and since 2R='95 in., a='59 R nearly. This is closer than could be expected considering the extremely rough measurement of the two commas. It will be remembered that the value of a is known to be generally about 55 R to 6R. IX. Notices respecting New Books. An Elementary Treatise on Spherical Harmonics and Subjects con- μ form, the elementary properties of the expressions known by the name of Laplace's functions, or Spherical Harmonics." More than two fifths of it, comprised in chapters ii. and iii., are devoted to the discussion of the particular case in which the spherical Surface Harmonic (P.) is a function of μ only. This function Mr. Ferrers calls a Zonal Surface Harmonic; it is the same function as that which Mr. Todhunter calls a "Legendre's Coefficient." The author investigates briefly and elegantly the chief properties of P1, and then applies them to determine the potential of various forms of attracting matter. Of these the last which he considers is the following comprehensive case:-to find "the potential of a spherical shell of finite thickness whose density is any solid zonal harmonic." These investigations serve as a foundation for those contained in the following chapters. Thus, in the fourth chapter the subject of General, Tesseral, and Sectorial Spherical Harmonics is somewhat briefly treated. It is well known that the general Surface Harmonic of the degree i consists of 2i+1 terms of the form to these terms individually Mr. Ferrers gives the name of Tesseral Surface Harmonics of the degree i and order; and the last of these terms, viz. those for which ai, he calls Sectorial Surface Harmonics of the degree i. In the fifth chapter he notices very briefly the Spherical Harmonics "of the second kind;" and in the sixth chapter he treats of Ellipsoidal Harmonics, a name which he proposes to give to the functions called by Mr. Todhunter "Lame's functions." It is well known that one of the standing difficulties of this subject resides in the proof of the theorem that "any function which does not become infinite between the limits of integration can be expanded in a series of Spherical Harmonics." Thus, Mr. Todhunter notices four or five proofs, and is not, to all appearance, completely satisfied with any one of them. It may therefore be of some interest to give a sketch of the proof adopted by Mr. Ferrers. The principal discussion takes place with reference to Zonal Harmonics, though a proof of the general case is given on pp. 93-95. The method, then, is as follows:-He first obtains an expression for the potential of a spherical shell of uniform small thickness, whose density is A for the part corresponding to the value of μ from 1 to A, and B for the part corresponding to the value of μ from A to -1. He then extends the same method to the case in which the densities are A from μ=1 to μ=λ,, B from μ=λ, to μ=λ2, and C from μ=λ, to μ=-1. His next step is to take λ=λ and λ=λ+dλ, and thus arrives at the result that dλ {1+... +(2i+1)P(X)P(μ) +.....} has the value unity from μ=λ to μ=λ+dλ, and zero for other values of μ. Now if we suppose A,, A, ... to be continuous values of A ranging from 1 to -1, it is evident that the expression dλ. f(x){1+...+(2i+1)P¿(^,)Pi(μ) + ..... }+ } dλ ƒ(λ2){1+ ...+(2i+1)P(^ ̧)P;(μ) + · · · }+... ... will equal f(A) when u=,, f(A) when μ=λ...; and consequently the whole expression must be f(p). But it is also plain that {ƒ(^,)P;(^,)+ƒ(^„)P¿(^2)+......+}dλ= ƒ(μ)Pi(μ)dμ, and consequently that f(u) can be expressed as a series whose general term is $(2i+1)P.(μ) ("' P.(μ)f(μ) . dp, the theorem to be proved. μ Instructions to Meteorological Observers in India, being the First Part of the Indian Meteorologist's Vade Mecum. By HENRY F. BLANFORD, Meteorological Reporter to the Government of India. Calcutta, 1876. Meteorology of India, being the Second Part of the Indian Meteorologist's Vade Mecum. By HENRY F. BLANFORD. Calcutta, 1877. Tables for the Reduction of Meteorological Observations in India. By HENRY F. BLANFORD. Caleutta, 1876. The works above mentioned constitute a complete Meteorological Library, and, although written expressly for India, are by no means restricted in interest to the Indian Peninsula, as they contain remarks of general application, especially relative to the instruments employed in Meteorological research. In the "Instructions" each instrument, including its varieties, is fully described; and the reader will find many valuable hints on the use of the Barometer, Thermometer, Actinometer, Hygrometer, Rain-gauge, Wind-vane, and Anemometer; also interesting articles on Cloud and Weather obser vations, with Hours and Reduction of Observations, the latter treating very fully of the most recent and exact methods employed. In the "Notes on Registration" and "Rules for Observers the amateur will find much important information. The second part of the Vade Mecum is a very valuable production: the portions of greater interest treat of the physical properties of air and vapour and the physical geography of India; the peculiar conformation of the surface of India, which is lucidly described, renders the country in relation to Meteorology an epitome of atmospheric physics. Students will derive much useful information from their conjoint study. The succeeding portions, on Temperature, Pressure, Wind and Rain, are full of important information; and the concluding part, on Storms, contains the most recent development of the Theory of Cyclones, especially the incurvature of the wind's motion in storms. X. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from p. 473.] March 20, 1878.-Henry Clifton Sorby, Esq., F.R.S., President, in the Chair. HE following communications were read: THE 1. "On the Chronological Value of the Triassic Strata of the South-western Counties." By W. A. E. Ussher, Esq., F.G.S. The author maintained that the general thinning-out of the Trias in the South-Devon and West-Somerset arca as it is traced northward, of which he adduced evidence, proves that this area was not connected with that of Gloucestershire and the midland counties until the later stages of the Keuper; and endeavoured to show by a comparison of sections that the area east of Taunton and south of the Mendips was not submerged before the deposition of the Lower Keuper Sandstone, and probably not until the later stages of its formation, the Quantocks acting as a barrier dividing the Bridgewater area from the Watchet valley. He thought that a subsidence progressing from south to north led to earlier deposition in South Devon, and to a consequent attenuation of the lower beds towards Watchet and Porlock. Hence the lowermost beds of the Trias of the south coast are much thicker than their more northerly equivalents, and probably were still thicker where the English Channel now flows, some beds perhaps dating as far back as Permian times. The presence of numerous fragments of igneous rocks (quartzporphyries) in the basement-beds of the South-Devon Trias, and the absence of known corresponding rocks in the county, led the author to infer that the cliffs and beds of the early Triassic sea were composed of such rocks, any undestroyed portions of which would probably occur either under the Triassic beds near Dartmoor and between Newton and Seaton, or in the area now occupied by the English Channel. As continuity is evident only in the upper division of the Trias, between the area of Devon and Somerset and that of the midland counties, and there is no unconformity in the former, the author maintained that the upper marls, upper sandstones, and probably the conglomerate and pebble-bed subdivision of Devon and Somerset, are equivalent in time to the Keuper series of the Midland counties, and that deposition took place in Devon and Somerset between Keuper and Bunter times, bridging over the hiatus marked by unconformity in the Midland counties. 2. "Note on an Os articulare, presumably that of Iguanodon Mantelli." By J. W. Hulke, Esq., F.R.S., F.G.S. 3. "Description of a new Fish from the Lower Chalk of Dover." By E. Tulley Newton, Esq., F.G.S. 4. Further remarks on adherent Carboniferous Productida." By R. Etheridge, jun., Esq., F.G.S. 5. "The Submarine Forest at the Alt Mouth." By T. Mellard Reade, Esq., F.G.S. April 3.-Henry Clifton Sorby, Esq., F.R.S., President, in the 1. "On an Unconformable Break at the base of the Cambrian Rocks near Llanberis." By George Maw, Esq., F.L.S., F.G.S. In a paper read before the Society on December 5, 1877 (Q. J. G. S. vol. xxxiv. p. 137), Prof. Hughes referred to an observation made by the author in 1867 as to the occurrence near Llanberis of an unconformable break, indicating the base of the Cambrian, and, while accepting the asserted existence of pre-Cambrian rocks in North Wales, placed the base of the Cambrian in a very different position, and maintained that the appearances described by Mr. Maw might be accounted for by lateral pressure acting upon beds of dissimilar texture and unequal hardness. The author had reexamined the section in question, and maintained his original interpretation of the phenomena, which he regarded as the earliest indication of the existence of a pre-Cambrian series. He accounted for differences observed in the supposed pre-Cambrian rocks at Moel Tryfaen and Llanberis by regarding them as having undergone different degrees of metamorphism. 2. "On the so-called Greenstones of Central and Eastern Cornwall." By J. Arthur Phillips, Esq., F.G.S. In this paper the author extended his investigations of the rocks formerly mapped as greenstones, from the western (see Q. J. G. S. vol. xxxii. p. 155) into the central and castern districts of Cornwall. He described in detail various rocks from different parts of these districts, the examination of which had led him to the following conclusions. The numerous lavas which occur here, in addition to the rocks met with in Western Cornwall, are so interbedded with the slates and schists as to lead to the conviction that they are con temporaneous; and, although much altered, they closely resemble lavas of more modern date. Sometimes they assume a distinctly schistose character. The crystalline greenstones are more varied and instructive than those of the western portion of the county; some of them are typical dolerites, while others are so altered as to consist only of a granular indefinite base, traversed by indistinct microlitic bodies. Their pyroxenic constituent is augite; and although many would call them diabases or melaphyres, the author regards it as more logical to regard them as ancient dolerites. Where these rocks are altered the augite is usually changed into hornblende and viridite, while the felspar becomes cloudy, and finally merges into a granular base. The crystals of augite are often gradually replaced by an assemblage of felted microlites; in other cases their outlines are preserved whilst their substance is replaced by hornblende, the rock being thus converted into a uralitedolerite or uralite-diabase. When these rocks do not contain augite, and are to a great extent composed of long bacillary hornblendic crystals made up of parallel belonites, the ends of which are frequently curved outwards, it is probable that hornblende was an original constituent of the rock, which is therefore a true diorite. Slaty or schistose greenstones are less frequent than in the western districts; but on St.-Cleer Down the "hornblende-slates" graduate imperceptibly from crystalline dolerites into clay-slate: these are not improbably of igneous origin. Some of the slaty blue elvans are identical in chemical composition with the dolerites, and may be highly metamorphosed ash-beds, although, from some of their characters, it seems more probable that they are true igneous rocks. The felspar in the brecciated slates is almost entirely plagioclase, and is derived from the disintegration of greenstones. With regard to the age of the rocks described, the author states that they are generally older than the granite; for the vesicular lavas and many slaty hornblendic bands are evidently contemporaneous with the slates among which they are bedded, while the latter are often displaced by the granite or traversed by granitic veins; and, further, the eruptive doleritic rocks which break through the sedimentary beds never traverse the granito, but are often interrupted by it. 3. "The Recession of the Falls of St. Anthony." By N. H. Winchell, Esq. Communicated by J. Geikie, Esq., F.R.S., F.G.S. The author's purpose in this paper was to arrive at an estimate of the date of the last glacial period from the rate of recession of the Falls of St. Anthony, near the junction of the Minnesota and Mississippi rivers. He stated that the country is covered with deposits of glacial origin, that between the present falls and Fort Snelling, a distance of eight miles, the existing river-gorge has been formed since the deposition of the newer Boulder-clay, and that the old river-valley is filled up with glacial deposits. The gorge is of very uniform character, being cut through hard limestones resting on soft sand rock, both lying quite horizontally. The country was settled in 1856; and the recession of the falls has since been very |