like and masterful views of women's powers and privileges. Women, he thought, ought to have every thing provided for them, and every trouble taken off their hands: so the less they meddled with business in any form, the better. But these very young notions gave way, as he saw more of life, to wiser and more practical ones. He found that women were not utterly helpless; and his love of justice, combined with his better opinion of their powers, made him quite willing to concede to them as much as he would have desired for himself; namely, full scope and opportunity for the exercise of all their faculties. This was shown by his giving lectures gratuitously in the Ladies' college for the first year after its foundation, and by the interest he felt in the success of those brave women who first attempted the study of medicine."

De Morgan's letters are of a kind which it is very interesting to receive at the natural intervals at which they are written. When taken en masse, the logico-mathematical language in which they are couched, amusing in small doses, and their wit, excellent but monotonous, become wearisome. It is too much like sitting down to a continuous reading of the Budget of paradoxes.

In regard to his ideas on religion, De Morgan was always extremely reticent; but in spite of the disastrous effect of his early training, and in spite of his strong aversion to unfounded beliefs, he preserved a deeply religious tone of mind, and a firm faith in the Christian religion. At the same time, nothing could be more frank and uncompromising than the way in which he meets the renewed insistance of his mother, upon the occasion of the death of a sister to whom he was much attached, that he should renounce his freedom of opinion. His letter, if somewhat severe and untender, is still a splendid example of that strong rectitude of mind which was characteristic of him, and which did not permit him to gain any thing, even family harmony, at the cost of concealment.

The last years of De Morgan's life were years of disappointment and grief. The university in which he had labored with untiring energy until the age of sixty became once more impossible to him. The reiterated pledges of its founders and subsequent directors, that the essence of its being should be absolute and complete religious equality in every portion of its organization, were broken; and De Morgan could not lend his countenance to a less liberal or a more worldly line of policy. Upon the refusal of the council to appoint to the

chair of mental philosophy and logic the Rev. James Martineau, who had been recommended by the senate on account of his wide reputation as a preacher of an unpopular sect, De Morgan once more handed in his resignation. A year later occurred the death of his second son, George, a young man of great mathematical promise, and one of the two first projectors of the present Mathematical society. From this time De Morgan's health and vigor were not what they had been; and after an attack of congestion of the brain, from which his recovery was slow, he died in 1871 of nervous prostration.

WHITE'S FOSSIL MOLLUSKS OF NORTH

AMERICA.

A review of the non-marine fossil Mollusca of North America. By C. A WHITE. Washington, Government printing-office, 1883. 1, 144, 3 p., 32 pl. sm. fo. [Annual report U. S. geological survey, 1881-82, separately paged.]

No work is more useful to the biologist, whether his studies relate to recent or to fossil forms, than the collection and careful illustration of scattered material. In the book under consideration, Dr. White has produced for the student of mollusks, in either their recent or their paleontological relations, a much-needed and permanently valuable work of reference. Owing to their wide range, fecundity and accessibility, the class of mollusks included under his title are, all over the world, better known, more thoroughly studied, and more easily collected, than those of the sea. Hence it is to be expected that the material for learning what lessons they have to teach will be available for students much sooner with the land and freshwater mollusks than with the marine species considered as a class. Publications such as this, perhaps more than any other single means, will serve to shorten the time which must elapse before such a condition of the science is reached. Stratigraphical paleontology will not be so much the gainer as biology in a wider sense, since the uniformity of lacustrine and fluviatile conditions interferes with that differentiation which makes of some groups of marine mollusks valuable indices of geological time.

Dr. White has brought together excellent figures of nearly all the species of the groups under consideration belonging to North American paleontology, from the oldest strata in which they are known, to and including the miocene tertiary. One doubtfully pliocene species is mentioned; but the fossils of the later marls, and such deposits as that of the Colorado

desert, are not considered. Most of these are known as recent shells also; but we think it would have been a useful addition to the collection if such extinct forms as Tryonia had been included.

To the catalogue in tabular form and the explanation of the plates are prefixed a statement of the object and method of the work, a résumé of the subject by zoological families, and some general considerations. In these last the author, we think, is the first to enunciate certain propositions, which, though simple, constitute an important advance over previous statements of the general topic. In brief, he points out the high probability that lacustrine, at first brackish-water forms, were derived from marine species by imprisonment due to rising seashores, forming, first estuaries, then lakes; afterward differentiated so as to become inured to water without salt, or, in other cases, exterminated by water too fresh, or in lakes without an outlet, by concentration of saline matters. This view is not wholly novel; but the author goes on to supplement it by pointing out how, from the gradual conversion of lakes into rivers, and the persistence of the latter through epochs of geological change, the remarkable persistency of fluviatile types is accounted for, and problems of present geographical distribution may

be solved.

Too much space would be required for an analysis of the work in detail: a few points have been noted for mention. It seems a little startling to have oysters, Anomiae, and mussels presented as non-marine, until we learn that they were of the peculiar brackish-water beds in the Laramie group, and were doubtless accustomed to almost lacustrine conditions. The oldest forms treated of are Naiadites and certain supposed Anodontae from the Devonian (the latter much suggesting in appearance Lithodomus and its allies); but if these were not, as is supposed, true fresh-water folk, then the earliest of the latter date from the trias. Six families of Conchifera, in all, and sixteen of Gastropoda, are represented in the catalogue. It might be suggested that an analogue of Unio belliplicatus may, perhaps, be found living in Nicaragua, and that Cerithidea lives rather abundantly on the Californian coast.

The proof-reading of this volume is not up to the usual standard of the Government printing-office, and the index is disappointingly meagre. The arrangement of the numbers to figures on the plates is confused and puzzling: it can hardly fail to cause a serious loss of time to those who consult them. On the other hand, the paper and press-work are above the average, and the execution of the figures unusually good.

GEODESY.

Geodetic night-signals. —Mr. C. O. Boutelle, of the U. S. coast-survey, finds that the magnesium light as used by the survey may be used for distances as great as forty-five to seventy miles, and that the ordinary student-lamp with a parabolic reflector may be seen as far as forty miles. A report on night-signals was published by the coast-survey last year. The advantages stated in the report, as derived from greater steadiness of the atmosphere, and comparative freedom from lateral refraction upon long lines of sight during night observations, have been signally verified during the seasons of 1881 and 1882.-(Rep. U.S. coast geod. surv., 1880.)

MATHEMATICS.

[859

A definite integral. — In a brief note, M. Korkines gives a simple proof of a theorem due to M. Tchébychef. The theorem relates to the integral f(x) (x) dæ, where ø and must satisfy one of the

two conditions: 1°, they simultaneously increase or simultaneously decrease for all values of x lying between zero and unity; 2°, or one of them must increase and the other decrease for the same values of x. In the first case, M. Tchébychef's theorem is

f(x) 4(x) dx > f(x) dx fy(x) dx;

ƒ9(x) 4(x) dx < f(x) dx f'(x)de.

M. Korkine makes these theorems the immediate consequence of a simple identity. - (Comptes rendus, Jan. 29.) T. C. [860

Linear differential equations. In a previous communication to the academy, M. Goursat has solved, for a special class of equations, the problem to find the entire number of substitutions to which a system of fundamental integrals of a given equation may be subjected, corresponding to all the different closed paths which the variable may describe. The general integral in that case was shown to be expressed by hypergeometric series of higher orders. In the present paper, M. Goursat develops more fully his method, and applies it to the equation of the third order, remarking that the method followed is identically the same for equations of any order. (Comptes rendus, Jan. 29.) T. C. [861

Functions of two independent variables. — M. Picard has given a series of notes upon this subject, determining the functions of two independent variables, u and v, which remain invariable when we effect upon u and v any of the infinite number of substitutions of a linear discontinuous group. In the present paper M. Picard considers, in a general

u = u' + iu", v = v' + iv'..

The author shows that every substitution of the group transforms each point of the limit of D into another point of the same limit. He also shows that there exist functions, F, of u and v, only defined in the region D, and which leave invariable all of the substitutions of the group. The only groups considered are those possessing this property; viz., we can always find in the region D a region R, having no point common with the limit of D, and such that, in the interior of R, there is one, and only one, point which corresponds to any point (u, v) by means of the substitutions of the group. (Comptes rendus, Jan. 29.) T. C. [862 Differential equations.-M. Steen treats certain differential equations of the second order, an account of which has already appeared in another place. The differential equations are of the form b tang x) y' + cy = 0, b tang x) v' + cv = 0;

y" (a cot x

"v" + (a cotx

Radius of gyration of a rifled projectile. Lieut. C. A. Stone deduces a formula for the determination of this value. Applied to the 700-lb. Butler shell, he obtains K = 4.1224"; while the bureau of ordnance, U.S.A., found by experiment for this shell, K 4.1005358". Lieut. Stone discusses, also, the ratio of the forces necessary to give translation and rotation to a rifled projectile, and the ratio of the ranges of a projectile measured on the horizontal and on an inclined plane in a non-resisting medium. — (Proc. U. S. nav. inst., viii. no. 4.) C. E. M. [864

Acoustics.

Hydrogen-whistles. Mr. Francis Galton has continued his researches upon the production of notes of excessively high pitch, and their audibility to different animals, wishing to test the powers of insects in this respect. The idea has occurred to him of blowing his high-pitched whistle with hydrogengas, and so increasing its shrillness. Preliminary experiments with coal-gas have given good results; and Mr. Galton thinks that he can produce a sound due to 624,000 vibrations per second. (Nature, March 22.) C. R. C. 1865

Intensity of sound. — Vierordt has studied the subject of the estimation of the intensity of sound by the process of dropping a body upon a sonorous plate. The intensity of the sound produced is proportional to he, where e is a co-efficient to be determined experimentally. A formula given by Oberbeck P

is,

log

lighter weight p, when e intensity of the sound produced by striking the plate is the same. A large number of measurements are recorded, from which the author concludes that there is a general measure of the strength of sound. With spheres of the same material, and plates of definite material and weight, the value of e varies but slightly with increasing weight of the sphere, or with variation in the height of fall. — (Ann. phys. chem., No. 3, 1883.)

Optics. (Photography.)

C. R. C.

[866

Astronomical photography. At the Meudon (France) observatory they are studying movements of photospheric matter with the aid of series of images obtained with the photographic revolver.' They are also working at photographic photometry, the principle being, that the intensities of two lightsources are in the inverse ratio of the time they take for the same photographic work; e.g., producing the same tint on two quite similar plates. The method will be applied to data of the comet of 1881, the full moon, etc.(Nature, March 15.) [867

W. H. P.

Astronomical photography. At the March meeting of the Royal astronomical society, Dr. Gould gave an account of his work at Cordova. He considered that he had been successful in photographing stars down to the tenth and a half or twelfth magnitude. Mr. Common showed a photograph he had taken of the great nebula in Orion, the appearance of which, in many parts, gave rise to an interesting discussion; the majority of those taking part inclining to the belief that the photograph represented certain unknown dark objects in space.(Brit. journ. phot., March 23.)

[No such appearance has been noted here in the excellent photographs of this object taken by the late Dr. Henry Draper.]-w. H. P. [868

Positive prints from a positive. - MM. Cros and Vergeraud have sent to the French photographic society a communication on the above subject. A suitable paper is covered with a solution of ammonium bichromate, 2 grams; glucose, 15 grams; water, 100 grams. This is dried, and exposed to the light under a positive. When the uncovered portions of the paper, which were at first of a decided yellow, have become gray, the exposure is discontinued, and a rapid immersion made in a silver bath, composed as follows: silver nitrate, 1 gram; acetic acid, 10 grams; water, 100 grams. The image appears immediately of a blood-red color, formed by the bichromate of silver. In all parts where the light has acted, the bichromate has been reduced by the glucose; and, where the variable opacities of the image have protected in different degrees the sensitive film, the bichromate of silver remains insoluble in the water of the subsequent washing. If dried by fire, the image remains red; if dried in the open air and in the light, especially in the sun, it becomes dark brown. To obtain a black image, it suffices to expose the dry prints to sulphurous-acid gas. A bath of sulphite of copper and potash in solution gives a more intense black.(Philad. phot., April.) W. H. P. [869

Electricity.

Electro-optical properties of quartz.-W. C. Röntgen confirms and extends results obtained in a former paper (Ann. phys. chem., no. 3). The specimens used were a thick circular plate, cut perpendicular to the principal axis of the crystal, and a sphere. The apparatus for investigating the quartz-sphere was an old microscope. The quartz was laid on the

object-stand, and the weighted microscope-tube let down upon it. There are three planes through the principal axis, making angles of 120° with each other, such that all pressures in these planes, or parallel to them, produce minimum electricity at the points of pressure. Pressure exerted perpendicular to these minimum planes produces maximum electricity. Each of the six fields into which the minimum planes divide the sphere possesses the property that all points of pressure within it are electrified to the same sign: these signs are opposite in adjacent fields. Pressure in the direction of the principal axis gives each of the six fields its peculiar sign: pressure in any other direction divides the sphere into two oppositely electrified halves, the plane of division passing through the principal axis. No direction of pressure produces electricity at the ends of the principal axis. If the direction of pressure is a maximum axis, the plane of division is the minimum plane perpendicular to it (the signs of the halves correspond to the signs of the fields in which the maximum axis lies); but, if the pressure is in this minimum plane, the electrification is exactly reversed. The experiments seem to show, that, if the direction of pressure rotates about the principal axis with an angular velocity w, the plane of division rotates in the opposite direction with a velocity 2 6. The author then shows that the optical properties of quartz in an electric field can be accounted for by the expansions and contractions which quartz undergoes under electrical strain, according to the principle of reversibility of piezoelectric effects pointed out by Lippmann. This result has also been reached independently by Kundt in Ann. phys. chem., no. 3. — (Ann. phys. chem., no. 4.) [870

J. T.

Tensions in guns.- Considering the longitudinal and hoop tensions in a thick hollow cylinder, Lieut. Stone, U.S.N., finds that the longitudinal tension is greatest on the outside, and the hoop tension is greatest on the inside, where an assumed distance of a point from the axis of the cylinder coincides with the internal radius. He shows the presence of a neutral surface, within which there is a longitudinal compression, and without, a longitudinal tension. The formula deduced, giving the value of the maximum hoop tension, differs considerably from that heretofore used. The existence of a neutral surface of longitudinal stress is of great interest in the construction of built-up guns. That a longitudinal contraction may accompany a circumferential expansion is a familiar result of experiment. These formulas may be used in calculating the tensions in built-up wire guns. · (Proc. U. S. nav. inst., viii. no. 3.) [872 Lighting buoys and railroad-cars. - The U. S. lighthouse board has placed a Pintsch lighted buoy at the entrance of New-York harbor at the request of the pilot commissioners. The Erie and the West Shore railroads have adopted this method of lighting cars in imitation of German railways. Gas made from coal-oil is stored by compression in reservoirs, and burned in peculiar burners, a regulator being used to preserve the desired pressure. (Marine reg.; R. R. gaz., April.) R. H. T.

C. E. M.

[873

A

Standard gauge system.-G. M. Bond, M.E., has described to the American society of mechanical engineers the system of standardizing gauges devised by Prof. Rogers of Harvard, and himself, for the Pratt & Whitney company of Hartford, and the comparator built for that company under their direction for establishing standard gauge measures. pair of standard inch-measures, worked down independently, were found to be exactly alike, the difference, if any exists, being less than 7 inch. Bond reports ready for inspection by the committee of the society, a set of end-measures varying by sixteenths of an inch, and a complete plant of tools and fixtures for producing standards, duplicating originals by machined work. - (Journ. Frankl. inst., May.) R. H. T. [875

CHEMISTRY. (Analytical.)

Estimation of sulphur in organic bodies. P. Claesson has perfected a method for the determination of sulphur in organic substances, which seems, from his results, to be capable of remedying the various defects that detract to a greater or less extent from the accuracy of the methods hitherto in use. It consists in burning the substance in a current of nitric dioxide and oxygen, and absorbing the sulphuric acid in a receiver containing water. The sulphuric acid may be determined by titration, or by precipitation as baric sulphate. The substance is placed in an ordinary combustion-tube, and behind it a roll of platinized asbestos. In front of the substance are placed several platinized asbestos rolls, and a small tube containing fuming nitric acid. combustion is conducted in the usual way, and finally the sulphuric as well as the nitric acid is expelled into the receiver. The author adduces results to show that a dilute solution of sulphuric acid may be evaporated to dryness on the water-bath without appreciable loss of the acid. (Zeitschr. anal. chem., xxii. 182.) C. F. M. [876

The

tracting the soluble arseniate with water, acidulating the solution with nitric acid, boiling to expel carbon dioxide, neutralizing carefully with ammonia (the reaction should be faintly alkaline rather than acid), and precipitating the arsenic in the cold with argentic nitrate as the brick-red salt Ag3 As 04. The latter is thrown on a filter, washed well, dissolved in nitric acid, and the silver determined by titration with ammonium or potassium sulpho-cyanate, whence the arsenic can readily be calculated. The results communicated showed very remarkable concordance, and apparently a high degree of accuracy. The exact degree of accuracy does not appear; since the percentage of arsenic in some of the substances tested was not determined gravimetrically, but assumed to be that required by theory. By this method, 0.1 gr. of enargite yielded 19.03 and 19.09% arsenic in successive trials. 0.05 gr. pure pronstite gave 15.08% arsenic, while 15.15% is theoretically required. An ore mixture gave respectively, 3.26, 3.30, 3.19, and 3.25% arsenic in different trials. copper matte yielded 0.47 and 0.46% arsenic in successive determinations. Antimony, the presence of which in solution would vitiate the results of analysis, is almost entirely excluded by the use of sodium carbonate in the fusion. In a mixture of the enargite above tested with stibnite, 19.13% arsenic was found. No experiments were made to test the solvent action of the ammonium nitrate in the solution on the argentic arseniate. The advantages claimed for the method are the great ease and rapidity with which a determination can be made, and the high degree of accuracy attainable, fully sufficient, at least, for technical purposes. (Col. sc. soc.; meeting Feb. 5.)

AGRICULTURE.

A

[879

Action of peat on insoluble phosphates.— In an extensive series of experiments carried out at the Moor experiment-station in Bremen, Fleischer finds that certain peats exert a very considerable solvent action on phosphates. The first experiments were made in the laboratory by intimately mixing finely ground peat and phosphate, adding water, and allowing the mixture to stand, usually for three days. Peat from the lowland moors showed no solvent action; but that from highland moors (sphagnum peat) acted upon the phosphates in every case but two, dissolving from three or four to over fifty per cent of the phosphoric acid present, according to the nature of the phosphatic material. The materials used may be arranged in about the following order, the more soluble first: pure dicalcic phosphate, precipitated tricalcic phosphate, fine raw bone, steamed bone, commercial precipitated phosphates, bone-ash, crude Mejillones guano, Lahn phosphate. The action appears to be due to the presence of free humic acid, which decomposes the phosphates. In several cases the action went so far as to produce free phosphoric acid. Addition of potash-salts was found to increase the solvent action. These results are entirely in harmony with those that have been obtained in fieldexperiments on these soils. Almost invariably, insoluble phosphates have given better results than soluble ones, the reason evidently being, that, owing to the small absorptive power of peat, the soluble phosphates are soon washed out of the soil, while the insoluble phosphates yield up their phosphoric acid so slowly that the plants can utilize most or all of it. Experiments were also made in composting phosphates and peat. Here, also, phosphoric acid was dissolved, but not to so great an extent as in the laboratory experiments, where a much more intimate

mixture of the materials was possible. From 0.6 to 9.2 per cent of the total phosphoric acid was dissolved. Potash salts increased the solubility of the phosphates. A large proportion of the phosphoric acid was rendered soluble in ammonium citrate; that is, brought into a condition similar to that of the socalled reverted phosphoric acid. In connection with these experiments, Kissling has studied the effect of the presence of various salts on the action of peat upon phosphates. Potassium sulphate increased the action decidedly, potassium chloride to a less degree, and sodium nitrate and kainit hardly at all. Gypsum and calcium chloride decreased the solvent action, and potassium carbonate destroyed it altogether, presumably by neutralizing the humic acid of the peat. The effect of the potassium sulphate was found to be almost exactly in proportion to the quantity used. Although the solvent action of peat, and of peat and potash salts, appears to be comparatively slight on the large scale, it is not without importance; since, in the soil, it may continue for a long time, and the products of the reaction may be continually removed by the movements of water in the soil and the action of vegetation. Fleischer found, that, after his mixtures of peat and phosphates were washed out, the action appeared to begin afresh ; and something very like this must occur in the soil. — (Landw. jahrb., xii. 129, 193.) H. P. A. [880

--

GEOLOGY.

The Bow and Belly River districts, NorthWest territory. The rocks of the foot-hills and east of the mountains, according to G. M. Dawson, are entirely of cretaceous and Laramie age, overlain by bowlder clay and other beds referable to the glacial epoch. The geology of the region is complicated by the fact, that, in the immediate vicinity of the mountains the beds change considerably in lithological character, the change being such as would be expected to occur on the approach to a shore-line. So far, no reason has been found to suppose that any beds newer than the Laramie (including under this general name the Judith River and Fort Union series) have been found in this district, or, indeed, in any part of the Canadian North-West territory. The general arrangement of the rocks is given in the following table:

I. Laramie (including Judith River series).-1. Beds of the Porcupine Hills massive sandstones, with shales, etc. 2. Willow Creek beds: reddish and purplish clays, with gray and yellow. ish sandstones. 3. St. Mary River series: sandstone shales and clays of general grayish or grayish-green colors. 4. Yellowish sandstones and shaly beds, with a mingling of fresh-water and brackish or marine mollusks.

II. Fore Hills.-1. Yellowish sandstones, with some shales, apparently irregular in thickness and character; mollusks all

marine.

III. Pierre group.-1. Blackish and lead-colored shales, with occasional sandstone intercalations, especially toward the mountains.

IV. Niobrara? - Belly River series: sandstones, shales, and sandy clays. Upper part generally grayish; lower, yellowish, and often banded by rapidly alternating beds. Fresh and brackish water mollusks.

Near its base, the Laramie of this region is a persistent lignite or coal-bearing formation. In the Pierre group, the most persistent coal-bearing horizon is at its base, although there is a coal-seam at its summit on Bow River. Mr. Dawson considers the coalbearing horizon at the base of the Pierre to be nearly equivalent to that at the base of the Chico group, which yields the coals of Vancouver Island at Nanaimo and Comox. (In this connection it is well to remember that the identity of the so-called Chico of Vancouver Island with the group of that name in