Assuming the width of the seas and continents to be 3,900 miles, the rigidity of the earth to be 3 × 108, as above, and the range of the tides to be 80 centimetres, Mr. Darwin computes and gives tables of the slopes, real and apparent, of the land at various distances from the coast. Such deflections, he thinks, might actually be observed at points near the coast, and the measurements thus obtained might possibly serve as a basis for computing a more trustworthy value of the earth's rigidity than we now possess.

Under the conditions above assumed, the amplitude of vertical displacement between high and low tide is 11.37 centimetres on the land at the coast.

"As long as h l"—i.e., the semi-range of the tide multiplied by the width of a sea or continent "remains constant, this vertical displacement remains the same; hence the high tides of ten or fifteen feet which are actually observed on the coasts of narrow seas must probably produce vertical oscillations of quite the same order as that computed." E. H. HALL.

LETTERS TO THE EDITOR.

[Correspondents are requested to be as brief as possible. The writer's name is in all cases required as proof of good faith.] Age of the rocks on the northern shore of Lake Superior.

PERMIT me, through the medium of your journal, to correct a mistake which Prof. N. H. Winchell has made (Tenth ann. rep. surv. Minn., p. 125) in stating that I regard the trap and sandstone of Lake Superior as Huronian.

Up to the present time I was not in a position, never having examined them, to express any opinion about the Lake Superior formations referred to.

During the past summer I have somewhat closely examined these around the whole of the Canadian shores, from Prince Arthur's Landing to Sault St. Mary, including the shores of Thunder Bay, Black Bay, and Nipigon Bay and Straits. I spent two months in this examination, travelling from point to point in a small boat.

My opinion now, respecting the character and age, - within certain limits of these rocks is very decided, and is as follows:

They occupy the geological interval elsewhere filled by those divisions of the great lower paleozoic system which underlie the Trenton group. Various considerations point to the Potsdam and Primordial Silurian (Lower Cambrian) as their nearest equivalents. They are entirely unconformable to, and physically distinct from, the Huronian. They are divisible on the Canadian shores into two, perhaps three, groups, between which there may be slight unconformities. These, however, are quite likely only such as might result from the intermingling of ordinary sedimentary strata with irregular layers of erupted volcanic material, molten, muddy, and fragmentary; the whole being subsequently, and even during their accumulation, further disturbed by faulting, and the irruption of igneous dykes and masses.

To my mind, there can be no doubt as to the nature of the causes which have built up the vast masses of strata, which now, together with ordinary sedimentary layers, form the so-called upper copper-bearing rocks of Lake Superior. They are essentially volcanic, subaërial, and subaqueous formations, and in every sense analogous to the wide-spread tertiary volcanic rocks of Australia and other regions. The only differences are their greater antiquity, and the consequent greater changes and modifications they have undergone through the operation of long-con

tinued metamorphic agencies, disturbance, and denudation; though these changes are far less than those which the rocks of the same age, and to some extent similar origin, have undergone in eastern America and in Britain; and in this they correspond with the higher fossiliferous groups in the respective regions.

The groups in ascending order are,

1. Black shales, flinty and argillaceous, banded chert, with black dolomites and beds of fine-grained dark-gray sandstone with mica in the bedding planes; the whole interbedded with massive diabase or dolerite, often columnar, the columns vertical. — Pie Island, McKay's Mountain, Thunder Cape, etc.

2. Red conglomerates, red and white and green mottled shales, red and white sandstones and dolomites; no gray or black beds. At perhaps a hundred and fifty or two hundred feet from the base, these become interstratified with massive beds of volcanic material, amygdaloids, melaphyres, tuffs, etc., making many thousand feet of strata. East shores of Black Bay, Nipigon Strait, St. Ignace and other islands, Michipicoton Island, Gargantua, Mamainse,

etc.

3. The Sault St. Mary sandstones. These may be only the upper part of 2, without any intermingling of volcanic material. The exposures on the Canadian side are too fragmentary and isolated to decide this. In any case the St. Mary sandstones are not younger than Chazy (Cambro Silurian), but in the absence of fossils it is impossible to correlate the Lake Superior groups exactly with any one of the subdivisions of the New York or the Atlantic coast series. This, however, is no sufficient reason for inventing and adopting new and unknown names for them; and I prefer to call them all Lower Cambrian, which includes Potsdam and Primordial Silurian. There is, at present, no evidence whatever of their holding any other place in the geological series. Through overlapping and faulting, all three divisions are found locally in contact, both with Huronian and with Laurentian rocks. The dips are generally southeastward, but vary greatly in amount, those of division 2 being often locally much higher than any observed either in divisions 1 or 3. A. R. C. SELWYN. Geol. and nat.-hist. survey of Canada.

Ottawa, December, 1882.

Movement of the arms in walking.

Every man has observed that the tendency to swing the arms while walking is a most natural one. The action is rhythmical, the anterior and posterior extremities of opposite sides of the body moving in unison. It is also involuntary, being performed most readily when thought is not bestowed upon it. When voluntarily suspended, as in the American army, it gives an air of stiffness.'

In view of these facts, does it not seem that the statement of Prof. J. D. Dana (Cephalization; Amer. journ. sc., xli. 1866, p. 167), sanctioned by Dr. T. Gill (Classif. families of mammals, 1872, p. 50), namely, that "Man stands alone among mammals in having the fore-limbs not only prehensile, but out of the inferior series, the posterior pair being the sole locomotive organs," must be somewhat modified? Have we not at least a ghost of a preexisting function? Does man walk by means of his feet and legs alone? FREDERICK W. TRUE. U. S. national museum, Washington, D.C.,

Nov. 18, 1882.

Cleaning birds.

When obliged to wash birds, collectors will find it an advantage to use salt and water instead of plain

water. The salt prevents the solution of the bloodglobules and consequent diffusion of the red haemaglobin. J. AMORY JEFFRIES.

THE ORIGIN OF CULTIVATED PLANTS. Origine des plantes cultivées, par ALPH. DE CANDOTLE. (Bibliotheque sc. internat., tom. xliii.) Paris: Baillière & Cie., 1883. 8vo.

It is a common saying, that the plants with which man has most to do, and which have rendered him the greatest service, are those of which botanists know the least. That this should hold true of the plants of immemorial cultivation, as regards both their limitation in species and their sources, is not to be wondered at. The reason why many of these cannot be identified with wild originals is because, in all probability, the originals have long been extinct. Even when spontaneous examples have been found, it is sometimes far more probable that these are the offspring of the cultivated plant relapsed into wildness, than that they are vestiges of an original stock. Indeed, plants of comparatively recent acquisition to Europe are still puzzles; of not a few the question is still open whether they originated in the new or in the old world. The herbalists and ante-Linnean botanists gave little attention to the original sources of the plants they described, and Linné still less. Following erroneous indications, he assigned the common sunflower to Peru; and its relative, the tubers of which we call artichokes, to Brazil; when he might have known that they both were sent to Europe from Canada. only within the present century that any considerable attempts have been made to solve such problems. Robert Brown, Humboldt, and the elder De Candolle opened the way; and Alphonse De Candolle, who has particular aptitude for this class of investigations, is one of the few who have undertaken to discuss this subject systematically. Almost thirty years ago, in his Géographie botanique raisonée (2 vols. 8vo, 1855), just before the Darwinian deluge, which swept away some of the old landmarks, and changed the face of many things, De Candolle discussed in detail the changes which have taken place in the habitation of species, and has a long chapter on the geographical origin of cultivated plants. In this the then existing knowledge is well brought up to date, systematized, and critically treated.

It is

This book is out of print. Greatly as it is needed, the author, who is older than he was, recoils before the labor of a new edition of the whole work. But he has taken up the

subject of the origin of cultivated plants anew, and the present volume is the result.

The number of species of cultivated plants. here passed in review seems at first sight to be wonderfully small, viz., only 247, or, reducing certain races to their supposed types, little over 240. But species cultivated for ornament and for medicine or for perfume are rigidly excluded; while, on the other hand, so insignificant a forage-plant as spurrey, so poor and weedy a pottage-plant as purslane, a plant which we know only in ornamental culture and for its medicinal product, castor-oil, and a fruit-tree of such slight pomological importance as the American persimmon, are included. The latter and its old-world analogue are, indeed, only enumerated; but no one cultivates persimmons in this country. It is said that no plant of established field-culture has ever gone out of cultivation, at least in modern times, except perhaps woad; but, thanks to the chemists, madder is doomed already, and indigo is to follow.

Although Humboldt could affirm, so late as in the year 1807, that the original country of the vegetables most useful to man remains an impenetrable secret, so great progress seems to have been since made that De Candolle is able to assort his 247 species into 199 furnished by the old world, 45 by America, and only three which are still doubtful in this regard. Here the chestnut, the red currant, the common mushroom, and the strawberry are counted as of European, properly enough; since they were first cultivated in the old world, although indigenous to North America as well. The latter country makes a poor show indeed, when it is said that its only indigenous nutritive plants worth cultivating are the sunflower-artichoke and a pumpkin, though Indian rice (Zizania) might have been turned to account if it were not for the true rice. We are not so clear as to any original inferiority, nor that these numbers might not have been more nearly equal if civilization had begun as early in the new as in the old world. Europe had the great advantage of lying adjacent to two other continents, and of being colonized from them by races which were already agricultural.

As respects the three plants of doubtful country, two are species of Cucurbita (moschata and ficifolia), comparatively unimportant and little known, which have reached Europe only recently, the latter within thirty or forty years; and the third is Phaseolus vulgaris, the bean of the Americans, whose right to it we propose to claim. And we would suggest that

its place in the list should be taken by the cocoanut, the only esculent species common to the two worlds within the tropics which we have reason to suppose was carried or drifted across the Pacific in prehistoric times. Being a littoral tree, with fruit capable of enduring long exposure to salt water, its dispersion is not so surprising. The question is, in which direction the dispersion was effected; and that perhaps can never be determined. In his general list De Candolle includes the Cocos nucifera among the plants of old-world origin, with queries whether of the Indian archipelago, or of Polynesia. In his former treatise he inclined to the theory of a transmission westward from the Pacific coast of Central America in the body of the present work, after full statements pro and con, he is disposed to reverse his former opinion. But, as the dispersion may have been mainly by natural agencies, the question may be relegated to another class of inquiries. The presumption arising from the fact that all other species of Cocos are American, may be offset by the asserted fact that, although the tree formed forests on the islands off Panama when these were first visited by Europeans, it would appear to have only recently reached the West Indies and the adjacent main. So useful a tree, if indigenous to one side of the isthmus, would have been transported to the other and to the islands beyond by the very earliest races of men.

As

to oceanic transport, judging from the charts, the drifting of cocoanuts from America to Polynesia by the great current south of the equator seems hardly more or less likely than the reverse by the return equatorial current north of it.

It would be well to give some account of our author's method of investigation and exposition, of the kinds of evidence which are brought to bear upon the questions discussed, botanical, paleontological and archeological, historical and linguistic, each bringing some light of its own sort, and in their coincidence giving all the assurance of which such inquiries admit. It would be interesting to show, moreover, that although in most cases the continent or even the country from which each plant came to Europe, or in which it has been immemorially cultivated, has been fairly well ascertained, their origin or parentage has not. Only one-third of them are really known to botanists in a natural or wild state; and from this number subtraction may be made of such as have been detected only once or twice, and which may merely have run wild: the common tobacco-plant of the new world, and

the bean of the old, are in this category. On the other hand, there are several which botanists confidently trace to indigenous originals from which the cultivated plant has undergone considerable alteration: of such are the olive, the vine of the old world, flax, and the garden poppy; and in America, the potato, the sunflower-artichoke, and the tomato. But we know not, and we probably shall never discover, the particular source or origin of the cereal grains of the old world, and of maize in the new; of sorghum and sugar-cane; of the pea, lentil, chick-pea, and peanut, and of the common white bean; of sweet-potato and yams; and nearly the same may be said of the peach, oranges and lemons, and of all squashes and pumpkins.

But we must conclude our brief review with a note upon two or three plants, the early history of which concerns our own country.

Lin

Phaseolus vulgaris, our common bean, 1 ranks in De Candolle's table as one of the three esculent plants, the home of which, even as to continent, is completely unknown. né credited it to India, as he did our Lima bean also; but he took no pains to investigate such questions. This has been so generally followed in the books, that even the Flora of British India in 1879 admits the species, adding that it is not anywhere clearly known as a wild plant. But Alph. De Candolle, in his former work, had discarded this view, on the ground that it had no Sanscrit name, and that there was no evidence of its early cultivation in India or farther East. Adhering, however, to the idea that our plant was the Dolichos and the Phaseolus or Phaselos of the Greeks, and of the Romans in the time of the Empire, he conjectured that its probable home was in some part of north-western Asia. But recently, as "no one would have dreamed of looking for its origin in the new world," he was greatly surprised when its fruits and seeds were found to abound in the tombs of the old Peruvians at Ancon, accompanied by many other grains or vegetable products, every one of them exclusively American. In his present very careful article he admits that we cannot be sure that it was known in Europe before the discovery of America, and that directly afterwards many varieties of it appeared all at once in the gardens, and the authors of the time began to speak of them; that most of the related species of the genus belong to South America, where, moreover, many sorts of beans were in cultivation before the

1 Bean in Great Britain is Faba (the fève of the French), and the varieties of Phaseolus are called French beans.

coming of the Spaniards: and the idea that it might have been native to both hemispheres is discarded as altogether improbable. Upon this showing, it would appear that the plant should have been set down as of American, rather than of wholly unknown, origin. Indeed, when all the evidence is brought out, the discovery of these beans in the Ancon tombs need excite no more surprise than that of the maize which accompanied them.

For maize, beans, and pumpkins were cultivated together, immemorially, all the way from the Isthmus to Canada. And, although some of the sorts of beans mentioned by Oviedo in 1526, as raised in great abundance in Nicaragua where they are native, and also of those everywhere met with by De Soto (1539-42) in his march from Tampa Bay in Florida to the Mississippi, doubtless belonged to Phaseolus lunatus, yet most if not all of those which at the same early period Jacques Cartier found cultivated by the Indians of Canada, must have belonged to Phaseolus vulgaris, or its dwarf variety P. nanus; for only these are well adapted to the climate of Canada especially the low and precocious variety, which alone has time to mature between the spring and the autumn frosts. Indeed those same beans, derived from the Indians along with maize and pumpkins, have doubtless continued here in New England in direct descent, to form that staple diet for which the northern part of the coast of Massachusetts has long been famous; so that when Rufus Choate, defending a ship-captain against a charge of ill-treatment in having fed his crew exclusively upon it, rehearsed, in his accustomed affluence of language, the praises of "that excellent esculent and superlatively succulent vegetable, the bean,' he was celebrating the good qualities of a distinctively and aboriginally American article of food.

We are not to suppose, however, that this species had its home in North America, at least north of Mexico. The same may be said of our squashes and pumpkin, for which similar reclamation may be attempted upon another occasion.

The cultivators of more than one department of science have reason to thank our author for having returned in mature age to the studies of a third of a century ago, and to admire the thoroughness, patience, sound judgment, affluence of knowledge, and felicity of exposition, which characterize this, as indeed they do all his writings. We are well pleased that the first number of our new journal should introduce to

the American public an important contribution to science by De Candolle. ASA GRAY.

NATURAL HISTORY OF MINNESOTA. The geological and natural-history survey of Minnesota. The tenth annual report for the year 1881. N. H. Winchell, State geologist. St. Paul 1882. 254 p., 14 pl. 8vo.

THE principal part of this volume consists in the Preliminary list of rocks and Typical thin sections of the rocks of the cupriferous series in Minnesota, articles which appear to be the result of the penurious way in which Minnesota, in common with many other states, deals with her geological survey, compelling the state geologist to do work that ought to be done only by competent skilled lithologists. The results in this case, as elsewhere under similar circumstances in our country, are the same as they would be with paleontology, were the average state geologist compelled to work up all the fossils of his survey. Good lithological work requires something more than a microscope, a few thin sections, and a fair knowledge of minerals.

The convenient summary of opinions which have been held of certain rocks in the LakeSuperior region given on pp. 123-126 appears to be a digest of the more elaborate statements made in Dr. Wadsworth's notes on the geology of this district (Bull. mus. comp. zoöl., vii. No. 1), with additions of a later date, although no credit is given to that writer; on another page of SCIENCE, Mr. Selwyn takes exceptions to the views accredited to him, though Mr. Winchell would seem at first sight to be warranted in his statements from Mr. Selwyn's Canadian report of 1877-78, pp. 9 A, 14 A. The execution of the three maps accompanying the Minnesota report is to be praised.

In the zoological section of the report, Mr. C. L. Herrick presents a second contribution to a knowledge of the fresh-water Crustacea of the state. In this, as in his first paper (Seventh report, 1878), he limits himself almost entirely to the microscopic Entomostraca. These two papers, with Birge's Notes on Cladocera (of Cambridge, Mass., and Madison, Wisc.), comprise about all the systematic work on these animals done in this country. There is as yet, then, no basis for a discussion of their geographical distribution. According to Mr. Herrick, sixteen out of the thirty-three species described are also European. Thirteen species are new, and two new genera are established. Looking over

the specific descriptions, it appears to us that Mr. Herrick trusts too much to such characters as the number and arrangement of the joints of the antennae, which change with the growth of the individual. Even sexual maturity in these animals does not determine the limit of structural change.

Besides the microscopic forms, two species of cray-fish are recorded, - Cambarus virilis Hagen and C. signifer sp. nov. Attention is again drawn to the curious fact that size does

not govern the transition from the second form or sexually immature (?) male to the 'first form or perfected state; the second form often exceeding the first in its dimensions. Zoologists whose lot it is to live in a cray-fish country cannot be too strongly urged to study the habits and physiology of these so-called dimorphic males. Types of the 'new' species, C. signifer, kindly communicated by Mr. Herrick, prove to be C. immunis Hagen. Eleven plates accompany this memoir.

MATHEMATICS.

Quadrature of the circle. In vol. xx. of the Mathematische annalen, Lindemann gave a proof of the fact that π cannot be a root of an equation of any degree with rational co-efficients. This is a most remarkable paper, as it thus contains the first direct, absolute proof that has ever been given of the impossibility of the quadrature of the circle. M. Lindemann's investigation is based upon, and presupposes a knowledge of, Hermite's earlier paper, in which he showed that e, the Napierian base, cannot be the root of an equation with rational co-efficients. The fact that Lindemann has started from Hermite's results makes his paper rather hard reading; and on this account, the author of the article at present referred to, M. Rouché, has thought it worth while to give an account of the work done by Hermite, and more recently by Lindemann, and at the same time to simplify the processes in both cases. M. Rouché has really done very little in the way of simplification, but by bringing together the proofs he has produced an interesting and valuable paper. He professes the belief that the last word has not yet been said on the subject, but that another and simpler proof will yet be given of the fact that cannot be a root of any equation of any degree with rational co-efficients. Lindemann has certainly done a splendid piece of work in thus absolutely proving the impossibility of 'squaring the circle;' and it is only to be regretted that his work will not carry conviction to the minds of those mistaken individuals, the 'circle-squarers.' But it is hardly to be supposed that they will be convinced of the futility of their task, any more than the perpetual-motion inventors were convinced by the discovery and enunciation of the principles of the conservation of energy. -(Nouv. annales, Jan., 1883.) T. C.

[1

Geodesic lines. The author, Herr A. v. Braunmühl, considers the case of geodesics upon triaxial surfaces of the second order. He derives first Weiertrass' formulas for a general geodesic, and obtains forms for the entering constants in terms of the double theta-functions, rendering them easy of computation. Examples are given of the computation of geodesic lines in the general and in several special cases. The latter, and newer part of the paper, contains a derivation of the equations of the envelopes of geodesics, and a discussion of the same. The envelope is determined by aid of the hyperelliptic functions, and special applications are made to the ellipsoid and two sheeted hyperboloid. Numerous references are given to previous investigations.-(Math. annalen, XX., 1882.) T. C.

[2

Abelian and theta functions. - Prof. Cayley in this memoir has reproduced with additional developments the course of lectures which he delivered in the Johns Hopkins University, in the winter and spring of 1882. The memoir has a special interest as being the first of any consequence upon this subject in the English language, and, indeed, one of the most important in any language. The chief addition to the theory consists in the determination made for the cubic curve, and also (but not as yet in a perfect form) for the quartic curve of the differential expression dПn (in Clebsch and Gordan's notation) or d П12 (in Prof. Cayley's notation) in the Π in the final normal

integral of the third kind

form for which

parametric points interchangeable. The notation and demonstrations of Clebsch and Gordan are much simplified, and the theory is illustrated by examples, in regard to the cubic, the nodal quartic, and the general quartic respectively. The first three chapters only of the memoir have yet appeared. - (Amer. journ. math., v., 1883.) T. C. [3

PHYSICS. Acoustics.

Instrument for measuring the intensity of aerial vibrations. The instrument is based on an experiment described by the author (Lord Rayleigh) in the Proceedings of the Cambridge philosophical society for November, 1880; from which it appeared that a light disk, capable of moving about a vertical diameter, tends to set itself at right angles to the direction of alternating aërial currents. A brass tube is closed at one end with a glass plate, behind which is a slit through which pass rays of light from a lamp. A light mirror with attached magnets, such as are used for reflecting galvanometers, is suspended by a fine silk fibre so that the light from the slit is incident upon it at an angle of 45°, and, after reflection, passes out through the side of the tube by a glass window. A lens is so placed as to throw an image of the slit upon a scale. The opposite end of the tube, prolonged to a distance equal to that between the slit and mirror, is closed by a diaphragm of tissue-paper. A sliding tube extends for some distance beyond this. If the instrument is exposed to sounds whose half-wavelength is equal to the distance from the slit to the tissue-paper diaphragm, nodes are formed at each