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MR. EDWARD ARNOLD'S NEW BOOKS.
THE EVOLUTION THEORY.

CARL ZEISSE

JENA.

MICROSCOPES

By AUGUST WEISMANN,
Professor of Zoology in the University of Freiburg.

TRANSLATED BY
Professor J. ARTHUR THOMSON and MARGARET THOMSON.
Two volumes, Royal 8vo. With many Illustrations. 32s, net.

BRANCHES-
NATURE.-"A work which, in its English no less than in its German
dress, will be read with extreme interest."

LONDON—29 Margaret Street, Regent Street, SPECTATOR. -"These two massive volumes are in themselves a monument of research and speculation that will out-live much of the Berlin. Frankfort o/M. Vienna. Hamburg. St. Petersburg perennial brass of the nineteenth century."

AN INTRODUCTION TO
THE THEORY OF OPTICS.

By ARTHUR SCHUSTER, Ph.D., Sc.D., F.R.S.,
Professor of Physics at the University of Manchester. Demy 8vo.

Suitable for Every With numerous Diagrams. 15s. net.

Class of Scientific TIMES."We have in Dr. Schuster's book a notable addition to the literature of Optical Theory, and one which will prove of value to every

and Technical student."

Research.
THE CHEMICAL SYNTHESIS
OF VITAL PRODUCTS,

PHOTO-
And the Inter-Relations between Organic Compounds.

By R. MELDOLA, F.R.S., Y.P.C.S., F.I.C., &c.,
Professor of Chemistry in the City and Guilds of London Technical College,

AND
Finsbury. Super Royal 8vo. 21s, net.
THE BECOUEREL RAYS
AND THE PROPERTIES OF RADIUM.

By the Hon. R. J. STRUTT,
Fellow of Trinity College, Cambridge. Demy 8vo. With Diagrams.

Write for Illustrated Catalogue is Mn" post
8s. 6d. net.

free on application.
London : EDWARD ARNOLD, 41 & 43 Maddox St., W. |
Verlag von WILHELM ENGELMANN in LEIPZIG.

VOR KURZEM ERSCHIEN:
NEWCOMB-ENGELMANNS

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MICROGRAPHIC PROJECTION

APPARATUS.

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POPULÄRE ASTRONOMIE.

DRITTE AUFLAGE.
Herausgegeben von Dr. H. C. VOGEL, Direktor des Astrophysikalischen Observatoriums

zu Potsdam.
MIT 198 ABBILDUNGEN IM TEXT UND AUF 12 TAFELN.

GR. 8". 1905. GEHEFTET M 15.-; IN LEINEN GEB. 1 16.-.
STANDARD FORKS.

The illustration shows one of our Standard Forks, mounted so that its vibration can be electrically maintained. The position of the electro-magnet can be adjusted lengthwise of the fork, as well as laterally and vertically. The height of

the mercury in the contact cup can also be finely adjusted.

Complete with 1 Standard Fork, £8.
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vibrations per second, as desired.)
Stand without Fork, £4.

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THE CAMBRIDGE SCIENTIFIC INSTRUMENT COMPANY, LTD.,

BE

THURSDAY, AUGUST 24, 1905.

under review it can be studied and developed with the completeness which its importance demands,

arithmetically, algebraically, and geometrically. SCHOOL MATHEMATICS.

Students are taught the use of logarithms, and also Easy Graphs. By H. S. Hall, M.A. Pp. vii +64. sufficient trigonometry to enable them to solve right

(London: Macinillan and Co., Ltd., 1905.) Price | angled triangles; they use compasses and setsquares, IS.

draw simple plans and elevations, and make dimenThe Rudiments of Practical Mathematics. By A. sioned free-hand sketches in pictorial or other pro

Consterdine, M,., and A. Barnes, M.A. Pp. jection, and they are introduced to the notion of a xv+332. (London : John Murray, 1905.) Price vector by means of displacement and velocity dia28. 6.

grams. In some places there may be an insufficient Elementary Practical Mathematics. By H. A. Stern, number of examples for the purposes of drill, but

V..., and W. H. Topham. Pp. viii + 110 + viii. altogether the subject is admirably developed and pre(London: George Bell and Sons.)

sented; the book is well adapted to its purpose, and 1 First Algebra. By W. M. Baker, M.A., and A. A.

its wide adoption would have a very beneficial effect. Bourne, M.A. Pp. X+176+ xxxv. (London : George

The “Elementary Practical Mathematics,” by Bell and Sons, 1905.) Price 25.

Messrs. Stern and Topham, is a preliminary volume Algebraical Grounding. By D. E. Shorto, M.A. comprising the first nine chapters of a more complete Pp. 46. (London : Rivington, 1905.) Price is, net.

text-book on which the authors are engaged. It reExamples in Algebra. By Charles M. Clay. Pp. | lates to physical measurement with exercises based vii + 372. (New York: The Macmillan ('o.; Lon

thereon, including the measurements of length, don: Macmillan and Co., Ltd., 1905.) Price 4s.

| angles, mass, area, volume, specific gravity, with the net.

practical calibration of certain glass vessels. The Geometrical Conics. By G. W. Caunt, M.A., and two first chapters deal with contracted arithmetical C. M. Jessop, M.A. Pp. vi + So. (London : Edward

processes and squared paper work, but otherwise a Arnold.) Price 25. 6d.

knowledge of “ theoretical ” mathematics is assumed. THE little book on “ Easy Graphs," by Mr. | The work is intended as a first course for the junior

1 H. S. Hall, is the result of ripe experi- forms of schools, and especially for boys preparing ence, and is intended to lead the beginner by for army examinations. The apparatus is fairly comvery easy stages and show him all the points that prehensive, and the experiments are well described. require special attention in squared paper work and The book will be very useful to those arranging a the lessons to be learnt therefrom. Great attention course in an important branch of practical matheis paid to the suitable choice of scales and the proper matics. figuring of the diagrams. Linear graphs with in- The “ First Algebra,” by Messrs. Baker and ferences and applications occupy fully half the book, Bourne, is adapted from the first part of the authors' the latter half relating to algebraical equations and larger work, and, proceeding in the customary order, graphs of the second degree with one or two cubics. carries the subject up to quadratic equations and The numerous examples are interesting and sugges fractional and negative indices. Arithmetical and tive, and all the answers are given at the end. We graphical illustrations are freely introduced, and a agree with the author in deprecating the undue em special feature of the work is its very easy graduaployment of graphs, especially as the field in which tion and the large number of examples, some oral, they may be legitimately used is sufficiently extensive.

| provided at every stage, so that students using the The book will be deservedly popular.

book properly cannot fail to obtain a full knowledge The “Rudiments of Practical Mathematics,” by of the subject. The answers are completely given, and Messrs. Consterdine and Barnes, is a very excellent themselves extend to thirty-five pages. The book treatise, intended more particularly for students above gives an admirable first course in algebra. twelve years of age who are preparing for industrial Mr. Shorto's “ Algebraical Grounding" is a colpursuits. The heuristic method is in the main fol. lection of the definitions, axioms, laws, rules, and lowed, and the material for exercises is largely drawn proofs belonging to the subject, without examples, from the students' own measurements, suitable ob and arranged in logical sequence. It is intended jects of a simple kind being provided for this purpose, as a summary of the oral teaching usually imparted, with appliances for measuring lengths, areas, and could well be used in conjunction with a collecvolumes, weights, and times. Thus every rule and tion of examples. It includes logarithms, the proprocess is definitely associated with some direct quan- / gressions, and the binomial theorem. titative application, and the subject assumes a real | The collection of eight thousand “Examples in and living interest and cannot fail to be assimilated. | Algebra," by Mr. Clay, has been accumulating for The subject-matter is purposely confined to that which the last twenty years, during which time the author is in daily use in industrial occupations, so that there has been engaged in teaching the subject in America, is time for this to be dealt with in a very thorough and has found that the examples provided in the manner. In this volume arithmetic, algebra, and ordinary text-books are deficient in both quantity and geometry are so interwoven that any attempt at variety, and not regularly graded. The teacher will separation would appear quite unnatural. Thus when here find examples in superabundance, increasing in an important principle, say that of proportion, is difficulty by almost insensible steps from the simpler exercises in the use of symbols to the difficult problems and also the time required for the completion of the in surds, theory of exponents, quadratics, and in arith- canal. Eventually, after the failure of the first metical and geometrical progressions. The work company, a New Panama Company was formed in shows no trace of having been influenced by the

1894 (given by a misprint as 1904 in the introduction): reform movement going on in this country, but and the works for a canal with locks were slowly proteachers will receive valuable hints and much useful ceeded with as funds permitted, until at length, last matter by consulting this thorough and extensive year, the l'nited States Government purchased the compilation.

undertaking with the view of carrying it out as a The “ Geometrical Conics " by Messrs. Caunt and national work. Early this year an engineering comJessop is a preliminary deductive course for students | mittee of the Panama Commission recommended a about to enter on a systematic study of analytical sea-level canal again, with a bottom-width of 130 feet geometry. Only the leading properties of conies are and a minimum depth of 35 feet, and the necessary dealt with, and these are established when possible duplicate tidal locks near the Panama end, capable of from corresponding properties of the circle by the aid accommodating vessels up to 1000 feet in length and of the modern methods of projection. The book is

100 feet in width. well suited to its purpose.

The principal objections to the formation of a canal across the isthmus at sea-level throughout, are the

time, difficulties, and cost involved in making a PANAMA CANAL.

cutting, reaching a depth of 317 feet, in unfavourProblems of the Panama Canal. By Brig.-General

able strata exposed to tropical rains, and the efficient Henry L. Abbot, U.S. Army. Pp. xi +248. (New

control of the River Chagres, which crosses the line of York: The Macmillan Company; London: Mac

the canal on the Atlantic slope in several places, and millan and Co., Ltd., 1905.) Price 6s. 6d. net.

the floods of which will become a more serious peril to

the maintenance of the canal in proportion as the THE author of this book acquired distinction in

water-level of the canal is lowered. The objection of I hydraulics in early life by the publication, in

cost, and, to some extent, that of time, are of con. conjunction with Captain Humphreys, of their wellknown “Report on the Physics and Hydraulics of the

siderably less importance in a national than in a Mississippi River " in 1861; and, accordingly, this

private undertaking; but the foods of the Chagres statement of the problems of the Panama Canal, in

appear liable to prove a standing menace to the safety which hydraulics are so largely involved, by such a

of a tide-level canal. The "Isthmian Canal Commis. high authority, who, as a member of the technical

sion of 1899–1901 expressed its disapproval of a sea

level project in the following words :committee of the New Panama Company, devoted seven years to their study, deserves the most careful " The cost of such a canal, including a dam at lha. consideration of the American nation, for whose guid- juela, and a tide lock at Miraflores near the Pacific ance this volume has been published. It appears at a end, is estimated at not less than 240,000,000 dollars. very opportune time, when the United States Govern

Its construction would probably take at least twenty

years. This Commission concurs with the various ment has undertaken the completion of the works, but

French Commissions which have preceded it, since has entrusted to a commission of engineers the con

the failure of the Old Company, in rejecting the seasideration of the precise designs for the canal.

level plan. While such a plan would be physicalh The chapters on the “ New Panama Company," practicable, and might be adopted if no other solution with which the author was connected. " The Rival were available, the difficulties of all kinds, and especiRoutes " of Panama and Nicaragua, the “ Physical

ally those of time and cost, would be so great that

a canal with a summit level reached by locks is to be Conditions of the Isthmus,” “ The Chagres River,"

preferred." with its torrential floods and difficulty of control, and the “Disposal of Rainfall," all present features of

The author regards these remaining difficulties as interest, and the last three are essential in a study | very important; and, after discussing them, and parof the works to be carried out; but undoubtedly the ticularly the problems concerning the control of the most interesting portion of the book for the British

Chagres, he concludes his book with the following public and engineers generally is contained in the

expression of his opinions : - -final chapter on “ Projects for the Canal.” It will be " It is the unanimous opinion of all the cngineer, remembered that when M. de Lesseps started the who have had practical experience in canal work, and scheme about twenty-five years ago he proposed the time to thoroughly study the problem, that no seaconstruction of a tide-level canal; and the works were

level projet without locks, and no sea-level canal commenced on this basis with very inadequate in

even with a tidal lock, is practicable that would be

comparable in ease and safety of transit to one vestigations of the nature of the strata to be traversed

equipped with modern locks, and planned to take ad. by the cuttings, especially through the Culebra ridge, vantage of all the desirable elements which the natural and the physical conditions of the locality. When ex conditions offer. Why, then, waste an extra ten ar perience had proved the unexpected magnitude of the

a dozen years, and untold millions of dollars, to undertaking, and the unforeseen difficulties to be over

execute a scheme which the investigations of thirty

five years have demonstrated to possess only a senti. come, the original company, approaching the end of

mental merit due to the imagination of M. de Lesseps ? its resources, decided in 1887 to introduce locks, I Congress and the American people are impatient for thereby greatly reducing the amount of excavation, ! the opening of the best possible canal."

OUR BOOK SHELF.

speculations concerning some of the extinct forms,

and there are more misprints than ought to be. The The American Thoroughbred. By C. E. Trevathan. |

book also lacks adequate illustrations. It is, how(American Sportsman's Library.) Pp. ix + 495;

ever, a worthy sequel to Mr. Pycraft's earlier illustrated. (New York : The Macmillan Company; |

“ stories” of birds and fishes, and we hope he may London: Macmillan and Co., Ltd., 1905.) Price

soon complete the series by a final volume on the 8s. 6d. net.

mammals. FROM the point of view of the naturalist, the interest of this volume (which is no doubt an admirable guide Digest of the Evidence given before the Royal Comto everything connected with racing on the other mission on Coal Supplies (1901–1905). Vol. i. side of the Atlantic) is concentrated on the author's Pp. lxiv + 474. (London : The Colliery Guardian remarks with regard to the origin and development | Co., Ltd.) Price 215. of the American thoroughbred. As a matter of fact, | The Colliery Guardian has done useful work in prethe racehorse in America has been produced mainly paring this digest of the evidence given before the from an English ancestry, and is thus essentially of Royal Commission on Coal Supplies. The 25,662 the English type; and the one matter for regret in questions and answers contained in the official his treatment of the subject is that the author does minutes of evidence do not constitute an attractive not appear to point out any features by which the form of technical literature; but with the matter reAmerican breed may be distinguished from its Euro

arranged and classified under separate heads, and the pean prototype, as it is difficult to believe that minor interrogative converted into the narrative form, it is differences between the two do not exist. The first

surprising to find what an enormous amount of valuthoroughbred imported into America seems to have

able information has been got together. With the been Bulle Rock, a horse foaled in England in 1718 exception of a brief historical introduction, no comand landed in Virginia in 1730. He was a scion of ment is made on the evidence, and such additions as the Darley Arabian, and had also the blood of the the witnesses have found desirable when revising their Byerly Turk on the maternal side. The product of

evidence have been printed as footnotes. The work native-bred mares (that is to say, mainly the de will be completed in three volumes, the subjects dealt scendants of horses imported by the Spanish con- with in the first being the working of thin seams. querors, which were themselves largely of Barb the limit of depth in mining, waste in working and blood) by Bulle Rock formed the first foundation of coal-cutting machinery. There is a good index and the modern American racing stock. Diomed was a useful bibliography of the subjects discussed. another famous English stallion imported into Printed in large type, with the illustrations admirably Virginia in the old days; but long after the definite reproduced, the work forms a valuable companion to establishment of an American thoroughbred stock, the official Blue-books, and, indeed, from the point considerable improvement was effected therein by the

of view of the mining student, may replace them importation in 1836 of Glencoe, at that time a re

altogether. nowned English horse. Glencoe was by Sultan, and while in England sired Pocahontas, the dam of Stock-! Wasps, Social and Solitary. By George W. Peckham well, Rataplan, and King Tom, the three greatest and Elizabeth G. Peckham. With an introduction sires the English turf has ever seen, and to one of by John Burroughs. Pp. XV+311; illustrated. which almost every living English racehorse can (London : Constable and Co., Ltd., 1905.) Price trace descent. With such a sire the future of the 6s. net. American thoroughbred was assured. In conclusion, This book is founded on a series of papers published we may congratulate the author on having added a

some years ago by the Wisconsin Biological Survey valuable volume to a valuable library, as well as on

under the title of “ Instincts and Habits of the Solihaving made an important contribution to our know

tary Wasps,” with much new matter added. It is a ledge of the ancestry of the American racehorse.

record of very patient field observations on the lines R. L.

with which Fabre's well-known “ Souvenirs Ento

mologiques" (constantly referred to, and compared by The Story of Reptile Life. By W. P. Pycraft.

our present authors with their own) have made us Pp. 212. (London: George Newnes, Ltd., 1905.)

familiar. Price is.

The wasps discussed are chiefly those which proviThis is a valuable addition to the “ Newnes' Library sion their nests with caterpillars and other insects, or of Useful Stories." Mr. Pvcraft not only writes in a with spiders; and the genera noticed are Vespa, readable and entertaining style, but also has the happy Ammophila, Sphex, Rhopalum, Odynerus, Aporus, faculty of selecting precisely those facts which enable Crabro, Bembex, Cerceris, Philanthus, Trypoxylon, him to expound general principles. The “ Story of Pompilus, Tachytes, Chlorion, Pelopæus, Astata, Reptile Life" is not an elementary book of natural | Oxybelus, &c., all of which (Sphex, Bembex, and history in the ordinary sense, but the outline of a Chlorion excepted) include British Species. Many really scientific treatise which is not too technical to persons are interested in the habits of insects who be understood by a beginner. After some introductory have not time or opportunity to observe them for remarks explaining that he has to deal with a race themselves, and to all such we heartily commend this ** whose glory has departed,” the author proceeds to important work on the manners and customs of North describe each of the groups of surviving reptiles, with | American wasps.

W. F. K. some reference to their immediate ancestors as revealed by fossils. In each chapter he treats first of

| X-Rays: their Employment in Cancer and other the most salient points in anatomy, and then proceeds

Diseases. By Richard J. Cowen. Pp. viii + 126. to select a few of the more important living species

(London : Henry J. Glaisher, 1904.) Price 2s. 6d. for detailed notice. The account of the existing net. reptiles is followed by two chapters on domestic life The author of this work states in his preface that he and reptilian liveries. The book then concludes with has made no effort to summarise all the valuable work chapters on the extinct flying reptiles, land reptiles, which has been done in radiotherapy, and he has only and sea reptiles. We have detected no serious tried to select such part as seems to him to be most errors, though it is difficult to accept all the author's ' likely to assist those practitioners in the therapeutic

properties of X-rays, the choice of apparatus, and the ducing radiation by artificial means, but the results have technique.

not yet proved themselves to be successful, at any rate In the first twenty-four pages the apparatus is

from an economic point of view. considered, and the remainder of the work, with the

The destruction of blossoms, however, is caused some

times by a low atmospheric temperature produced by exception of two short chapters, is devoted to brief

means other than surface radiation. This was the case consideration of a number of skin affections, including

in the present year, when the destructive cooling agent malignant disease. The book will certainly be of

was a cold wind. A warm, low situation, with plenty of service to those for whom it is intended, and many

shelter, will afford some safeguard against damage from practitioners who desire to become acquainted with such a source: and these, unfortunately, are just the conthis new branch of electrotherapeutics will find it a ditions which will increase the danger from radiation useful introduction. The work is well written and frosts. unpretentious, and Dr. Cowen has succeeded in the There is no doubt, however, that the damage done by aim laid down in his preface.

a low temperature is not always done in a direct manner.

A continued spell of cold weather at the blossoming season Neue Abhandlungen über den menschlichen Verstand.

is inimical to the activity of the various insects on which By G. W. v. Leibniz. Translated, with introduc pollination mainly depends, and we are not yet in a position tion, by C. Schaarschmidt. Second edition. Pp. to say that a sluggish action of the roots and leaves mas Ixviii + 590. (Leipzig: Dürr'sche Buchhandlung, not itself be directly detrimental to the process of fertil1904.) Price 6 marks.

isation. The number of apples and, still more, of pears Immanuel Kant's Logik. By G. B. Jäsche. Third

which have been imperfectly fertilised, and have, therefore, edition. New edition by Dr. W. Kinkel. Pp.

dropped prematurely, have been very noticeable this year.

What part the nature of the soil plays in modifving xxviii + 171. (Leipzig : Dürr'sche Buchhandlung,

the action of cold on the trees is one which is very difficult 1904.) Price 2 marks.

to foretell or to determine. We can never have two Lazarus der Begründer der Völkerpsychologie. By

plantations in different soils while being in exactly similar Dr. Alfred Leicht. Pp. 11. (Leipzig : Dürr'sche 1 positions; and the question whether a blossom will be Buchhandlung, 1904.) Price 1.40 marks.

reduced to a lower temperature by radiation in the moist The first two of the above-mentioned works appear as

air overlying a clay soil than it would be in the dryer air parts of the excellent “ Philosophische Bibliothek."

overlying a gravel soil, or whether, if reduced to the The translation of the Leibniz into the philosopher's

same temperature in both cases, it would suffer more in

the one than in the other, is a question on which we native tongue appears to be all that could be desired,

cannot dogmatise. We must not be misled by the feeling and the introduction gives an analysis of the work.

of cold experienced in two such cases by the human subWe gather that some 460 explanatory notes are to be ject; indeed, watering the trees and ground is one of the found in the succeeding volume of the series. This methods suggested for obviating the effects of radiation edition of “Kant's Logik” is intended to supersede frosts. Differences of soil, also, will act indirectly in the the uncritical one of Von Kirchmann, who relied only matter by affecting the root-action and the forwardness on the second Hartenstein edition of 1868. The present of the blossoms. editor has gone back to the original text of Jäsche,

On one point, however, I think there can be nu

doubt, namely, that the best safeguard against injury by and has also compared the other important editions,

frost, where frost is inevitable, is a healthy condition of the first Hartenstein and the Rosenkranz, both of

the tree itself. It has been a matter of continued observ1838. The spelling is completely modernised. Prof.

ation that with similarly situated plantations, and with Moritz Lazarus was, with Steinthal, the founder of similar trees in the same plantation, those which are most the Zeitschrift für Völkerpsychologie und Sprachwis healthy will nearly always suffer least from frost. It is senschaft in 1859, and his works not only contain specially noticeable that with trees which are weakly. much sound psychology, but are also permeated by a even when they carry (as will often happen) a great fine ethical spirit. His long life and labours are here

abundance of blossom, injury from frost is very severe, described by a singularly appreciative disciple.

although the abundance of blossom should be favourable to some of these being preserved from destruction.

It is in this direction---the general health of the trees LETTERS TO THE EDITOR.

and the raising of healthier and hardier varieties-that [The Editor does not hold himself responsible for opinions

success in diminishing loss by frosts will most probably

be achieved. It is hardly probable, I think, that much expressed by his correspondents. Neither can he undertake

will be effected, at any rate in the case of apples. he to return, or to correspond with the writers of, rejected

raising varieties blossoming late enough to escape frets. manuscripts intended for this or any other part of NATURE.

These frosts, as we all know, often occur very late in the No notice is taken of anonymous communications.)

year, and though every day by which the blowoming is British Fruit Growing.

retarded must, on the average, diminish the risk of its

destruction, there would appear to be but little chanır The question of “the diversity of yield from farms in

of our being able to retard it sufficiently to diminish that the same neighbourhood ” to which you referred in your

risk to any material extent. It must be remembered, article on the report of the fruit committee is, as Mr.

also, that though we might raise a late blossoming apple, Alfred Walker remarks, one of very great complexity. No

it is a hundred chances to one that the fruit would be evidence on this subject, however, was offered to the fruit

able to compete in the market with known varieties. committee by the numerous growers who appeared as

The flowers of the large majority of English apples witnesses before them, and it would certainly seem to be

would appear to open within a period of about ten days. a subject more suited for investigation at an experimental

Observations made this year on 117 varieties gave a total station than one which could be dealt with by a depart

range of 16 days, but 98 per cent. of these varieties opened mental committee.

within a range of 13 days, and 84 per cent. within a Meteorological conditions are, no doubt, primarily

range of 9 days. The extent of the variation, therefore, responsible for most failures of cropping, and, in a climate is not sufficiently large to offer much promise of success such as that of our islands, we can never hope to do more

in raising a variety which would escape frost by its latethan mitigate the evil effects of inopportune cold. The

ness of flowering. It is noticeable, however, that our destruction of the blossoms is generally due-as in 1903-| English apples appear to be rather earlier in their flowering to cooling by radiation, and the best safeguard against

than varieties belonging to other countries, when all are this form of cooling is a fairly elevated position, and a lie

grown under the same conditions. The results obtained of the ground favourable to the draining away of the at Woburn this year were as follows, the dates being those cold air from the plantation. Good air drainage is prob- of the opening of the first flowers, and the fractions of ably more important in fruit growing than good water dates arising, of course, through the taking of the means drainage. Various means have been investigated for re- | The number of varieties under observation are given, and

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