curately determinable than cross-section. Another somewhat serious mistake, since it is fundamental, is the statement on page 18, that specific resistance is 'the resistance of any particular substance as compared with the resistance of a piece of some other conductor, such as silver, both being of unit dimensions.' As a matter of fact, specific resistance, which is a very important term, is the resistance in ohms of a unit volume, and is entirely independent of any particular standard substance. The use of the term 'magnetic resistance,' on pages 219 to 221, is open to objection, since the term ' reluctance' is now almost universally employed to distinguish this quantity from electrical resistance.

Taken as a whole, however, the errors are not numerous, and the work is recommended as a text or reference book for those who desire to learn the principles, general construction and action of the various kinds of electrical machinery and instruments, with the exceptions already noted. F. B. CROCKER.

PHYSIOLOGICAL PHYSICS.

On the Spontaneous Heating and Ignition of Hay. BERTHELOT. Ann. Chim. Phys., 7, 2. p. 430. 1894.

The author finds that poorly dried hay may ignite when the rise in temperature is only to 140° C. (280° Fh.). The evolution of heat necessary for this rise of temperature is due to the absorption of oxygen in spite of the interrupted sprouting, which will only take place when the hay is quite wet. The chemical process involving this absorption of oxygen may continue until the hay is thoroughly dry.

Druck und Arbeitsleistung durch Wachsende Pflanzen. W. PFEFFER. Abh. d. Math.Phys. Kl. der K. Sachsicher Gesellschaft der Wiss., 20. p. 235. 1893.

Mr. Pfeffer investigated very carefully and ingeniously the pressure exerted by

parts of plants in growth, and found, for example, that a root point could exert a pressure of 10-15 atmospheres. He ascribes these forces to osmotic pressure, and criticises the view concerning the growth of the cell-wall, which ascribes it to simple plastic expansion.

La Lumière Physiologique. R. DUBOIS Rev. gén. des Sciences, 5. p. 415 and p. 529. 1894.

Part first contains a review of light emitting organisms, and a description of the organs involved. In part second the author treats the subject of the emission more thoroughly, describing the character of the light radiated, and finds that the brightest Pyrophorus radiates 1, 4 X 10 calorie in ten minutes.

The author summarizes his extensive investigations as follows:

Neither a perfect organ nor a perfect cell is necessary for the coming and going of the light. The cell produces the photogenic substance which, once formed, may light or not, according to the conditions surrounding it.

They must fulfill the conditions necessary for life, must contain oxygen and water, and have a suitable temperature.

The light (luminous energy) is found to be 90% of the total energy radiated.

Dubois made a fluorescent substance from the blood of Pyrophorus, which, like that from the animal itself, lost its peculiar property on being treated with weak acetic acid and regained it on treatment with ammonia.

All the causes which excite or destroy the activity of the protoplasm have a similar effect upon the production of the physiological light.

The production of light depends upon the change of living protoplasmic granulations into the condition of lifeless crystalline matter.

It is to be remembered that the secretions of Orya barbarica are acid, thus in this case excluding the explanation of Radziszewski. WILLIAM HALLOCK.

number which is restricted to one plane; no account is taken of the two essentially different meanings of V-1, and the idea of the versor is not distinguished from that of the vector.

MATHEMATICS.

The Principles of Differentiation in Space-Analysis. By A. MACFARLANE, D. Sc., LL. D. According to Hamilton the differentiation of a function of a quaternion presents novel difficulties due to the non-commutative character of a product of quaternions. There is in general no derived function, and it is necessary to define the differential in a new manner. Under certain conditions

there is an analogue to Taylor's Theorem, but it is very complex, and no use is made of it. Hamilton does not differentiate the general transcendental functions, but only these functions restricted to a constant plane.

The author shows that these anomalies are true of products of vectors, but not of functions of versors. In versor analysis there is a derived function, satisfying a generalized form of Lagrange's definition; and Taylor's Theorem takes on a form similar to that in ordinary analysis, only the order of the two quantities must be preserved. Let x and h denote two versors, then

f(x+h)=f (x)+f′ (x)h+} f′′ (x)h2+, etc., provided the order of the x and h be preserved throughout.

The author finds the derived functions of various transcendental functions in space. He also shows that there are two essentially different meanings of V-1; one, when made definite, means a quadrant of rotation. round a specified axis; while the other has no reference to direction, but distinguishes the area of a hyperbolic angle from the area of a circular angle. He also remarks that the theory of functions must be imperfect, because it is based upon a complex

* A paper read before the meeting of the American Mathematical Society, January 26, 1895. (Abstract.)

METEOROLOGY.

Neudrucke von Schriften und Karten ueber Meteorologie und Erdmagnetismus.

Dr. G. Hellmann, of Berlin, has undertaken the republication of certain old and rare writings relating to meteorology and terrestrial magnetism which have an important bearing on the history and development of these sciences. Very rare or typographically interesting works are printed in facsimile. Each reprint is preceded by an introduction, containing a general description of the book and its author. Although facsimile publications generally are so dear that only connoisseurs are able to buy them, yet, owing to the aid of the German Berlin Meteorological Society and its branch, the reprints are offered at a relatively low price by A. Asher & Co., Berlin. A few copies may also be had of A. L. Rotch, Blue Hill Observatory, Readville, Mass., at the publishers' prices. Each year one or two of the reprints will be issued, but the whole number will not exceed twelve. The following have already appeared: No. 1. Wetterbuechlein von wahrer Erkenntniss des Wetters. REYNMAN, 1510. 41 pages introduction and 14 pages facsimile. Price 6 M. = $1.50.

This is the oldest printed meteorological work in the German language and was very popular, having 34 editions in seventeen years. Nevertheless, it is now so scarce that hardly thirty-six copies can be found. No. 2. Récit de la Grande Expérience de l'Equilibre des Liqueurs. BLAISE PASCAL. Paris. 1648. 10 pages introduction and 20 pages facsimile. Price 3 M. = 75 cents. This little work is of the greatest impor

al Society of London.

LORD RAYLEIGH is delivering a course of six lectures on Waves and Vibrations at the Royal Institution of London. On April 5th he will lecture on 'Argon.'

THE Massachusetts Horticultural Society invites subscriptions for the erection of a monument in honor of the late Francis Parkman.

DR. KOSSELL, of Berlin, has accepted a call to the Professorship of Physiology at Marburg.

PROFESSOR C. L. DOOLITTLE, of Lehigh University, has been called to the chair of Mathematics in the University of Pennsylvania, and Mr. A. P. Brown has been appointed Assistant Professor of Geology and Mineralogy.

PROFESSOR JOHN B. CLARKE, of Amherst College, has accepted a call to a professorship of Political Economy in Columbia College.

DR. D. HACK TUKE, editor of the Journal of Mental Science, and well known for his writings on insanity, died in London, on March 5th, at the age of sixty-eight.

MR. J. W. HULKE, President of the Royal College of Surgeons of England, died re

and the other an advanced text-book. The same publishers announce: Louis Agassiz, his Life, Letters and Works, by Jules Marcou.

SOCIETIES AND ACADEMIES.

Two

BIOLOGICAL SOCIETY OF WASHINGTON, FEB. 23. MR. F. E. L. BEAL read a paper on the food habits of woodpeckers, based on the examination of more than 600 stomachs. He found that the Hairy and Downy woodpeckers (Dryobates villosus and pubescens) feed chiefly on insects, most of which are harmful species. They also eat wild fruits and seeds. The food of the flicker (Colaptes auratus) consists largely of ants. stomachs contained each more than three thousand ants, and these insects formed 45 per cent. of all the stomach contents examined. The Flicker also ate other noxious insects and some wild fruit, such as dogwood berries and wild grapes. The Redheaded woodpecker (Malanerpes erythrocephalus) feeds largely on insects, all of which are harmful species except a few predacious beetles. The vegetable food of the Redhead comprises wild fruits and some corn and cultivated fruit. The Yellow Bellied woodpecker, or Sapsucker (Sphyrapicus varius), is

the only one in which the vegetable food exceeds the animal. It feeds largely on the inner bark and sap of trees, and also on insects. More than two-thirds of the latter in the stomachs examined were ants.

Dr. C. Hart Merriam, commenting on this paper, said that one result of the study of birds' stomachs by the Division of Ornithology and Mammalogy of the Department of Agriculture had been to show a wider range of food than previously suspected. Each bird has its favorite foods, but when these fail it is usually able to find something else on which it can subsist. Furthermore, the food of most species varies in different localities and at different times of the year, so that the examination of a series of stomachs, however large, from a single locality is utterly insufficient to furnish a reliable index to the range of food of the species. Thus, while the 600 stomachs of woodpeckers examined by Professor Beal failed to show a single beech-nut, it is nevertheless true that in northern New York beech-nuts form, during winters followingnut years,' the principal article of food of three of the five species mentioned.

Mr. L. O. Howard remarked that it had been queried whether or not ants were more injurious than beneficial, and stated that as harborers of aphids and mealy-bugs they indirectly cause much damage, and are to be considered on the whole as decidedly injurious. He gave an interesting illustration of the manner in which ants had placed colonies of mealy-bugs on the artificially enlarged foliar nectar glands of certain Liberian coffee trees which had been placed in the hot-house of the Department of Agriculture.

Mr. F. A. Lucas described the general structure of the tongue of woodpeckers, noting the great difference between the tongue of the sapsucker (Sphyrapicus) and of most woodpeckers. In the sapsucker

the tongue was of moderate length and margined for some distance back from the tip with hair-like bristles, some standing out, others directed backward, thus forming a brush for securing syrup. In the other woodpeckers examined, the tongue was excessively long and armed towards the tip with a few sharp, reverted barbs, an arrangement which seemed admirable for extracting grubs from holes in trees.

Mr. B. E. Fernow, in closing the discussion, said that he was glad to see the rehabilitation of the woodpecker, a bird which, once considered very beneficial, had been latterly condemned as injurious, while the evidence now presented seemed to be in its favor.

Mr. F. A. Lucas exhibited some Abnormal Feet of Mammals, saying that abnormalities in the way of digits could be mostly grouped under three heads, duplication of digits, irregular additions to the number of digits, the extra ones budding out from the others, and increased number of digits due to reversion. The latter he considered to be the rarest of the three, most of the extra digits of polydactyle horses being simply cases of duplication, as in the specimen shown. The feet of a pig exhibited illustrated the irregular addition of digits, while two feet of a three-toed cow were thought to be cases of reversion. Feet of an old and young llama illustrated the transmission of abnormalities.

Mr. M. B. Waite gave notes on the flora of Washington and vicinity, which were the result of his own collecting. Two species were added to the flora, namely: Floerkia proserfinacoides, Willd. (already published), and Kyllingia primila, Michx.

Selaginella rupestris, Spring, which had not been found for many years, was rediscovered at Great Falls. New localities were given for a number of rare plants. Attention was called to some spurious and doubtful additions to the local flora. The