Morgan immediately addressed a letter to the council, saying that he considered it discreditable to hold a professorship one moment longer in a college in which a professor might be removed and disgraced without any fault on his part. His resignation was accepted; but, after five years of private teaching and voluminous writing, he returned to his university. The sudden death of his successor at the end of a summer vacation induced him to offer to fill the vacancy until Christmas; and his belief, that, owing to changes in the management, his former objections to holding office would not recur, led him to accede to the request of the council that he should permanently resume his chair.

De Morgan's life is chiefly a record of his labors and his publications. He gave regularly twelve lectures every week, besides occasional extra courses; and for half an hour after each lecture he remained in his place to give personal assistance to those students who needed it. This, with an hour for correcting exercises, made four hours of solid work for each day in the week, without counting the time required for preparation. As a lecturer, he showed unrivalled skill. Mr. Sedley Taylor writes," His exposition combined excellences of the most varied kinds. It was clear, vivid, and succinct; rich, too, with abundance of illustration, always at the command of enormously wide reading and an astonishingly retentive memory. A voice of sonorous sweetness, a grand forehead, and a profile of classic beauty, intensified the impression of power which he made upon his auditors." He had a great hatred of cram, and no confidence in the power of an examination to determine the true value of a student's knowledge. "The claims which college examinations might be supposed to have on the studies of his pupils were never allowed to influence his programme in the slightest degree." He wrote the following in illustration of a Cambridge examination: Q. What is knowledge?

A. A thing to be examined in.

more economical to extract from a man of less than De Morgan's ability. He wrote onesixth of the Penny cyclopaedia, and he made voluminous contributions to the Journal of education, the British almanac and companion, the Dublin review, Notes and queries, the Athenaeum, the insurance journals, and to the memoirs and obituary notices of the Astronomical society, in whose affairs he took an active part for thirty years. His most important contributions to science are his papers on the Foundations of algebra and on the Syllogism, his text-books on Formal logic and on the Calculus, and his treatises in the Encyclopaedia metropolitana on the Calculus of functions and the Theory of probabilities.

Such an amount of labor left very little time for pleasure or relaxation; and, in fact, De Morgan writes near the end of his life, "I have never been hard working, but I have been very continuously at work. I have never sought relaxation. And why? Because it would have killed me. Amusement is real hard work to me." He had, however, an interesting circle of friends, who came frequently to his house, and in whose society he found great pleasure. Libri (the author of the History of mathematics), Arthur Hugh Clough, Miss Muloch, and Mrs. Follen the abolitionist, were among them. Throughout his life, also, he was an inveterate reader of novels, good and bad. Puzzles, and even puns, were interesting to him. He made a collection of over eight hundred anagrams on his own name; and his fondness for paradox was so well known that the circle-squarers all sent him their most curious investigations. was a thorough believer in the phenomena called spiritual. After describing some striking occurrences in spirit-rapping, he writes, "I was perfectly satisfied that some thing, or some body, or some spirit, was reading my thoughts;" and in regard to mesmerism, "Of the curative powers of this agent I have no more doubt than one has of things which he has constantly seen for years." His feelings on the subject of slavery were very intense, and he sat up the greater part of one night to finish Uncle Tom's cabin.

He

De Morgan presents another instance of the fact that a man's views of women in general are seldom dissociated from the result of his observations upon the few women who stand nearest to him. His clever wife had the effect of dispelling the prejudices with which his rather narrow-minded mother had inspired him. She writes, "I must not conceal the fact, that, in the earlier part of his life, he held man

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

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.

a

Too much space would be required for an analysis of the work in detail: a few points have been noted for mention. It seems 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) da, where 9 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 f1⁄4(x) dx;

f(x) 4(x) dx < f(x) dx f'v(x)dx.

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 y" (a cot xb tang x) y' + cy = = 0, v" + (u cotx b tang x) v + cv = 0;

-

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

lighter weight p, when the 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 è 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 26. 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

C. E. M.

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. [873

Heavy steel guns.- The chief of ordnance has called for information from the steel-makers of the United States, relative to the feasibility of making steel for ordnance, giving analyses of desired qualities. The act of 1883 provides for arming fortifications with steel guns. (Bull. iron steel assoc., April, 1883.) R. H. T. [874

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. A pair of standard inch-measures, worked down independently, were found to be exactly alike, the difference, if any exists, being less than 3 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