planktonic foraminifera through the entire Pleistocene and upper Pliocene. The oxygen isotope record is readily correlated with the SPECMAP stack (Imbrie et al. 1984) and with the record from DSDP 607 (Ruddiman et al. 1986) but a significantly better match with orbital models is obtained by departing from the timescale proposed by these authors below Stage 16 (620 000 years). It is the stronger contribution from the precession signal in the record from ODP Site 677 that provides the basis for the revised timescale. Our proposed modification to the timescale would imply that the currently adopted radiometric dates for the Matuyama–Brunhes boundary, the Jaramillo and Olduvai Subchrons and the Gauss–Matuyama boundary underestimate their true astronomical ages by between 5 and 7%.

Granites and related volcanic rocks of the Lachlan Fold Belt can be grouped into suites using chemical and petrographic data. The distinctive characteristics of suites reflect source-rock features. The first-order subdivision within the suites is between those derived from igneous and from sedimentary source rocks, the I- and S-types. Differences between the two types of source rocks and their derived granites are due to the sedimentary source material having been previously weathered at the Earth's surface. Chemically, the S-type granites are lower in Na, Ca, Sr and Fe3+/Fe2+, and higher in Cr and Ni. As a consequence, the S-types are always peraluminous and contain Al-rich minerals. A little over 50% of the I-type granites are metaluminous and these more mafic rocks contain hornblende. In the absence of associated mafic rocks, the more felsic and slightly peraluminous I-type granites may be difficult to distinguish from felsic S-type granites. This overlap in composition is to be expected and results from the restricted chemical composition of the lowest temperature felsic melts. The compositions of more mafic I- and S-type granites diverge, as a result of the incorporation of more mafic components from the source, either as restite or a component of higher temperature melt. There is no overlap in composition between the most mafic I- and S-type granites, whose compositions are closest to those of their respective source rocks. Likewise, the enclaves present in the more mafic granites have compositions reflecting those of their host rocks, and probably in most cases, the source rocks.

S-type granites have higher δ18O values and more evolved Sr and Nd isotopic compositions, although the radiogenic isotope compositions overlap with I-types. Although the isotopic compositions lie close to a mixing curve, it is thought that the amount of mixing in the source rocks was restricted, and occurred prior to partial melting. I-type granites are thought to have been derived from deep crust formed by underplating and thus are infracrustal, in contrast to the supracrustal S-type source rocks.

Crystallisation of feldspars from felsic granite melts leads to distinctive changes in the trace element compositions of more evolved I- and S-type granites. Most notably, P increases in abundance with fractionation of crystals from the more strongly peraluminous S-type felsic melts, while it decreases in abundance in the analogous, but weakly peraluminous, I-type melts.

The Central Asian Orogenic Belt (CAOB), also known as the Altaid Tectonic Collage, is characterised by a vast distribution of Paleozoic and Mesozoic granitic intrusions. The granitoids have a wide range of compositions and roughly show a temporal evolution from calcalkaline to alkaline to peralkaline series. The emplacement times for most granitic plutons fall between 500 Ma and 100 Ma, but only a small proportion of plutons have been precisely dated. The Nd-Sr isotopic compositions of these granitoids suggest their juvenile characteristics, hence implying a massive addition of new continental crust in the Phanerozoic. In this paper we document the available isotopic data to support this conclusion.

Most Phanerozoic granitoids of Central Asia are characterised by low initial Sr isotopic ratios, positive εNd(T) values and young Sm—Nd model ages (TDM) of 300-1200 Ma. This is in strong contrast with the coeval granitoids emplaced in the European Caledonides and Hercynides. The isotope data indicate their ‘juvenile’ character and suggest their derivation from source rocks or magmas separated shortly before from the upper mantle. Granitoids with negative εNd(T) values also exist, but they occur in the environs of Precambrian microcontinental blocks and their isotope compositions may reflect contamination by the older crust in the magma generation processes.

The evolution of the CAOB is probably related to accretion of young arc complexes and old terranes (microcontinents). However, the emplacement of large volumes of post-tectonic granites requires another mechanism, probably through a series of processes including underplating of massive basaltic magma, intercalation of basaltic magma with lower crustal granulites, partial melting of the mixed lithologic assemblages leading to generation of granitic liquids, followed by extensive fractional crystallisation. The proportions of the juvenile or mantle component for most granitoids of Central Asia are estimated to vary from 70% to 100%.

In this paper my object is, primarily, to investigate the properties of a certain operative symbol which appears to be of great utility in discussing q-functions. The first part of the paper will consist of an investigation into the various forms of

and the nature of the inverse operations symbolised by Δ−n. With certain restrictions as to continuity, etc., φ(x) will denote an arbitrary function of x.

A classification is proposed, based mainly on major element analytical data plotted in a coherent set of three simple chemical-mineralogical diagrams. The procedure follows two complementary steps at two different levels. The first is concerned with the individual sample: the sample is given a name (e.g. granite, adamellite, granodiorite) and its chemical and mineralogical characteristics are determined. The second one is more important: it aims at defining the type of magmatic association (or series) to which the studied sample or group of samples belongs. Three main types of association are distinguished: cafemic (from source-material mainly or completely mantle-derived), aluminous (mainly or completely derived by anatexis of continental crust), and alumino-cafemic (intermediate between the other two types). Subtypes are then distinguished among the cafemic and alumino-cafemic associations: calc-alkaline (or granodioritic), subalkaline (or monzonitic), alkaline (and peralkaline), tholeiitic (or gabbroic-trondhjemitic), etc. In the same way, numerous subtypes and variants are also distinguished among the aluminous associations using a set of complementary criteria such as quartz content, colour index, alkali ratio, quartz–alkalies relationships and alumina index.

Although involving a new approach using partly new criteria, this classification is consistent with most of the divisions used in previous typologies. The method may also be used in the classification of the volcanic equivalents of common plutonic rocks.

When we trace the parts of which this terrestrial system is composed, and when we view the general connection of those several parts, the whole presents a machine of a peculiar construction by which it is adapted to a certain end. We perceive a fabric, erected in wisdom, to obtain a purpose worthy of the power that is apparent in the production of it.

The prospect of partial melting of the subducted oceanic crust to produce arc magmatism has been debated for over 30 years. Debate has centred on the physical conditions of slab melting and the lack of a definitive, unambiguous geochemical signature and petrogenetic process. Experimental partial melting data for basalt over a wide range of pressures (1–32 kbar) and temperatures (700–1150°C) have shown that melt compositions are primarily trondhjemite–tonalite–dacite (TTD). High-Al (> 15% Al2O3 at the 70% SiO2 level) TTD melts are produced by high-pressure (≥ 5 kbar) partial melting of basalt, leaving a restite assemblage of garnet + clinopyroxene ± hornblende. A specific Cenozoic high-Al TTD (adakite) contains lower Y, Yb and Sc and higher Sr, Sr/Y, La/Yb and.Zr/Sm relative to other TTD types and is interpreted to represent a slab melt under garnet amphibolite to eclogite conditions. High-Al TTD with an adakite-like geochemical character is prevalent in the Archean as the result of a higher geotherm that facilitated slab melting. Cenozoic adakite localities are commonly associated with the subduction of young (<25 Ma), hot oceanic crust, which may provide a slab geotherm (≍9–10°C km−1) conducive for slab dehydration melting. Viable alternative or supporting tectonic effects that may enhance slab melting include highly oblique convergence and resultant high shear stresses and incipient subduction into a pristine hot mantle wedge. The minimum P–T conditions for slab melting are interpreted to be 22–26 kbar (75–85 km depth) and 750–800°C. This P–T regime is framed by the hornblende dehydration, 10°C/km, and wet basalt melting curves and coincides with numerous potential slab dehydration reactions, such as tremolite, biotite + quartz, serpentine, talc, Mg-chloritoid, paragonite, clinohumite and talc + phengite. Involvement of overthickened (>50 km) lower continental crust either via direct partial melting or as a contaminant in typical mantle wedge-derived arc magmas has been presented as an alternative to slab melting. However, the intermediate to felsic volcanic and plutonic rocks that involve the lower crust are more highly potassic, enriched in large ion lithophile elements and elevated in Sr isotopic values relative to Cenozoic adakites. Slab-derived adakites, on the other hand, ascend into and react with the mantle wedge and become progressively enriched in MgO, Cr and Ni while retaining their slab melt geochemical signature. Our studies in northern Kamchatka, Russia provide an excellent case example for adakite-mantle interaction and a rare glimpse of trapped slab melt veinlets in Na-metasomatised mantle xenoliths.

This paper is a structural and tectonic approach to the emplacement and deformation of granitoids. The main methods available in structural geology are briefly reviewed and this emphasises that (a) a wealth of data, particularly strain and shear sense, which pertain to these problems, can be determined in and around plutons; (b) given the nature, unlike many other crustal rock types, of granites to crystallise from isotropic through weakly anisotropic crystal suspension fluids, that deformation which has occurred in these states may not be well preserved; and (c) it is entirely possible, using this methodology, to separate deformation resulting from externally originating tectonic stresses from that which is associated with internal magma-related stresses. It is also recommended that the genetically-based Cloosian classification of granite fabrics and structures into “primary” (magmatic flow/magmatic flow current) and “secondary”, be abandoned and that a more observationally-based approach which classifies granite deformation fabrics and structures according to their time of occurrence relative to the crystallisation state of the congealing magma, be adopted (i.e. pre-full crystallisation deformation and crystal plastic strain deformation).

Examples of recent, structurally based, studies of emplacement mechanisms of plutons within tectonic settings are described and these show that, in general, space for magma can be created by the combination of tectonically-created cavities and internal magma-related buoyancy. This occurs in both transcurrent and extensional tectonic settings and there is no reason to doubt that it can happen in compressive-contractional regimes. It is concluded that transient and permanent space creation, such as may be exploited by available magmas, is a typical feature of the tectonically stressed and deforming lithosphere and this, in combination with the natural buoyancy and ascending tendency of magmas, can generate the varied emplacement mechanisms of granites.

Four balanced cross sections, supported by longitudinal sections, structure contour maps, stratigraphic separation diagrams and hangingwall sequence diagrams are keys to this interpretation of the Moine thrust, which forms the western margin of the Caledonides in NW Scotland. New basement and cover correlations between foreland and thrust belt give new slip estimates for the Moine thrust (∼ 77 km), the Loch More klippe (≥ 43 km), Glencoul sheet (20–25 km), Ben More sheet (∼28 km), Achall and Dundonnell ‘sheet II’ (∼28 km).

Like other major thrusts the Moine thrust moved in a smooth or rough fashion at different places and times, and many structures are a footwall response to its passage. Widely developed duplexes vary in thickness so that the roof thrust is folded and occasionally faulted; many late Caledonian folds in the Moine metasediments are of this origin. The presence of igneous bodies with contact aureoles increased the propensity to rough slip and this, by causing thickening in the footwall to the Moine thrust, is partly responsible for the Assynt culmination.

The previously accepted sequence of thrusting from foreland to hinterland, which has been deduced from the concept of ‘overstep’ of the Moine thrust across lower thrusts, is considered to be a misconception of thrust geometry. Instead, a ‘piggy-back’ sequence of thrusts, from higher to lower, is proposed.

The research of which this paper gives an account was originated by the late Dr Alexander Bruce and undertaken in conjunction with him; most of the material used had been accumulated by him during the later years of his life. The following preliminary communication made to the Pathological Society of Great Britain and Ireland in July 1910 represents in brief outline the position which had been reached at the time of Dr Bruce's lamented death:—

Metamorphic rocks showing an inverted metamorphic zonation from upper amphibolite fades immediately beneath the peridotite to greenschist fades at lower levels, crop out discontinuously along the base of the Semail ophiolite thrust sheet in the Oman Mountains of eastern Arabia. These metamorphic rocks show polyphase deformation, mylonitic fabrics, and have been disrupted, folded and imbricated, and in places form tectonic inclusions in a serpentinite melange. In the more intact sequences, garnet-clinopyroxene amphibolites, with rare hornblende-bearing marbles and banded quartzites, occur at the higher levels, whilst a wide range of metasedimentary and metabasaltic rocks occur in the greenschist fades. Low glaucophane content of amphiboles and low jadeite content of clinopyroxenes suggest relatively low pressures of crystallisation. The distribution coefficient KD for co-existing garnet and clinopyroxene suggests a temperature range of 670 to 750°C. Residual heat from the recently formed ophiolite probably provided the dominant heat source for metamorphism, although frictional heating could have supplemented this. The metamorphic rocks were produced during Cenomanian-Turonian (late Cretaceous) times.

The sub-ophiolite metamorphic rocks, together with basal serpentinite, Triassic alkaline and tholeiitic basalts (Haybi volcanic group), mountain-sized ‘exotic’ limestones and an upper Cretaceous sedimentary melange, comprise a distinct thrust slice termed the Haybi complex, which always overlies marine sediments of the allochthonous Hawasina complex and underlies the Semail ophiolite. The rocks of the Haybi complex are bounded by major thrust planes, the Semail thrust above and the Haybi thrust beneath, which truncate all schistosities, fold axes, imbricate thrusts and associated features. A model for ophiolite obducton is presented based on a palinspastic reconstruction of the allochthonous rocks on the Oman continental margin.

Thermal, mechanical and chemical exchange occurs between felsic and mafic magmas in dynamic magma systems. The occurrence and efficiency of such exchanges are constrained mainly by the intensive parameters, the compositions, and the mass fractions of the coexisting magmas. As these interacting parameters do not change simultaneously during the evolution of the granite systems, the exchanges appear sequentially, and affect magmatic systems at different structural levels, i.e. in magma chambers at depth, in the conduits, or after emplacement. Hybridisation processes are especially effective in the plutonic environment because contrasting magmas can interact over a long time-span before cooling. The different exchanges are complementary and tend to reduce the contrasts between the coexisting magmas. They can be extensive or limited in space and time; they are either combined into mixing processes which produce homogeneous rocks, or only into mingling processes which produce rocks with heterogeneities of various size-scales. Mafic microgranular enclaves represent the most common heterogeneities present in the granite plutons. The composite enclaves and the many types of mafic microgranular enclaves commonly associated in a single pluton, or in polygenic enclave swarms, are produced by the sequential occurrence of various exchanges between coexisting magmas with constantly changing intensive parameters and mass fractions. The complex succession and repetition of exchanges, and the resulting partial chemical and complete isotopic equilibration, mask the original identities of the initial components.

The postcranial skeleton of Acanthostega gunnari from the Famennian of East Greenland displays a unique, transitional, mixture of features conventionally associated with fishand tetrapod-like morphologies. The rhachitomous vertebral column has a primitive, barely differentiated atlas-axis complex, encloses an unconstricted notochordal canal, and the weakly ossified neural arches have poorly developed zygapophyses. More derived axial skeletal features include caudal vertebral proliferation and, transiently, neural radials supporting unbranched and unsegmented lepidotrichia. Sacral and post-sacral ribs reiterate uncinate cervical and anterior thoracic rib morphologies: a simple distal flange supplies a broad surface for iliac attachment. The octodactylous forelimb and hindlimb each articulate with an unsutured, foraminate endoskeletal girdle. A broad-bladed femoral shaft with extreme anterior torsion and associated flattened epipodials indicates a paddle-like hindlimb function. Phylogenetic analysis places Acanthostega as the sister-group of Ichthyostega plus all more advanced tetrapods. Tulerpeton appears to be a basal stemamniote plesion, tying the amphibian-amniote split to the uppermost Devonian. Caerorhachis may represent a more derived stem-amniote plesion. Postcranial evolutionary trends spanning the taxa traditionally associated with the fish-tetrapod transition are discussed in detail. Comparison between axial skeletons of primitive tetrapods suggests that plesiomorphic fish-like morphologies were re-patterned in a cranio-caudal direction with the emergence of tetrapod vertebral regionalisation. The evolution of digited limbs lags behind the initial enlargement of endoskeletal girdles, whereas digit evolution precedes the elaboration of complex carpal and tarsal articulations. Pentadactylous limbs appear to have stabilised independently in amniote and amphibian lineages; the colosteid Greererpeton has a pentadactylous manus, indicating that basal amphibian forelimbs may not be restricted to patterns of four digits or less.

Two figures are reciprocal when the properties of the first relative to the second are the same as those of the second relative to the first. Several kinds of reciprocity are known to mathematicians, and the theories of Inverse Figures and of Polar Reciprocals have been developed at great length, and have led to remarkable results. I propose to investigate a different kind of geometrical reciprocity, which is also capable of considerable development, and can be applied to the solution of mechanical problems.

In this concluding part of the series of papers on the plants preserved in the Rhynie chert-band, various remains of lower plants that occur in the peat will be described, and some general questions concerning the accumulation and preservation of the deposit considered. The paper is divided naturally into the parts enumerated below.

1. An account will be given of a number of forms of Fungi which are met with in the decayed remains of the vascular plants, and also in the peaty matrix. The fungal remains are so generally distributed that they can be regarded as forming an integral part of the peat. In connection with them, the question as to whether there is evidence of a mycorrhizal relation between any of the Fungi and the Vascular Cryptogams will be considered.

Finite difference numerical simulations were used to characterise the rates of diffusion-controlled dissolution and growth of zircon in melts of granitic composition under geologically realistic conditions. The simulations incorporated known solubility and Zr diffusivity relationships for melts containing 3 wt% dissolved H2O and were carried out in both one and thre dimensions under conditions of constant temperature, linearly time-dependent temperature and for a variety of host system thermal histories. The rate of zircon dissolution at constant temperature depends systematically on time (t½−12;), temperature (exp T−1) and degree of undersaturation of the melt with respect to zircon (in ppm Zr). Linear dissolution and growth rates fall in the range 10−19 10−15 cm s−1 at temperatures of 650-850°C. Radial rates are strongly dependent on crystal size (varying in inverse proportion to the radius, r): for r>30 μm, dissolution and growth rates fall between 10−17 and 10−13 cm s−1. During crustal magmatism, the chances of survival for relict cores of protolith zircons depend on several factors, the most important of which are: the initial radius of the zircon; the intensity and duration of the magmatic event; and the volume of the local melt reservoir with which the zircon interacts. In general, only the largest protolith zircons (>120 μm radius) are likely to survive magmatic events exceeding 850°C. Conversely, only the smallest zircons (<50 μm radius) are likely to be completely consumed during low-temperature anatexis (i.e. not exceeding ≍700°C).

The effects of stirring the zircon-melt system are unimportant to dissolution and growth behaviour; except under circumstances of extreme shearing (e.g. filter pressing?), zircon dissolution is controlled by diffusion of Zr in the melt.

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.”

I-type granites are produced by partial melting of older igneous rocks that are metaluminous and hence have not undergone any significant amount of chemical weathering. In the Lachlan Fold Belt of southeastern Australia and the Caledonian Fold Belt of Britain and Ireland there was a major magmatic event close to 400 Ma ago involving a massive introduction of heat into the crust. In both areas, that Caledonian-age event produced large volumes of I-type granite and related volcanic rocks. Granites of these two areas are not identical in character but they do show many similarities and are markedly different from many of the granites found in Mesozoic and younger fold belts. These younger, dominantly tonalitic, granites have compositions similar to those of the more felsic volcanic rocks forming at the present time above subduction zones. The Palaeozoic granites show little evidence of such a direct relationship to subduction. Within both the Caledonian and Lachlan belts there are some granites with a composition close to the younger tonalites. A particularly interesting case is that of the Tuross Head Tonalite of the Lachlan Fold Belt, which can be shown to have formed from slightly older source rocks by a process that we refer to as remagmatisation which has caused no significant change in composition. Since remagmatisation has reproduced the former source composition in the younger rocks, the wrong inference would result from the use of that composition to deduce the tectonic conditions at the time of formation of the tonalite. Granites, particularly the more mafic ones, will generally have compositions reflecting the compositions of their source rocks, and attempts to use granite compositions to reconstruct the tectonic environment at the time of formation of the granite may be looking instead at an older event. This is probably also the case for some andesites formed at continental margins.

Several arguments can be presented in favour of a general model for the production of I-type granite sources by underplating the crust, so that the source rocks are infracrustal. Such sources may contain a component of subducted sediments with the consequence that some of the compositional characteristics of sedimentary rocks may be present in I-type source rocks and in the granites derived from them. The small bodies of mafic granite and gabbro associated with island arc volcanism have an origin that can be related to the partial melting of subducted oceanic crust or of mantle material overlying such slabs and can be referred to as M-type. These rocks have compositions indistinguishable from those of the related volcanic rocks, except for a small component of cumulative material. The tonalitic I-type granites characteristic of the Cordillera are probably derived from such M-type rocks of basaltic to andesitic composition, which had been underplated beneath the crust. Some of the more mafic tonalites of the Caledonian-age fold belts may also have had a similar origin. More commonly, however, the plutonic rocks of the older belts are granodioritic and these probably represent the products of partial melting of older tonalitic I-type source rocks in the deep crust, these having compositions and origins analogous to the tonalites of the Cordillera. In this way, multiple episodes of partial melting, accompanied by fractionation of the magmas, can produce quite felsic rocks from original source rocks in the mantle or mantle wedge. These are essential processes in the evolution of the crust, since the first stages in this process produce new crust and the later magmatic events redistribute this material vertically without the addition of significant amounts of new crust.

The mammalian hair-fibre, together with the “inner root-sheath” (i.e. the axial layers of the follicle wall), grows upward by a proximal addition of cells. Changes in the inner root-sheath are responsible for the final shape and surface sculpture of the fibre. At its distal limit the inner root-sheath disintegrates owing to the effect of a de-keratinizing chemical agent.

A bent, undulated, or “crimped” fibre is due to a differentiated progress of the changes leading to keratinization of the “fibre cortex”. The cells which give rise to a “medulla” are different chemically and less compressible than cortical cells.