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under state laws and have no additional municipal regulations. A number of cities such as Baltimore, Buffalo, Los Angeles and Milwaukee have local provisions in addition to state laws. In 1910, sixteen states had laws providing for the state inspection of meters and of the purity of gas-Connecticut, Georgia, Kansas, Maryland, Massachusetts, Nevada, New Hampshire, New Jersey, New York, Ohio, Oklahoma, Vermont, Virginia, Washington, Wisconsin and California (B. of S. Circular No. 32). Doubtless the list is now larger.

In 1910 the net income to the state of Massachusetts in meter-testing alone was over $5,000. The total cost of the tests on quality, purity, pressure, etc., was assessed on the operating companies according to their sales. Meter-testing is on the fee basis. There is no good reason why such a department in North Carolina would not yield a revenue to the state.

That the Corporation Commission in North Carolina should have the power and machinery at its command to protect the interests of citizens seems obvious for the following reasons: Under existing law it is the duty of the commission to regulate the rates to be charged by gas companies. The proper price is determined in a large measure by the quality of product sold and this is almost at the will of the producer. Gas in New York City furnishes 680 heat units per cubic foot and is sold at 80 cents. Gas in Durham furnishes at times less than 500 heat units and is sold at $1.50. In one city in this state gas furnishing 412 heat units sold for $1.60. The standard requirement in regulated states is around 600 heat units. The difference in quality means a loss of from five to twenty thousand dollars per year to consumers in various towns of this state and the loss would easily run into hundreds of thousands to the state at large. While it may be to the interest of certain communities to sell a cheap, poor gas it is safe to say that it is always against public interest to have a cheap, poor gas sold at a rich, high price. To fairly meet its responsibility the commission must know from its own tests the quality of the product sold. The consumer is entirely helpless.

Aside from the question of rates, the public is vitally interested from the standpoint of health. In the method of manufacture used by one company in this state, carbon monoxide and hydrogen are produced in equal quantities. Both of these gases are odorless and one is a deadly poison. Combined they give a cheap gas furnishing about 300 heat units. This gas causes a meter to register just as fast as a 600 heat unit gas. It is the duty

of this company to carburet this gas with an oil which not only brings its heat value to standard, but gives it a very pungent odor that makes it noticeable in case of a leak. In this town a series of fatal accidents have occurred due solely to the neglect of the service company. In other methods other deleterious elements are introduced by carelessness so that in all cases public interest demands systematic testing under the authority of the state.

It is just as reasonable to let manufacturers sell anything called fertilizer without tests as to composition as it is to permit of the sale of untested gas. Our duty to test meters is just as obvious as our duty to test weights and measures.

The advantages resulting from such an act would not even be principally with the citizen. An expert employed by the state to travel from plant to plant observing and testing, corrects irregularities and errors in manufacture that may mean thousands of dollars saved to the companies. If ammonia appears in the gas it means that a valuable by-product is being lost. So it is with other errors of manufacture. The fact that meters are tested by the state brings a feeling of confidence to the consumer that is worth much to the gas companies. Uniform, improved and economical manufacture brings new and profitable business and this more than compensates for any costs involved.

No abstracts have been received for the following papers:

The relative toxicity of uranium nitrate in animals of different ages, by Wm. DeB. MacNider. Trembles, by Frederick A. Wolf.

Permanency in fleshy fungi, by H. C. Beardslee. Sound-wave photography (lantern), by Andrew H. Patterson.

Evolution in sponges and changes in classification, by H. V. Wilson.

The revision of the atomic weight of zirconium, by F. P. Venable and J. M. Bell.

Recent investigations about cottonseed meal, by W. A. Withers and F. E. Carruth.

The physics of the shrapnel shell, by Andrew H. Patterson.

Portolan charts (lantern), by Collier Cobb. The idea of force in mechanics, by Andrew H. Patterson.

The times we think in, by George W. Lay. The life history of the pecan trunk borer, by R. W. Leiby.

E. W. GUDGER, Secretary

Cornell University

Medical College

in the City of New York

Holders of a Baccalaureate degree or Seniors who can present a degree before entering the Second Year, who also present the requisite courses in Chemistry, Physics, and Biology, are admitted from recognized Colleges or Scientific Schools. The Session opens on the last Wednesday in September. The first year is devoted to Anatomy, Chemistry, and Physiology and may be taken either in Ithaca or New York City. The last three years are chiefly Clinical and must be taken in New York City.

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Washington University

Medical School

REQUIREMENTS FOR ADMISSION Candidates for entrance are required to have completed at least two full years of college work which must include English, German, and instruction with laboratory work in Physics, Chemistry and Biology.

INSTRUCTION

Instruction begins on the last Thursday in September and ends on the second Thursday in June. Clinical instruction is given in the Barnes Hospital and the St. Louis Children's Hospital, affiliated with the medical school, the St. Louis Mullanphy Hospital, the St. Louis City Hospital, and in the dispensaries connected with these institutions.

COURSES LEADING TO ACADEMIC
DEGREES

Students who have taken their premedical work in Washington University, are eligible for the degree of B.S. upon the completion of the first two years of medical work.

Students in Washington University may pursue study in the fundamental medical sciences leading to the degree of A.M. and Ph.D.

TUITION

The tuition fee for undergraduate medical students is $150 per annum.

The catalogue of the Medical School and other information may be obtained by application to the Dean.

Euclid Avenue and Kingshighway St. Louis

Syracuse University College of Medicine Tulane University of Louisiana

Entrance Two years of a recognized course in arts or in science in a registered college or Requirements School of Science, which must include German, Physics, Chemistry, and Biology. Six and seven years' combination courses are offered.

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The Fourth Year Course

is clinical. Students spend the entire forenoon throughout the year as clinical clerks in hospitals under careful supervision. The clinical clerk takes the history, makes the physical examination and the laboratory examinations, arrives at a diagnosis which he must defend, outlines the treatment under his instructor and observes and records the result. In case of operation or of autopsy he follows the specimen and identifies its pathological nature. Two general hospitals, one of which is owned and controlled by the University, one special hospital and the municipal hospitals and laboratories are open to our students. The afternoons are spent in the College Dispensary and in clinical work in medical and surgical specialties and in conferences.

Summer School-A summer course in pathology covering a period of six weeks during June and July will be given in case there is a sufficient number of applicants.

Address the Secretary of the College,
SYRACUSE, N. Y.

307 Orange Street

COLLEGE OF MEDICINE

(Established in 1834)

School of Medicine

Admission: One year of college work in the sciences and a modern foreign language.

After January 1, 1918, all students entering the Freshman Class will be required to present credits for two years of college work, which must include Biology, Chemistry and Physics, with their laboratories, and one year in German or French.

Graduate School of Medleine

A school for physicians desiring practical clinical opportunities, review, laboratory technic or cadaveric work in surgery or gynecology. Excellent facilities offered in all special branches.

School of Hygiene and Tropical Medicine, including Preventive Medicine

Systematic courses offered, leading to certificates in Public Health, diploma in Tropical Medicine, and to the degree of Dr. P. H. Laboratory, Clinic and Field Work. School of Pharmacy

Admission: Three years of high school work, or 12 units. Two years for Ph.G. degree. Three years for Ph.C.degree.

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1765 School of Medicine of the University of Pennsylvania

1917

The One Hundred Fifty-second Annual Session of this institution will open September 28, 1917, and continue until June 19, 1918. The first and second year classes are limited to one hundred students, and application for admission should be in the hands of the Dean before July 1st.

REQUIREMENTS FOR ADMISSION: Candidates must have successfully completed the work prescribed for the Freshman and Sophomore Classes in colleges recognized by this University, which must include at least one year of college work in Physics, General Biology or Zoology and Chemistry (Qualitative Analysis is required; Organic Chemistry is recommended, and in 1919 will be required), together with appropriate laboratory exercises in each of these subjects, and either French or German of more than elementary grade. For detailed information send for catalogue.

UNDERGRADUATE COURSE: The course of instruction extends over four annual sessions, the work so graded that the first and second years are largely occupied by the fundamental medical subjects. The third and fourth years are largely devoted to the practical branches, prominence being given to clinical instruction, and the classes sub-divided into small groups so that the individual students are brought into particularly close and personal relations with the instructors and with the patients at the bedside and in the operating room. After graduation further hospital work is undertaken by the members of the class; and more than 90 per cent. attain by competitive examination or by appointment positions as internes in hospitals in this city or elsewhere. The Pennsylvania Bureau of Medical Education and Licensure requires of applicants for license a year spent in an approved hospital.

POST GRADUATE WORK: (1) Any graduate possessing a baccalaureate degree may pursue work in Anatomy, Physiology, Physiological-Chemistry, Bacteriology, Pathology, Pharmacology, Research Medicine and Mental Diseases with view of obtaining the higher degrees of Master of Arts or Science and of Doctor of Philosophy in the Graduate School of the University. For information address Dean of Graduate School, University of Pennsylvania.

(2) Courses in Public Health (inaugurated in 1906) leading to diploma (Doctor of Public Hygiene, Dr. P.H.), are open to graduates in medicine who have had a preliminary education similar to that required for admission to the Medical School. The subjects comprehended in the course are: Bacteriology, Medical Protozoology and Entomology, Chemistry, Sanitary Engineering, Sanitary Architecture, Meat and Milk Inspection, School Inspection, Vital Statistics, Sanitary Legislation, and Personal and General Hygiene.

The full course extends over one academic year. Special subjects in the course may be taken by any one possessing suitable preliminary qualifications. For details address Director of Laboratory of Hygiene.

(3) From the opening of each term to about February 1 courses in Tropical Medicine are open to graduates in Medicine comprehending instruction in Medical Climatology and Geography, Hygiene of Tropics and of Ships, Tropical Medicine, Bacteriology, Protozoology, Entomology, Helminthology, and General Medical Zoology, Pathology, Skin Diseases, Eye Diseases, and Surgery of Tropical Affections.

(4) During the academic session special courses in any of the branches of the medical curriculum are open to graduates of this or other regular schools of Medicine, both in the clinical subjects and in laboratory studies. The excellent hospital facilities offered by the University Hospital, the neighboring Philadelphia General Hospital and other institutions with which the members of the staff of instruction are connected, guarantee exceptional opportunities for clinical observation.

TUITION FEE: Undergraduate study, $200 annually; fees for special courses on application. For detailed information or catalogue address

DEAN OF SCHOOL OF MEDICINE

University of Pennsylvania

University of Alabama

School of Medicine

Mobile, Alabama

Entrance Requirements

The satisfactory completion of two years of study, in an institution of collegiate grade, to include Biology, Chemistry, Physics, and a reading knowledge of French or German. In addition to four year High School diploma.

Combined Course

The Combined Course which is now offered by the University in connection with its Medical Department gives to the student the opportunity of obtaining the B.S. and M.D. degrees in six years. This course is recommended to all intending students.

The equipment of the school is complete. The clinical facilities ample. Eight full time teachers.

For catalog and any desired information, address

Tucker H. Frazer, M.D., Dean
School of Medicine

St. Anthony and Lawrence Sts.,
MOBILE, ALA.

Philadelphia, Pa.

University of Georgia

MEDICAL DEPARTMENT
Augusta, Georgia

The eighty-sixth session begins September 12, 1917;
closes May 29, 1918

ENTRANCE REQUIREMENTS

Candidates for entrance this session must have completed one full year of work in an approved college in addition to four years of high school. The college work must have included Physics, Chemistry, Biology and French or German. Beginning in 1918 two years of college work will be required.

INSTRUCTION

The course of instruction occupies four years. The first two years are devoted to the fundamental sciences, and the third and fourth to practical clinic instruction in medicine and surgery. All the organized medical and surgical charities of the city of Augusta and Richmond County, including the hospitals, are under the entire control of the Board of Trustees of the University. This arrangement affords a large number and variety of patients which are used in the clinical teaching. Especial emphasis is laid upon practical work both in the laboratory and clinical departments.

TUITION

The charge for tuition is $150.00 a year except for residents of the State of Georgia, to whom tuition is free. For further information and catalogue address,

The Medical Department, University of Georgia

AUGUSTA, GEORGIA

SCIENCE

FRIDAY, AUGUST 31, 1917

CONTENTS

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LIEBIG'S LAW OF THE MINIMUM IN RELATION TO GENERAL BIOLOG

ICAL PROBLEMS1

THE Law of the Minimum has never been accurately defined, although the idea that it involves is relatively simple. Professor B. E. Livingston says in a recent paper2 that "this principle is still quite incomplete logically and its statement will assuredly become much more complex as our science advances." In order to get a clear understanding of the law so that it may be stated accurately, we will begin with a simple application to chemical reactions.

One molecule of KOH reacts with one molecule of HCl to form one molecule of KCl and one of H2O. If only one molecule of KOH is present, only one molecule of KCl can be formed, no matter how many molecules of HCl are present; and likewise if only one molecule of HCl is present, only one molecule of KCl can be formed, no matter how many molecules of KOH are present. By considering the weights of the reacting substances, the situation is somewhat complicated: 56.1 grams of KOH react with 36.5 grams of HCl to form 74.6 grams of KCl and 18 grams of H2O. In round numbers 3 parts by weight of KOH and two of HCl give 4 parts by weight of KCl and one of H2O: 3/4 gr. of KOH and 1/2 gr. of HCl are necessary to form a gram of KCl. Let us call these fractions, 3/4 and 1/2, the specific reactive weights of KOH and HCl in respect to the formation of a unit quantity of KCl. Suppose x amount of KOH and y of HCl are given. If x and 1 Paper read before the Biological Club of Yale University, April 19, 1917.

2

2 Plant World, 20: 1-15, 1917.

y are divided by their respective specific

4

reactive weights, we get x and 2y. The 3 smaller of these quantities is a direct measure of the weight of KCl that can be formed from x KOH and y HCl. If, for example, x and y are both equal to three grams, four grams of KCl can be obtained.

These facts can be generalized. If A, B and C are substances which react to form S and u A, v B and w C are necessary for the formation of a unit amount of S, then u, v and w may be called the specific reactive values of A, B and C, respectively. They may be weights, volumes, numbers of molecules or what not. In any particular case, where pA, qB and rC are reacting, the amount of S formed is the smallest of the fractions p/u, q/v, r/w. When the amounts of the reacting substances are divided by their specific reactive values, the smallest quantity so obtained is equal to the amount of the product formed.

This conclusion is directly applicable to the problem of fertilizers. It is known that most of the higher plants must obtain seven elements in combined form from the soil. They are S, P, N, K, Ca, Mg and Fe. If aS, BP, yN, SK, Ca, Mg and Fe are required for a unit amount of growth in some particular plant, say wheat, and if aS, bP, cN, dK, eCa, ƒMg and gFe are present in a particular soil in available form, the maximum amount of wheat that can be grown in that soil will be the smallest of the fractions a/a, b/ß, c/y, d/8, e/e, f/l, g/n. In this case a, ẞ, y, etc., may be called specific growth values for the plant under consideration. When the available amounts of the essential inorganic food constituents are divided by their respective growth values, the smallest quantity obtained gives the maximum amount of growth possible.

It was in this connection that Liebig3 first "Die Chemie in ihre Anwendung auf Agricultur und Physiologie," 7te Auflage, 2: 225, 1862.

formulated the Law of the Minimum which, as commonly stated,' says that "the yield of any crop always depends on that nutritive constituent which is present in minimum amount." The use of the term minimum is not strictly accurate, as can be seen from the example of KOH and HCl. If three grams of each are present, the amount of KOH determines the yield of KCl, although both HCl and KOH are present in equal amount. However, the above statement of the law is convenient because of its simplicity.

A much broader application of the Law of the Minimum was indicated by the work of F. F. Blackman, whose conclusions are summarized in his paper on "Optima and limiting factors." Blackman called attention to the complexity of the process of carbon assimilation, the rate of which depends

on at least six factors—

1. Temperature,
2. Light intensity,

3. Carbon-dioxide supply,
4. Water supply,
5. Chlorophyll,
6. Enzymes.

plotted.

Where it is possible to vary one of these factors independently of the rest, its effect on the rate of assimilation can be measured, under suitable conditions, and a curve plotted. In this way a temperature-assimilation curve, a light-assimilation curve and a carbon-dioxide-assimilation curve can be constructed. The other factors are more difficult to control. The following curves were constructed by Blackman and Smith from a study of the rate of assimilation in Elodea.

The light curve and the carbon-dioxide curve are straight lines. The rate of assimilation varies directly with the inten

4 Cf. F. Czapek, "Biochemie der Pflanzen," 2: 841, 1905.

Annals of Botany, 19: 281-295, 1905. • Proc. R. Soc., B., 83: 389-412, 1910.

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