298 CARNEGIE INSTITUTION OF WASHINGTON. 



found; the situation is given a geometrical interpretation; and it is 

 shown how to reduce the number of places used in the calculations, 

 without impairing the accuracy, to the number of places to which the 

 final results are determinate. The question, which has important 

 astronomical applications, is illustrated by a numerical example. 



(2) A direct and general method of determining orbits: 



The contribution to this much-worked problem is both theoretical 

 and practical. Among the theoretical features are: (a) a direct 

 application of the geometrical and dynamical conditions, carried out 

 so that no artificial difficulties are introduced; (6) an investigation of 

 the degree of indetermination of the solution; (c) a complete discus- 

 sion of the exceptional cases which may arise; (d) proof that the 

 apparent motion of the observed body can not be permanently in a 

 great circle unless it moves along the ecliptic ; (e) a general analytic 

 solution of the problem which avoids all successive approximations. 

 The greatest practical contribution is that almost at the very begin- 

 ning, after the indetermination in the final results has been found, the 

 number of places used in the computations may be correspondingly 

 reduced. In most cases which arise in practice in preliminary orbit 

 computation five-place tables are sufficient. 



(3) The introduction to celestial mechanics: 



This has been completely revised and is in the hands of the 

 printers. 



(4) The Lagrangian solutions of the problem of bodies: 



The Lagrangian solutions of the problem of three bodies are those 

 in which the ratios of the mutual distances of the bodies are constants. 

 The methods of Lagrange apply only to three bodies. It is shown 

 how to find the number of solutions when there are any number of 

 bodies. The method of treatment depends on the theorem that no 

 solutions can appear or disappear as the masses of the bodies vary. 



(5) On the fission of stars: 



The difficulties of the theory that binary stars originate by fission 

 of single stars are brought out by a discussion of the conditions for 

 equilibrium of a mass whose rotation increases only as a consequence 

 of its contraction. 



METEOROLOGY. 



Bjerknes, V., University of Leipzig, Leipzig, Germany. Grant No. 835, 

 allotted December 13, 1912. Preparation of a work on the applica- 

 tion of the methods of hydrodynamics and thermodynamics to practical 

 meteorology and hydrography. (For previous reports see Year Books 

 Nos. 5-11.) $1,800 



During the past year a German edition has appeared of the first 

 and second volumes "Statics" and "Kinematics" of the author's 

 book "Dynamic Meteorology and Hydrography." 



