JUN 1 1917 -^1 



^i^ \^ 1. ^:d X^ \^ XJ^ 



Fbiday, June 8, 1917 



The Derivation of Oriits, Theory and Prac- 

 tise ; Professor A. 0. Leuschner 571 



Scientific Events:— 

 The Third Interstate Cereal Conference; 

 The Society of Industrial Engineers; Sub- 

 committees of the Council of National De- 

 fense; The American Physiological Society 

 and the War 584 



Scientific Notes and News 586 



University and Educational Neivs 588 



Discussion and Correspondence: — 



The Physiography of the Lower Amazon 

 Valley as Evidence bearing on the Coral 

 P.eef Prollem: John L. Rich 589 



Quotations : — 

 A Pioneer in Physics 590 



Scientific BooTcs: — 



Evans on the Birds of Britain : J. A. A. . . . 591 



Special Articles: — 

 Factors in the Growth and Sterility of the 

 Mammalian Ovary: Professor Leo Loeb. 



Nematodes : N. A. Cobb.. . 591 



Societies and Academies:- — • 



The Botanical Society of Washington: Dr. 

 H. L. Shantz. The Biological Society of 

 Washington : Dr. M. "W. Lton, Jr 593 



MSS. Intended for publication and books, etc.. intended for 

 review should be sent to Professor J. McKeen Cattell, Garrison- 

 On-Hudson, N. Y. 



THE DERIVATION OF ORBITS, THEORY 

 AND PRACTISEi 



Less than twenty-five years ago it was 

 commonly accepted among astronomers and 

 mathematicians alike that the orbit prob- 

 lem had been solved both in theory and in 

 practise. Without detailing the well-known 

 history of the development of orbit meth- 

 ods before that time it is sufficient to re- 

 mind you that although Newton, after suc- 

 cessfully integrating the differential equa- 

 tions in the problem of two bodies and 

 verifying Kepler's laws, proposed a geo- 

 metrical method which was successfully 

 applied by Halley particularly in deter- 

 mining the orbit of the well-known comet 

 which bears his name, the integrals derived 

 by Newton were not translated into a thor- 

 oughly practical method for determining 

 the constants or elements from the initial 

 conditions furnished by observation until 

 1797 when Olbers published his i;amous 

 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 New- 

 ton of the equations of motion in the two- 



1 Address of the vice-president and chairman of 

 Section A, American Association for the Advance- 

 ment of Science, read at a joint meeting of Section 

 A, the American Mathematical Society and the 

 American Astronomical Society, on Thursday, De- 

 cember 28, 1917, at New York. 



