58 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



face, so that the calculations based thereon in the above-mentioned 

 three articles must necessarily lead to incorrect results. 



The oldest of these, however (by von Baeyer), appears of special 

 interest as in it reflections are made which betray a tendency to 

 abandon the Hadlerian motion. On p. 380 von Baeyer says: "a 

 particle of air put in motion at a definite angle to the meridian on 

 the surface of our spheroid of rotation at rest and continuing its 

 way in the direction given to it without any hindrance or disturb- 

 ance under the general influence of gravity would describe a short- 

 est line. . . . Let us now imagine the terrestrial spheroid put 

 in motion from its condition of rest, then the particle of air when set 

 in motion in the direction a will already have this motion of rotation, 

 it can therefore no longer describe a shortest line but its path will 

 be the development of the shortest line on the spheroidal surface 

 according to the circumstances of the rotation pertaining to it." 

 It is to be regretted that these fruitful ideas were completely set 

 aside in the course of the mathematical discussion in favor of the 

 Hadlerian theory. When I first became acquainted, this year, with 

 von Baeyer's article the above lines reminded me forcibly of a pro- 

 cess I had made use of in the year 1879 to set forth the origin of the 

 relative paths in simpler cases of a rotating system such as the earth 

 presents and to base on it also a derivation of the equations of rela- 

 tive motion. 3 



My treatment was simply, as follows : If a plane disk revolves 

 uniformly, then will a body or material particle influenced by no 

 forces whatever or by those whose direction is perpendicular to the 

 disk, progress uniformly in a right line (that is when considered 

 absolutely) and the relative path on the disk will be the continuous 

 series of points which come in contact successively with the body. 

 This conception, which evidently agrees essentially with that of 

 General von Baeyer, can be extended to the rotating system of the 

 spheroid which is under discussion, but at the same time it is evi- 

 dent at a glance that the first part of the above quotation from von 

 Baeyer's article contains an inaccuracy. The course of the point 

 on the surface of a spheroid at rest can be a shortest or geodetic 

 line described with constant velocity, only when the attractive force 

 of the earth is everywhere perpendicular to the surface; in reality, 

 however, it is the force of apparent gravity, that is to say, the result- 



3 Sprung: Studies concerning the wind and its relations to air pressure, 

 Part I; On the mechanics of the motions of the air. From the archives of 

 the Deutschen Seewarte (German Marine Observatory), No. 1, 1879. Zeit- 

 schrift der Oesterreichisches Gesellschaft fur Meteorologie, XV, 1880. 



