Cornell University Medical College in the City of New York Admits holders of baccalaureate degrees or seniors who can present a degree at the completion of the first year. All students must have completed College courses in Physics, Chemistry and Biology. Instruction by the laboratory method continued throughout the course. Classes divided into small sections facilitating personal contact of student and instructor. Clinical teaching concentrated in those services of Bellevue and New York Hospitals under direct control of Cornell. Additional facilities in other Hospitals. Graduate Courses leading to the degrees of A.M. and Ph.D. are offered in the scientific departments of the Medical College under the direction of the Graduate School of Cornell University. Session opens the last week in September and oloses the second week in June. Fees including all College charges do not exceed $200 a year. For further information and catalogue address The Dean, Cornell University Medical College Department B. First Avenue and 28th St. New York City 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 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 Johns Hopkins University Tulane University of Louisiana Medical School The Medical School is an Integral Part of the University and is in close Affiliation with the Johns Hopkins Hospital ADMISSION The charge for tuition is $240 per annum, payable in three instalments. There are no extra fees except for rental of microscope, certain expensive supplies, and laboratory breakage. Summer Work for Gradautes in Medicine Beginning June 1st, courses in Medicine, Surgery, and various specialties, as well as in several of the underlying scientific branches, wil be available for graduates in Medicine. These courses will extend over six weeks and are fully described in a special circular. The annua! announcement, application blanks, and circular describing graduate courses may be obtained by addressing the Dean of the Johns Hopkins Medical School Washington and Monument Sts. BALTIMORE, MD. 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 Medicine A school for physicians desiring practical clinical oppor tunities, 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. 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 appoint ment 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 Requirement 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 St. Anthony and Lawrence Sts., Philadelphia, Pa. Syracuse University College of Medicine 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. The First Two The Third Year The Fourth are spent in mastering by laboratory methods the sciences fundamental to clinical medicine. is systematic and clinical and is devoted to the study of the natural history of disease, to diagnosis and to therapeutics. In this year the systematic courses in Medicine, Surgery and Obstetrics are completed. 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 clínical 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, 307 Orange Street SCIENCE 571 584 586 THE DERIVATION OF ORBITS, THEORY LESS than twenty-five years ago it was commonly accepted among astronomers and mathematicians alike that the orbit problem had been solved both in theory and in practise. Without detailing the well-known history of the development of orbit methods before that time it is sufficient to remind you that although Newton, after successfully integrating the differential equations in the problem of two bodies and verifying Kepler's laws, proposed a geometrical method which was successfully applied by Halley particularly in deter588 mining the orbit of the well-known comet which bears his name, the integrals derived by Newton were not translated into a thoroughly practical method for determining the constants or elements from the initial conditions furnished by observation until 1797 when Olbers published his famous method of determining parabolic orbits for comets from three observed positions. This special method was followed at the dawn of the last century by the general method of Gauss which permits of the determination of the elements from three observations without previous hypothesis regarding the eccentricity, a method applicable equally to comets and to planets. It is to be noted that both Olbers's and Gauss's methods rest on the previous analytical solution by Newton of the equations of motion in the two 589 590 Evans on the Birds of Britain: J. A. A. ... 591 Special Articles: Factors in the Growth and Sterility of the Societies and Academies: The Botanical Society of Washington: DR. H. L. SHANTZ. The Biological Society of Washington: DR. M. W. LYON, JR. 593 MSS. intended for publication and books, etc., intended for review should be sent to Professor J. McKeen Cattell, Garrisonon-Hudson, N. Y. 1 Address of the vice-president and chairman of Section A, American Association for the Advancement of Science, read at a joint meeting of Section A, the American Mathematical Society and the American Astronomical Society, on Thursday, December 28, 1917, at New York. body problem. In fact these orbit methods may be characterized as an evaluation of the numerical values of the constants or elements from given positions on the basis of the integrals found by Newton. It might be supposed that the mere evaluation of the numerical values of the constants of integration in a given case when the form of the integrals is known ought not to involve any considerable difficulties. But the solution of the unknown elements from the given equations of condition leads to very complicated expressions which can be solved only by successive approximations. This unfavorable condition arises from the occurrence of series in which the coefficients depend upon the unknown elements. Until the early nineties of the last century the chief aim of astronomers and mathematicians had been to modify the methods of Olbers and Gauss by transformations which would increase the degree of accuracy of the first and the convergence of later approximations. The most successful orbit methods would then be those which would yield the elements with the greatest degree of accuracy and with the minimum of numerical work. The observations in general furnish three directions of three heliocentric positions of the body, each seen from one of three different positions of the observer. The problem of the older methods is to pass a plane through the center of the sun which cuts the three directions in such a manner that the body moves in accordance with the law of areas in the conic, which is defined by the three intersections of the plane with the directions, and by the center of the sun. It is evident at once that if the three directions are taken at short intervals they must be given with the utmost precision so that the parameters of the conic may be determined with any degree of accuracy. In general a very large number of planes satisfying the required conditions may be drawn within the unavoidable errors of observation, so that every preliminary orbit is more or less indeterminate. Thus while a perfect theory might be available for the evaluation of the elements, in practise the numerical accuracy of the orbit will be limited. This limitation of accuracy in general increases with the ratio of the errors of observation to observed motion. In addition, even with perfect observations distributed over a sufficiently long heliocentric arc, cases occur in which the mathematical expressions for the solution of the elements lead to indeterminate forms. In some cases these indeterminate forms are inherent in the physical conditions of the problem. In other cases they may be avoided by proper mathematical devices or by a different mathematical treatment of the problem. One of the best known cases of indeterminateness arising from physical conditions is that in which the orbit plane coincides with the ecliptic. In this case the position of the orbit plane, usually defined by two elements, is given at once, but since each of the three observed directions furnishes but one independent condition, namely the longitude, while four elements remain to be found, the problem becomes indeterminate and requires a fourth observation for its solution. One of the best known cases of the other type of indeterminateness arising from the mathematical formulation of the method is the so-called Ausnahmefall (exceptional case) of Oppolzer in Olbers's parabolic method. When the orbit is supposed to be parabolic only five elements need to be determined from the six conditions furnished by observation. The observed direction is usually given in right ascension and declination and may be considered as the intersection of two planes which may be introduced as given condi orbit tions. Since the choice of these planes is arbitrary, as long as their intersection coincides with the line of sight Olbers reduces the number of available conditions by rejecting one of the arbitrary planes for the middle place or second observation and adopts for the other arbitrary plane that which corresponds to a great circle drawn through the observed place of the body and through the sun. = Since the three distances of the body are not furnished by observation they enter the problem as additional unknowns. Usually the distances are derived first, whereupon the solution of the elements becomes comparatively simple. In Olbers's method one of the fundamental relations for the determination of the distances at the first and third dates has the form PMP, where M is equal to the product of the ratio of two triangular areas into the ratio of the trigonometrical sines of the perpendicular ares drawn from the first and third observed places, respectively, to the great circle through the sun and the second observed place. The ratios of the triangles referred to form a very important consideration in many orbit methods. The triangles are contained between successive radii vectores from the sun to the body. For short arcs or intervals these triangles differ but little from the corresponding sectors bounded by the conic, and since according to the law of areas the sectors are proportional to the intervals, the triangles are very nearly proportional to the intervals. The ratios of the triangles may then be developed in series of which the first term is identical with the ratio of the intervals and of which the later terms contain the powers and products of the intervals, the inverse powers of the heliocentric distances r and their derivatives. They may be made to depend on the second heliocentric distance r and its derivatives. Since r and its derivatives depend on the elements in the orbit their values in general can not be known until the first approximation has been accomplished by placing the ratios of the triangles equal to the ratio of the intervals. The series representing the ratios of the triangles have been the subject of intensive study in connection with the orbit methods resting on the integrals of Newton. The most exhaustive study of the true radii of convergence of series of this type is due to Moulton. He demonstrates analytically the empirical conclusions of astronomers that the series may lose their applicability for comets observed near perihelion at a moderate distance from the sun, while for minor planets in general they give universal satisfaction. In referring to the indeterminateness in Olbers's method I am not at this moment concerned with any inaccuracies that may arise from his using in the first approximation the ratios of the intervals for the ratios of triangles. The indeterminateness I am referring to arises from the fact that when the first and third observed positions lie on the auxiliary great circle through the second place and the sun, referred to above as being introduced by Olbers, then both the perpendiculars from the first and third places on this great circle become zero and M becomes indeterminate. It becomes nearly indeterminate when the three observations lie approximately in the great circle through the sun, and the degree of indeterminateness in such cases depends upon the magnitude of the errors of observation as compared with the magnitude of the perpendiculars. It is evident that perpendiculars of but perpendiculars of but a few seconds accurately derived from precise observations would still yield a working first approximation, while larger perpendiculars comparable to the errors of observation would lead to fallacies or yield nothing. Here |