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infinite and undounded as applied to space, we shall content ourselves with a few remarks on the number of dimensions of space.
In ordinary geometry we say that the limit or boundary of a solid is a surface, the limit of a surface is a line, the limit of a line is a point, while the point is indivisible. The same thought is expressed in other words when we say a solid has three dimen sions, a surface two, a line one, while a point has no dimensions. Although the question of three dimensions of space has engaged the attention of many philosophers, no one has succeeded, to the present, to give a deep reason which is not based upon our experiences why after three passages over the limits (beginning with a solid) we should arrive at the indivisible.
to conceive solids or figures of more than three dimensions does not disprove their existence. If we imagine a world of two dimensions, in which all things consist of two dimensional figures, in which the inhabitants are so constituted that they can receive impressions only from things in the surface which constitutes their universe, and if we consider how unthinkable to such beings might appear figures of three dimensions, we may perhaps be prepared to admit the possibility of a space of more than three dimensions."
The relations of algebra and geometry are such that an equation involving n unknowns (n3) finds its geometric interpretation in a space whose dimensions are equal to the number of unknowns in the equation. The dual (algebraic and geometric) solution of algebraic equations enhances greatly their value and interest. Algebra does not restrict itself to a fixed number of unknowns. The question whether there is a corresponding practical geometry of a space whose dimensions are not fixed is of the greatest interest. We shall designate such a space by E, (0n∞), hence
En contains all the points of this space.
In constructing a geometry for E, it is necessary to select a set of axioms. These axioms must be so chosen that when E becomes an Ea (0a3) this geometry will lead to results barmonizing with our experiences. We proceed to give a few of the assumptions from an approved work on n-dimensional space." Through each point pass many E having the following properties:
ples of the ordinary geometry and plane trigonometry apply, independent of the axiom of parallels. If one angle of a triangle becomes an infinitesimal while the others remain finite, the ratio of the sides including the infinitesimal angle has unity for its limit.
Given a triangle with a constant finite side (c) and a constant adjacent angle ß, while the other adjacent angle (a) is infinitesi mal. The side (a) opposite a must also be infinitesimal. The lines which divide this a into n equal parts also divide a into n equal parts. Hence the ratio depends not upon a (a remaining infinitesimal) but upon c and 3. The limit of this ratio when and a is in the act of vanishing is denoted by ƒ (c). For
a' __ ƒ (c + h)
infinitesimal h, and
on which the may be made to
occupy completely its first position, while the individual points have changed their positions.
In each E there are many E on which the E n 2 n 3 When a = : 0, it follows that b = c, y = πmay be rotated in itself. By this rotation each point will de- log C, and the equation takes the form scribe a closed curve.
Starting with such assumptions, a geometry is constructed by collecting and classifying theorems which rest ultimately upon them. It is perhaps worthy of remark that attempts have been made to prove the impossibility of a fourth dimension."
As the main object of this article is the presentation of the nonEuclidean geometry of two dimensions, we proceed to develop the foundations on which rests a still more general two-dimensional geometry than the one noted in the fore-part of this paper. The understanding of the following processes will demand some mathematical attainments beyond what is required to appreciate the preceding. The formula which we desire to use is given in Killing's Nicht-Euklidische Raumformen, p. 14. We shall here give a simple outline of its development, referring the reader to that work for the rigorous proofs of some of our statements. We give here two almost axiomatic theorems which we shall need later.
To a triangle whose sides are all infinitesimals all the princi
1 Killing's Nicht-Euklidischen Raumformen, p. 64.
2 A short romance, entitled "Flatland," depicts the difficulty an inhabitant of a two-dimension world (a square) had to conceive of three-dimensional space, even after he had acquired some idea of a one-dimension, or line, world. The book is published by Roberts Brothers, Boston, Mass.
:s Killing's Nicht-Euklidischen Raumformen, p. 65.
4 Max Simon, Zu den Grundlagen der nicht-euklidischen Geometrie, p. 26.
In which k is some constant.
Substituting from (1) we obtain
= 0, we obtain da =
1 dy, which, from the triangle k2 in which these occur, is equivalent to saying, the sum of the angles of a plane triangle is constant and equal to two right-angles. This hypothesis leads to the Euclidean, or parabolic, geometry, making <0 makes dy > da, which shows that the sum of the angles of a plane triangle is less than two right-angles, and leads to Lobatschewsky, or hyperbolic, geometry. Finally, the hypothesis > 0 makes da > dy and indicates that the sum of k2 the angles of a plane triangle is greater than two right-angles. This gives rise to the elliptic geometry. The last is divided into two divisions - the single elliptic geometry and the double elliptic geometry. The names parabolic, hyperbolic, single elliptic, and double elliptic were applied to these spaces by Klein. The last two kinds of space are nearly alike. Euclidean geometry may be regarded as the common limit of the hyperbolic and the elliptic geometry. Considerations similar to the preceding lead to four kinds of n-dimensional space, and hence there are four kinds of n-dimentional geometry.
BY JOHN GIFFORD, SWATHMORE COLLEGE, PA.
IN the southern part of Louisiana there is an interesting region called the Altakapas Country It was once inhabited by a tribe of Indians of that name. They have the reputation of having been cannibals, but the later generations were peaceful and industrious. A few of them, they say, still exist and are famous for the skilful manner in which they make a peculiar kind of basket-work. Specimens of this may be seen in the museum of the Tulane University of Louisiana.
Roughly speaking, the region referred to embraces the land bordering the Gulf, west of the Atchafalaya and east of the Mermentan River. There is some discussion as to the extent of the country known by that name. As ordinarily used the term is elastic, but in a map printed in 1826 it includes all of what was then known as La Fayette, St. Mary's, and St. Martin's parishes and what is now known as Vermillion, La Fayette, St. Martin's, and St. Mary's.
Excepting five islands to which I shall refer later, this country is low, level, and rich. It is a part of the alluvium of the delta, which is intersected by many bayous, the arteries of Louisiana. The Atchafalaya is sometimes called "Old River," and was once no doubt the bed of the Mississippi. To-day it is reddened by the water from the Red River, in the mouth of which it begins. It is now perhaps the largest collateral artery of the main trunk. It was once clogged by an enormous raft, which was removed by the State in 1835. According to LeConte, it was a mass of timber eight miles long, seven hundred feet wide, and eight feet thick. It had been accumulating for more than fifty years, and at the time of its removal was covered with vegetation, and even with trees sixty feet high."
The Altakapas country consists of tilled lands, low meadows, and sea-marshes. The thriftiest of the first extends along that tortuous, sluggish stream called Bayou Teche. It is very rich and well cultivated, and by many is considered the garden-spot of the State. The banks of the Teche are lined by beautiful sugar plantations with old-time palatial residences and many modern refineries. Cane is there worked, and sugar and molasses manufactured according to the latest scientific methods. Enormous quantities of sugar, molasses, rice, cotton fibre, oil, and meal, and cypress lumber are shipped from this region. Even the moss on the trees is the source of an income of no little consequence.
This bayou begins in a network of streams in the Red River country and empties into the Atchafalaya below Grand Lake.
In few places in the world will you meet with such scenery. A trip down the Teche from St. Martinsville, a quaint town grey with age and finished" long ago, once called the little Paris, the land of Evangeline." on a sugar-packet is claimed by many, for scenery of its kind, to be unrivalled outside of Louisiana.
West of the Teche are miles of meadow-land, where many herds of horses and cattle pasture. Southward bordering the bays and Gulf is a region of sea-marshes and floating prairies. In the midst of this marsh, near Vermilion and Atchafalaya Bays, there is a chain of five islands, the highest land in lower Louisiana. The most western is called sometimes Miller's. sometimes Orange, and sometimes Jefferson's Island. It is the centre of Joseph Jefferson's famous plantation. The second is called Petite Anse or Avery's Island, where the Avery salt mine is located, the like of which, they say, does not exist in this country. The third is Week's Island. the fourth Cote Blanche, and the last Belle Isle.
The fact that five islands exist, much different from the surrounding country, of a different formation, in a straight line, about six miles apart, in the Mississippi Delta is curious. But stranger still the core of Avery's Island is a mass of rock salt of the purest kind, the only impurity, in fact, is .120 per cent of gypsum.
While prospecting for the opening of another mine, they found the bones of the mastodon, giant sloth and perhaps of other extinct animals in layers of material of a peaty nature. Here, also, were found beautiful potsherds and kitchen middens of the Indians who once lived there. There were also indications, I was told, that the Indians knew of the presence of this salt, although, according to Dr. Hilgard, it was not discovered by the whites until 1862. The bones and potsherds which were found there are now in the museum of the Tulane University of Louisiana.
To scientists and sightseers these mines are well worthy a visit, but unfortunately are rather inaccessible. It is easiest reached from New Iberia on the Southern Pacific Railroad There is a freight train running to the mines, which carries a passenger car. This remains, however, only long enough to collect the freight, which is seldom more than thirty minutes. There is only one train daily. The wagon-road is dangerous at times and never pleasant for vehicles owing to much mud, bad bridges and a pole-road over the marshes. The best way to reach it is on horseback, and for this purpose the Acadian ponies have no equal. They have a peculiar gait, faster than a fast walk, and lift their feet in a quick peculiar manner, which comes, they say, from pulling their feet quickly out of miry places.
The island is visible a long way off, and owing to the contrast with the surrounding country is very striking and prominent. The soil is pure sand and clay, in places mixed to form a loam.
To enter the mine you are apparently instantly dropped down a shaft one hundred and seventy feet deep. You are then in a huge cake of salt resembling ice. The weight above is supported by huge pillars of salt. Enormous quantities have been removed and the supply seems exhaustless. In places it is as clear and transparent as ice, in others granular, in others dark in color, and in others in irregular waves as though contorted by pressure. Here and there are pockets in which beautiful cubical crystals may be found, some of which the writer collected were 14 × 1 × 1 inches in size.
Although it affords ventilation, they have been troubled by a slight cave, which of course gradually washes larger in size, and a fine sand is thus washed into the mines.
In the Smithsonian Contributions, Vol. XXIII., Dr. Eugene Hilgard has described this formation in a paper entitled Geology in Lower Louisiana and the Salt Deposit of Petite Anse Island."
One of the other islands borders on the bay, where there is a bluff from which the formation may be studied.
Over in the neighboring parish of Calcasieu, near Lake Charles, there is a bed of sulphur which promises to become an important industry.
LETTERS TO THE EDITOR.
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On request in advance, one hundred copies of the number containing his communication will be furnished free to any correspondent.
The editor will be glad to publish any queries consonant with the character of the journal.
Nervous Diseases and Civilization.
IN Dr. Brinton's note on "Nervous Diseases in Low Races and Stages of Culture" in your issue of Dec. 16, he holds that those are in error who claim that "diseases of the nervous system have greatly increased with the development of civilization." My own very positive conviction, based upon a somewhat extended experience in the treatment of neurasthenic cases, is quite the reverse of this. In hospitals, in dispensaries, and among the very poor everywhere, a typical case of neurasthenia is difficult to find, but among the well-to-do and the intellectual, and especially among those in the professions and in the higher walks of business life who are in deadly earnest in the race for place and power, this peculiar impoverishment of nerve force that we term "neurasthenia" appears with alarming frequency.
Dr. Brinton says also that "civilization, so far from increasing this class of maladies, is one of the most efficient agents in reducing them in number and severity, especially when freed from religious excitement and competitive anxieties."
It should, however, be remembered that these "competitive anxieties." this worry of business and professional life, are the very conditions that civilization fosters and intensifies, and therefore civilization itself, with all that the term implies, with its railway, telegraph, telephone, and periodical press, exciting in ten thousand ways cerebral activity and worry, is the primary cause of this increase of nervousness among the higher classes in all countries. American nervousness is becoming almost a distinctive phrase, and it cannot be denied that in this country there are climatic conditions, and business and social environments, to the influence of which the nervous system is peculiarly susceptible, especially if complicated with evil habits, excesses, tobacco, alcohol, worry, and special excitements. In the older countries men plod along in the footsteps of their fathers, generation after generation, with little possibility, and therefore little thought, of entering a higher social grade. Here, on the contrary, no one is content to rest, with the possibility ever before him of stepping higher, and the race of life is all haste and unrest.
It has been aptly said that “the human body is a reservoir of force constantly escaping, constantly being renewed from the one centre of force the sun." A perfectly healthy man has a large amount of nerve force in reserve, and this reserve is not often exhausted, even approximately, by the necessary toil and wear of mind and muscle. A nervously exhausted man has a small amount of nerve force in reserve, and this reserve is often and speedily exhausted.
The margin on which he can draw is narrow, may be almost wiped out under the calls of emotion and of mental and bodily labor, but, just as with the strong man, the force is renewed from without by food and repose, so, like the strong man, he can keep on thinking and worrying until he dies, which may be long after the death of the strong man. While nervousness makes life painful and irritating, it does not of necessity shorten life, nor does it always destroy its usefulness. "The Indian squaw, sitting in front of her wigwam, keeps almost all of her force in reserve. The slow and easy drudgery of the savage domestic life in the open air, unblessed and uncursed by the exhausting sentiment of love, without reading or writing or calculating, without past or future, and only a dull present, never calls for the full quota of available nerve force; the larger part is always lying on its The sensitive white woman - pre-eminently the American woman with small inherited endowment of force; living indoors; torn and crossed by happy or unhappy love; subsisting on fiction, journals, receptions; waylaid at all hours by the cruelest of all robbers, worry and ambition, that seize the last unit of her force, can never hold a powerful reserve, but must live, and does live, in a physical sense, from hand to mouth, giving out quite as fast as she takes in,- much faster oftentimes,- and needing
longer periods of rest before and after any important campaign, and yet living as long as her Indian sister,- much longer it may be, bearing age far better, and carrying the affections and the feelings of youth into the decline of life" (Beard's "Sexual Neurasthenia," edited by A. D. Rockwell, M.D., E. B. Treat, New York publisher).
While Americans are undoubtedly a particularly nervous people, it is well to remember that a large number who think themselves nervously exhausted altogether misconceive their real condition. There is a vanity of disease as well as of dress. Many would rather be thought nervous than bilious or gouty, and are pleased with a diagnosis which touches the nerves rather than the stomach, bowels, or liver. As a matter of fact, the nervous system in many of these cases is strong enough, and would give no trouble were it not poisoned by the abnormal products of digestion that enter the blood and circulate freely through every tissue of the body, and the practical and all-important point is, to differentiate between these two classes. The array of symptoms in each class of cases is so much alike that real impoverishment of nerve force due to overwork and worry is often confounded with a poisoned condition of the system, the result of indolent habits and an excess of food; and, instead of rest, quiet, and soothing draughts, there is need of mental and physical activity,― less not more food, depletion rather than repletion.
Observations on the Cretaceous at Gay Head. SINCE my good friend Mr. David White has thought it worth while to give me a gentle reminder that I have been "a little confident and hasty in naming the various terranes at Gay Head,” it seems becoming and necessary that I should offer a few short remarks in elucidation of my statements published in these columns Sept. 23, 1892, and somewhat more fully in the Transactions of the Maryland Academy of Sciences, 1892, pp. 204-212. The points of difference between Mr. White and myself are not so great as to cause questions of moment to arise from their statement. It seems evident to me that if we could visit Gay Head together for only a few hours he would not be able to resist the evidence of observation which results from clearing away the covering of the face of the bluffs. My statements were derived from an examination of the body of the hill behind the loose, or thrown, material spread upon its faces In order to get at the beds in place, and which really constitute the promontory of Gay Head, it was necessary to dig away a few feet, or inches, of sand, clay, marl, and other slipped material from many parts of the face of the bluffs. This I did with the assistance of men from the neighborhood, and by this means it became possible for me to see that the axis of the whole system was a lead-colored clay, and that upon this eroded ridge of clay, which descends below lowest tidelevel, all the other geological members rest in their usual nearly horizontal order of sequence, as in Maryland and New Jersey. Since my return home, I have compared this clay more thoroughly with samples from the Woodbridge and Amboy districts of New Jersey, and the conviction is pressed upon me that the two are identical, as far as regards elements and type of structure. Nevertheless, as I have not found fossils in this clay, it is not possible for me to decide as to its exact horizon. From its relative posi tion in the column of strata, it should belong near the middle of the Albirupean formation, and therefore it should be a homologue of the dark member of the clay which occurs in the upper middle portion of the terranes at both Amboy and Woodbridge. The fact should not be forgotten that there are three distinct types of • Variegated Clay," and that these three belong to levels wide apart, and in three different formations, viz, the Potomac, the Albirupean, and the Raritan All these become variegated by disturbance and saturation with iron-bearing waters, while in their unchanged condition they are either lead-colored or drab. The use of the term "Potomac " in the papers above cited was in deference to the usage of Messrs. McGee and Darton, but with the accumulated evidence now present to my mind it does not seem likely that the axial clay of Gay Head and Martha's Vineyard can be referred to the "Variegated Clay" of the Potomac formation. as designated by Professor Fontaine and myself.
With regard to the Miocene fossils, especially the Cetacean vertebræ, settled into the broken surface of the Greensand, I did not enter into detail as to a wider distribution of those remains. It was not necessary for me to open out another series of observations beyond my immediate purpose. Let it suffice to say, however, that these remains are not confined to the surface of the Greensand, but that other specimens of the same were found by my own efforts at various points beyond this section of the bluffs. I cannot admit that "each season presents new phases and unsettled local stratigraphic complications" in more than a su¡ erficial sense. The body of the promontory is not broken up, although every storm does abstract from or disturb a part of its face. Photographs in my possession show various changes which have been made from time to time in the ends and sides of the beds there exposed, but not a dislocation of the main body of the ridge. They confirm also the observation that several buttresses of the Raritan" resting upon the lead-colored clay extend outward in original order from the ridge, while the intervening ones flanking the gullies are built of overthrown strata.
The so-called faulting is of a type common to clayey and sandy terranes, such as we are familiar with in the tide-water region of Maryland, where atmospheric agents, especially frost and thawing, open cracks somewhat parallel to the brow of a bluff. These cracks gape wider and extend deeper as the power of the sun increases, and at length cause a down-slide or fall when the beds become weakened by saturation with rain-water. Such fissures are also opened more widely and deeply by the dropping into them of coarse sand and pebbles, which spread apart by freezing and thawing. A notable example of this kind occurred to my observation on the projection of a heavy body of massive granite on Jones's branch, near Baltimore, where a fissure caused by freezing and thawing was gradually opened by an influx of sand, but which burst apart with almost explosive force one afternoon in the spring, following a season when numerous quartz pebbles had fallen into the crack from the overlying soil. The same phenomenon may be seen in the broken masses of granite which occur in places along the shores of Fisher's Island, near New London, Conn.
Several years ago, when many of the trees had been cleared from the brow of the cliffs of Potomac clay, along the shores of the Patapsco River, fissuring took place at intervals near the borders of these hills, and downthrows from the front of the bluffs were of common occurrence. In connection with such movements, and especially following a season of heavy autumnal rains, large cavities were rent in the cracking clays. some of which were large enough to admit a moderately large boy.
An example of the Gay-Head type of slipping, crushing, and swelling out, on a somewhat smaller scale, may be seen adjoining Sullivan's Cove, at the north western end of Round Bay, Severn River, Md., and several of the same features, on a grand scale, may be studied next the face of Maulden's ridge, on the Northeast River, Md.
The type of cutting and downthrow of the bluffs on the Vineyard Sound side of Gay Head is far more complex and varied than that of the south-west, or Atlantic, side. On the former the diagonal stroke of a surf from the south-east would cut deeper than the straight forward blow of the Atlantic on the south shore, and accordingly would be more effective in undermining the face of the terrane. The effects of those two methods of erosion are well shown on the opposite sides of this coast.
With regard to the aggregation of the non-marine lower portion of this series of formations, it seems probable that they were begun in the rocky hollows along the whole Atlantic coast from Maine to Cape Hatteras: that rapid currents carried large accumulations of broken stone and the elements of the crystalline rocks many miles out into a shallow sea, which was later barred out by the thick accumulations of these deposits, that thus a series of almost closed sounds was connected with the border of the continent, and that these sounds. extending in a sinuous north-east line, were the places of deposition of all the beds and strata which we now recognize as the Potomac, Albirupean, and the Raritan formations.
It has been my pleasure to read carefully both of Professor
Shaler's accounts of Gay Head, and to recognize the many good statements that he has made regarding particular features of the region; but I fail to see that he has given an adequate account of the real structure of the promontory, of its relations to other parts of the island, or of its relations to the similar deposits in Massachusetts, Rhode Island, and Long Island. P. R. UHLER.
Baltimore, Md., Dec. 19.
The Reticulated Structure of Protoplasm.
AFTER I had read the proof of the article on the reticulated structure of human red blood-corpuscles published in Science for Sept. 16, 1892, I received a book recently issued in Paris, and entitled "La Cellule Animale, sa Structure et sa Vie, Étude Biologique et Practique, par Joannes Chatin, Professeur adjoint à la Faculté des Sciences de Paris, Chargé du Cours d'Histologie à la Sorbonne, Membre de l'Académie de Médicine." In this delightful treatise, which brings the knowledge of the animal cell to the present time, there are one or two statements in regard to the structure of protoplasm which I should have liked to quote in the paper mentioned, but as that is now impossible, I bave asked the editor kindly to allow me to call attention to the following: —
C'est seulement en 1880, à la suite des recherches de Heitzmann, de Fromann et surtout des publications de Hanstein, que l'on commence à modifier la conception générale du protoplasma, pour le considerer, non plus comme une masse indifférente, mais comme une substance structurée.
Cette interprétation recontra une assez vive opposition. Il est des esprits scientifiques qui tiennent à demeurer constamment fideles aux principes dont ils se sont inspirés dès leurs premières études et qu'ils ne consentent que difficilement à abandonner. ... On doit distinguer dans le protoplasma deux parties: l'hyaloplasma et le paraplasma (Fig. 49).
L'hyaloplasma est une substance fibrillaire, hyaline, réfringente, formant un réseau au milieu d'une substance fluide, moins réfringente, qui est le paraplasma. Qu'on se représente une éponge a travées très tenues et contractiles, plongée dans une substance visqueuse et granulée qui remplirait ses cavités. Cette comparaison donne une idée grossière, mais assez exacte, de la masse protoplasmique prise dans son ensemble.
Elle paraît homogène si les mailles de l'hyaloplasma sont uniformes et qu'on fasse usage d'un faible grossissement. C'est ainsi que le protoplasma avait été étudié durant longtemps, et l'on s'explique d'autant mieux l'erreur dans laquelle on demeurait à l'égard de ses parties constitutives, qu'elles ne se distinguent en général qu'après l'intervention de certains réactifs comme l'acide osmique. Cependent l'histologie zoologique permet de les observer directement, et j'ai deja eu l'occasion de mentionner à cet égard l'exemple des cellules glandulaires de la Testacelle.
La structure réticulée du protoplasma s'observe dans les cellules amiboïdes comme dans les éléments à forme définie; l'étude des globules sanguins des Invertébrés (Vers, Crustacés, etc.), permet de constater aisément ce fait, d'abord révoqué en doute par des observateurs qui limitaient leurs recherches aux éléments de quelquels animaux supérieurs. ALFRED C. STOKES. Trenton, New Jersey.
netic instruments through the day. This great magnetic storm exhibited, if I am not mistaken, its phenomena in the southern, in the northern, in the eastern, as well as in the western, hemispheres. I watched the display for most of the two nights at West Springfield, Mass., and read many notices of it in the public prints.
I will add that at 10.45 P.M., Dec. 5. 1892, I saw, to me, an unique phenomenon. The moon was shining brightly, when diverging bands from the horizon in the north-north-west spread at the zenith 60° wide and converged again at the horizon in the south-south-east. They were like thin clouds, through which the stars were easily seen. The belt of Orion was exactly then in their midst. I can liken their shapes to nothing more than the vibrations of a cord, stretched from horizon, over the zenith, to horizon again. But they were stationary, and had so far disappeared at 11.30 P.M., standard time, that only curious traces and patches remained. I fancy that had not the moon been shining, these beautiful bands would have shown luminosity.
I judged that the radiating point in the north north-west was a trifle west of the magnetic meridian there; but our western declination here is some nine degrees. These were, of course, parallel bands, the divergence and convergence points being the effect of perspective. JAMES HYATT.
Honeymeadbrook Station, N. Y., Dec. 19.
Alleged Extinction of Mulatto.
A FEW months since an article appeared in a medical journal affirming that the pure mulatto colonies of southern Ohio were dying out after the fourth generation. Can any reader point me to the article in question, or to any definite information bearing on the permanence of the mulatto as a species (or variety)? Polytechnic Society, Louisville, Ky. JAS. LEWIS HOWE.
Lessons in Elementary Mechanics. By Sir PHILIP MAGNUS. New York, Longmans, Green, & Co, 1892. 370 p. 12°. Elementary Manual of Applied Mechanics. By ANDREW JAMIESON. London, Griffin & Co. 265 p. 12°. $1.25.
THESE two little treatises on mechanics illustrate two very distinct lines of college and school work, and are each characteristic of its class. Sir Philip Magnus has been distinguished for many years for his success as an author in this field, and his "lessons" have gone to their thirtieth thousand. The method of treatment of the subject is that which has been endorsed by authority and become "standard." The usual division of the subject into kinematics and dynamics is observed; and the latter is again subdivided, as customary, into kinetics and statics. Motion, as a more elementary idea than force, is first discussed, then follows the study of force and its effects in the production of equilibrium. The study of kinetics and of statics brings out the differences in effect when the body is free to move and when the forces produce no motion. The special feature of the book is the admirable manner in which energy is discussed and its operation illustrated. The extent of the work is such as is expected to suit the wants of the scholar of the first year, and is well adapted to the needs of those proposing to take the London University course or other of similar character. For this country it will make an excellent high-school course.
Professor Jamieson's work is characterized by its constant utilization of the principles taught, by application in the problems of every-day life and of constructive work. Even its illustrations have the advantage of being selected from among those of builders of machinery illustrating the principles treated. It is intended to meet the needs of students preparing for science and art examinations; but should be found of special value to those proposing to enter upon a course of technical education. It would be an admirable work for the better class of manual training schools, from which students pass into the technical colleges and professional schools of engineering. This establishment of a close relation between the principles taught and their useful applications in industry, and in the design and construction of machines,
is a matter in which the older text-books have utterly failed, but in which the author uniting a knowledge of principles with familiarity with practice may always succeed, and with great advantage to himself in competition with the teachers of the abstractions alone. Even the average practitioner would be uone the worse for a careful review of this little primer of mechanics. The best of books have their little defects; and we observe, in both these primers of mechanics, the old, and long-ago exploded, ideas on friction; no distinction being made between the laws of solid and those of fluid friction and the " mediate" friction of lubricated surfaces. Here are the old laws and the actual fact in "parallel column":
By J. HOWARD GORE. Bos218 p. 169. $1.25.
By MANSFIELD MERRIMAN. 170p. 8°.
ton, Houghton, Mifflin & Co. Introduction to Geodetic Surveying. New York, J. Wiley & Sons. THE first of these books is an historical account of the science of geodesy from the time of the ancients to the present, written in popular and interesting style. and is likely to prove most acceptable to the average reader, not an expert, who may desire to know something of the methods which have been adopted in the determination of the dimensions of the ear.h and their results. Its author has enjoyed the rare privilege of working from the original documents, as he states in his preface, and his sketch thus comes as authoritative. He commences his task by reference to, and brief descriptions of, the primitive notions of the older peoples, and their rude attempts to measure the earth. When their comparative ignorance of the subject, and their lack of instruments of exact measurement are considered, their approximations to the actual value of these dimensions seem little less than marvellous. The Chaldeans not only knew the earth to be "round" but made the degree equal to 4,000 steps of a camel, and the circumference of the earth about 24,000 miles. The Greeks and Romans took this quantity to be 250,000 stadia; the Arabians found it to be between 56 and 57 miles, 71 of our miles, per degree. Fernel, a French geometer of about 1550, measured the degree, and made it about 69 miles. Snell, in 1615, made the first scientific measurement of importance, however, making the arc of a meridian 55,072 toises, which is about 2,000 toises short. The toise is 6.4 feet.
Picard, in 1670, made the degree 57,060 toises, and so nearly correctly as to give to Newton his famous proof of the extension of the gravitation of the earth to its satellite. Later work is familiar to all interested in the subject, and it is a pleasure to note that the U. S. Coast Survey has done its share. It is considered by Professor Gore that the computations of Professor Harkness, making the ellipticity of the earth 1:300.2, and the quadrant to measure 10,001,816 meters, will prove most exact, although those of Bessel and Clarke are now generally received.
Professor Merriman's work is a formal and scientific treatise on the work of geodetic surveying. It includes a number of lectures on the figure of the earth, prepared as introductory, and also a discussion of the "Method of Least Squares," written especially for surveyors and engineers, as well as for students. The third and concluding part contains a synopsis of the methods and computations of precise triangulation. The introductory portion gives a history of the development of modern methods and some interesting facts relative to the work of the older geometers and