claims of the theoretician, on the one hand, and the practician, on the other, furnishes the mathematical text-book writer with a perpetually fascinating problem; for the theoretician and the practician have nothing in common save their insistency; in other respects they are as wide apart as the poles; the theoretician is a rigorist, a logician, a lover of the abstract, demands a minimum of assumption and a maximum of proof; the practician hates the abstract, loves the concrete, and mainly depends for his happiness on getting results by the use of rules and formulas that he neither understands nor cares to understand. To win the unqualified approval of both these types of critic is impossible, a contradiction in terms; to incur the unqualified condemnation of both is not impossible; the target to be aimed at is somewhere between; to locate it and to hit it squarely two very different things-require a rare combination of sanity, skill and good luck.

It may be added that in these times the text-book writer receives additional stimulation from the keen competition of other subjects and from the challenge of certain cunning educators who have shrewdly discovered that the educational value of mathematics has always been greatly overestimated.

The aim of Professors March and Wolff has been to present "the calculus in such a way that it will appeal to the average student rather as a means of studying scientific problems than as a collection of proofs and formulas." The aim is commendable but in saying so we do not intend to imply, and the authors would probably not contend, that the calculus must appear either as such a means or as such a collection" for it has other aspects, aspects both attractive and worthy. Integration is introduced at an early stage. In connection with the employment of infinitesimals, Duhamel's theorem is used but without too much finesse. There are numerous applications to elementary classical problems of geometry, physics and mechanics. A brief introduction to analytical geometry of three dimensions is inserted for such readers as may require it. The phrasing is in general so careful and so

good that its very excellence operates as a challenge, and one is tempted to ask whether it would not be a trifle better to say that the phrase, division by zero, is meaningless than to say (p. 30) that "division by zero is an impossible operation"; to say that the fraction, (x2 —4): (x —2), has no value for x= = 2 than to say "its value is not determined at this point"; to say in such a case that there is no quotient than to say that "the quotient has no meaning." The volume closes with a very brief chapter dealing with simple types of differential equations.

To differential equations Professor Love devotes three chapters amounting to more than fifty pages. Integration is not presented earlier than page 116. This is preceded by a chapter on curve tracing. The reader is impressed with the possibility of calculating the most important mass-moments of first and second order by means of simple integration. Applications are drawn exclusively from geometry and mechanics with unusual emphasis on the latter. The importance of checking results, particularly in integration problems, is stressed. An excellent feature is the presence

of

"worked examples" to assist the reader in making transition from theory to practise. In Professor Love's book as in that of Professors March and Wolff the fundamental theorems respecting limits are set down without proof.

In Mr. Barker's book we have a pretty plain specimen of plane trigonometry. Trigonometric series are not present. Of the wider bearings and higher attachments of the subject the reader is not made aware. Much attention is rightly given to simple applications. The large page and open type please the eye. The punctuation is unusual and not consistent with itself. The radian is defined as if it must be conceived as always having its vertex at the center of a circle. The words "these" and "this" (pp. 2, 3) are assigned to duties that they are unable to perform. In article 4 one is at a loss to determine the significance of the repeated phrase," said to be." The author has sometimes allowed himself the freedom of such colloquial expressions as "Expand the left members and we have" (p. 86).

Physically, mechanically and stylistically Professor Skinner's College Algebra is a tidy piece of work. It is up-to-date in its inclusions, exclusions and emphases. Its early use of geometric representation is happy. The notion of function occupies a dominant place in the entire perspective. In the definition of this notion (p. 49) the meaning of the term "known" may lead to interesting dialectic, especially if the function be implicit. Five convenient tables are inserted at the end of the volume.

Professor Dowling's "Projective Geometry' is a handsome introduction to the most exquisitely beautiful of mathematical subjects. The treatment, which is in the manner of Reye's classic "Geometrie der Lage," is synthetic as distinguished from algebraic, and presupposes no knowledge beyond ordinary elementary geometry and a very little trigonometry. It does not aim at the rigor of the postulational method, but is preliminary thereto and admirably qualifies the reader to appreciate the nature and the value of that method.

In his "Elliptic Integrals" Professor Hancock has compressed a large amount of matter into a small compass. If the work be too compact for most of those who would like to read it, the fault is not that of the author but rather that of the editors who desired him to write a work which "shall relate almost entirely to the three well-known elliptic integrals, with tables and examples showing practical applications, and which shall fill about one hundred cctavo pages." This assigned task has been done faithfully, and the reader will thank the author for his full citation of the literature of the general subject.

families with a mean winter production of 52.5 eggs and to several Cornish females. The latter are poor winter layers with a mean of 8.47 eggs. There were 33 pullets from the Cornish and Rhode Island Red cross with a mean winter production of 49.2 eggs, the range being 21-86.

The offspring of this male with pure Cornish females were 11 in number and with the exception of a single individual were poor winter layers, the average of all being 11.6 eggs.

The result from the Cornish male and Rhode Island Red female cross is diametrically opposed to that obtained by Pearl from Cornish males (of the same strain that I used) bred to Barred Plymouth Rock females which are good winter layers. The offspring of this cross gave a mean winter production of 16.7 eggs. The reciprocal cross, viz., Barred Rock males and Cornish females, gave an average winter production of 30.7. We have no data at present from the corresponding cross with Rhode Island Reds. It is clear from the results of my experiment that high-producing hens are able to transmit this ability directly to her daughters, that is, high fecundity in Rhode Island Reds is not sex-linked.

B. A Theory of the Inheritance of Winter Egg Production Alternative to Pearl's.—It has been found that the observed ratios in which high and mediocre producers occur, both in Pearl's data on Barred Plymouth Rocks and my own with a large series of Rhode Island Reds, can be explained satisfactorily by assuming that high egg production depends upon two factors that follow the usual dihybrid Mendelian scheme. One factor alone, in either simplex or duplex condition, is assumed to give mediocre production. This theory encounters only one difficulty, viz., in a few instances there is a deficiency in the expected numbers of high producers, a result easily explicable with a physiological character such as egg production. Pearl's theory, however, encounters the reverse difficulty, i. e., high producers appear where none are expected. This difficulty is explained by Pearl on the very reasonable assumption that it is due to an overlapping of phaenotypes.

There is, however, a serious difficulty with the data from both sources. This difficulty lies in the fact that the average number of daughters per mother is extremely small. The average number of daughters per mother in Pearl's experiment was 2.85, while in mine it varies from 2.6 in the early years to 6.75 in later years. Because of the small size of the families it is possible to fit any family into a place in either scheme, since the ratios expected for the various matings differ only slightly from one another. In spite of the doubt raised as to the mode of inheritance of winter egg production it is clear that this character is inherited, for high and low fecundity lines are readily established by suitable matings along family lines.

H. D. GOODALE

MASSACHUSETTS AGRICULTURAL EXPERIMENT STATION

THE AMERICAN ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE

SECTION D-ENGINEERING

THE first session was held on the morning of Friday, December 28, in Thaw Hall, University of Pittsburgh, Vice-president Dr. Henry S. Drinker in the chair, with an attendance of about thirty. It was announced that the Sectional Committee had recommended for election to the General Committee, for the office of vice-president, Dr. Ira N. Hollis, of Worcester, and for the office of secretary, Dr. Frederic L. Bishop, University of Pittsburgh. The following officers were elected by the Section:

Member of Council-Dr. George F. Swain, of Harvard University and the Massachusetts Institute of Technology.

Member of General Committee-Charles Henry Davis, of Cambridge, Mass.

Member of Sectional Committee-William Bowie, of Washington, D. C.

The program of the session was as follows:

Railroad track, its defects and abuses, and their amelioration: G. H. BARBOUR. Historical: The age of the drawn and that of the driven wheel; ancient English tramways; the institution of that distinctively American principle now governing the construction of railroad

track as now practised by all the steamroads in the world, wherein the equipment upon its track constitutes a flexible superstructure upon an elastic roadbed. Defects: Weak rails; narrow railheads; excessive deflections; joints. Abuses: Worn and ragged wheels; improper wheel spacing; dynamic augments; lateral thrusts. Ameloriation: Increased bearing on ballast; decreased depth of ballast; augmentation of rail; increased lateral strength; broader head; more frequent lateral fastenings; maintaining height of rail at the mini

mum.

The scientific principles of building codes: J. A. FERGUSON. A good building code occupies a very responsible position among the vital issues of municipal welfare. Properly planned, a building code should insure safety to life, limb, health and property, and should function to minimize loss or injury to either. Progress in the arts has introduced many new factors in the occupation of buildings, which necessitate the scientific handling and classification of the requirements and progress in building has made it possible to classify the various forms of building construction into distinct groups. The same progress has made it possible to classify occupancies and construction of buildings and to specify the minimum allowable construction for the various occupancies. This it is now proposed to do in one notable case for the city of Pittsburgh, Pa. Other phases of this subject are susceptible of scientific definition, and in order to properly regulate buildings it is becoming increasingly necessary to classify and define in a scientific manner all subjects. The paper gives typical arrangement for a code and explains the reasoning upon which it is based as well as for the classification of other regulatory provisions in a good building code.

Relative efficiency of different methods of repairing bituminous macadam and bituminous concrete pavements: GEORGE H. BILES. The bituminous macadam and bituminous concrete pavements in their various stages of disrepair offer excellent opportunity to the highway engineer for study and experiment. The methods of repairs to pavements of these types have advanced to such a degree in recent years that there are innumerable instances where pavements have been reclaimed by scientific analysis of the causes of deterioration and by efficient application of the principles of repair applicable to each case. Central bituminous mixing plants are advisable where the amount of yardage and its accessibility warrant as in cases of municipalities. In most other cases,

general repairs can be made successfully with cold bituminous preparations.

The efficiency of the application of cold bituminous materials for surface treatments on gravel and broken stone roads: JULIUS ADLER. In the development of bituminous surface treatment practise during the past ten years, the most important step forward has been the recognition of the fundamental necessity of a road well built in every respect, and having a mosaic surface especially adapted to receive the bituminous material. In the selection of the latter, a greater and desirable degree of uniformity of practise will follow upon a clear understanding of the characteristics which identify them as most suitable to serve the two functions of: (a) Priming; (b) smoothing and rendering impervious the road surface. The precise limits of suitability of bituminous-treated roads can hardly be determined definitely in traffic units because of the difference in materials in use, and combined traffic and climatic conditions. From an economical standpoint, they represent a high annual maintenance charge which is an argument in favor of their use in the preservation of existing roads, rather than in a program of new construction. The full possibilities in their use, however, will not be realized until high-grade original construction, scientific selection of materials and systematic maintenance are all combined.

Present status of granite block pavements: C. D. POLLOCK. This paper describes the improvement of the granite block pavement from its early form to the latest types of smooth surface, close jointed pavements. The latest and best joint fillers are shown and likewise the various cushions or beds for the blocks. The great improvements which have been brought about in making granite blocks and also in laying this pavement, in recent years, are due entirely to the cooperation between the engineers and the quarrymen. The engineers learned enough of quarrying to draw specifications calling for the best practicable block and the quarrymen have exerted themselves to make that block.

Rattler tests for paving brick of various depths: WILLIAM C. PERKINS. Discussion of the rattler used for testing paving brick and a short history of same. The testing of paving brick of different depth and the theoretical determination of an allowance or differential for same. Discussion of a modification of the abrasive charge in rattler in the testing of paving brick.

Motor trucks and long distance highway transportation: MAURICE B. GREENOUGH. Statistics

show that the railroads have nearly if not quite reached the limit of their capacity for freight hauling. At the same time there is a growing shortage of cars. They themselves have advocated the use of motor trucks on the public highways for short hauls to relieve congestion. Increased highway construction and organized effort to encourage the use of highways are essential to make the potential relief an actuality.

The construction and maintenance of highways under war conditions: ARTHUR H. BLANCHARD. Since the United States entered the war, motor truck transportation on country highways has rapidly developed due to the following causes: First, the marked increase in the tonnage and bulk of shipments; second, the lack of railroad equipment to efficiently handle freight and express transportation; third, the inadequacy of railroad terminal facilities; fourth, the United States government priority orders; and fifth, the intensified consideration of economic problems, the solution of which would lower prices of the necessities of life. Suggestions relative to construction and maintenance of highways under war conditions: (1) Maximum use of motor truck transportation of materials and machinery; (2) amendment of onerous traffic regulations which prevent economic use of motor trucks; (3) modification of state laws to permit construction and maintenance of highways by day labor; (4) award of contracts to responsible contractors on a cost plus a profit on labor and rental of equipment, all materials being furnished by the state or county; (5) modification of contracts and specifications which place all liabilities on contractors; (6) maximum use of labor-saving machinery; (7) maximum utilization of convicts and prisoners of war; (8) construction and maintenance of military highways by the United States government.

The second session was held on the afternoon of December 28 in the Lecture Hall of the Mellon Institute, Vice-president Dr. Henry S. Drinker in the chair, with an attendance of about one hundred ten. This meeting was a joint session with Section C; Society for the Promotion of Engineering Education; Engineer's Society of Western Pennsylvania; Pittsburgh Section, American Electro-Chemical Society, and the Pittsburgh Seetion, American Chemical Society. The program of the session was as follows:

Vice-presidential address, some needs of engi neering: DR. HENRY M. HOWE. Printed in the is sue of SCIENCE for January 25.

Mechanical manufacture of window glass: Dr. F. L. BISHOP.

A manufacturer's experience with graduate chemical engineers: S. R. CHURCH. Two years' experience with about one hundred graduate chemical engineers has suggested the following apparent deficiencies in training seemingly common to men from a large number of colleges:

1. Lack of judgment necessary to weigh correctly (a) the value or limitations of test data; (b) the degree of accuracy required; (c) the occasion for choosing quantitative or qualitative methods of analysis.

2. Lack of sufficient imagination to grasp the indicated possibilities for further work pointed out by experiments themselves partial or complete failures.

3. Lack of ability to write a report sufficiently well ordered and comprehensive to do justice to the merits of the work accomplished. The writer favors the five- or six-year course for chemical engineers but urges that especially in abbreviated courses the student be given a better practical sense of commercial values.

A survey of high-school chemistry in Pennsylvania: ALEXANDER SILVERMAN. The report includes graphs and tabulated answers on college preparatory chemistry from 126 of 971 schools receiving information blanks. Answers cover length of course, when given, whether preceded or followed by physics, number of lecture periods per week, recitation periods, length and number of laboratory periods, number of sections of each and number of pupils per section, text-books employed, laboratory manuals employed, elements omitted, theories, laws and principles omitted. Also information about general science and other chemistry courses given, number of subjects taught by instructors together with number of hours of lecture, recitation and laboratory practise conducted. Further, the training received in preparation for teaching. The great lack of uniformity already observed leads the author to recommend standardization by a state commission, or preferably by the United States Commissioner of Education, with power to enforce standards so that colleges and universities may begin their work where the high schools end, thus avoiding duplication.

The following resolution was unanimously adopted:

Resolved, That the thanks of the Joint Conference be extended to the New York World, the New York Times and the Jeweler's Circular for cooperating with the chemists of the United States

in the conservation of platinum by excluding the word platinum from their advertising columns.

The third session was held on the morning of Saturday, December 29, in the Applied Science Building of the Carnegie Institute of Technology, Vice-president Dr. Henry S. Drinker in the chair, with an attendance of about forty-five. The program of the session was as follows:

Solution of spherical triangles by diagrams: HORACE R. THAYER. All spherical triangles may be solved by the use of two simple formulæ. If now these be accurately computed and plotted, they may be employed to solve many cases which occur in practise with a minimum of cost, at the same time lessening the danger of serious error.

Conservation of fuel through smoke regulation: J. W. HENDERSON. Conservation that merely contemplates withholding the natural resources from use, keeping them in their natural state, can hardly be considered conservation in its broadest application. The logical starting point is that of "taking stock" of the natural resources. Having this knowledge, conservation can be carried on, on the basis of "the application of common sense to common problems for the common good."' The needless waste of fuel and of recoverable by-products, in this country, has been conservatively estimated at one billion ($1,000,000,000) dollars annually. Investigations and experience demonstrate that the production and emission from stacks, of smoke prohibited by law, means waste— direct waste of combustible materials and their byproducts and contributory, contingent waste of building materials, household goods, vegetation. and of human energy, both physical and mental. In a few cases smoke regulation is under state control. Many foreign countries have placed it within the activities of their central governing powers. The work in Pittsburgh has proved that smoke regulation is a fuel conservation problem. Smoke means waste. Proper smoke regulation results in saving fuels. Conservation as proposed will induce complete combustion of them and stop the production of smoke. Smoke regulation is so closely related to conservation as to indicate the necessity of the government adopting it in its program of conservation. The work can not be of a constructive and permanent character if left to the fluctuating political activities of the cities, counties or states. The way to meet the requirements is to not make the smoke. This is accomplished by securing more perfect combustion. The subject deserves the attention of scientists and of practical engineers and of every thinking man and woman