332 ' SCIENTIFIC RECORD FOR 1884. 



of gravity is perpendicular to the surface of a sphere. He prefers him- 

 self, however, to consider the earth as a spheroid formed by the rotation 

 of a fluid mass, and to assume that the direction of the plumb line is 

 always towards the center of the spheroid; this he thinks corresponds 

 better to the practical taste of the American, and is about the same as 

 Professor Ferrel has adopted. He then shows that of the three com- 

 ponents into which Professor Davis analyzes the deviating force of the 

 earth's rotation, only the first actually exists. {Z. 0. G. M.^ xviii, p. 

 376.) 



256. H. Bruns, of Leipsic, in reference to the movement of the atmos- 

 phere over the earth's surface, states that Itothand other authors have 

 generally assumed the earth's surface as perfectly smooth; he, therefore, 

 gives the formulae required when we introduce the considei'ation of 

 friction, and shows that assuming the earth to be a surface of rotation 

 the friction will not afiect the azirauthal deviation known as Ferrel's 

 law. {Z. 0. G. ili., XVIII, p. 425.) 



257. F. Rotij, under date of October, 1883, communicates a note on 



the deviations of motions of the earth's surface, in which he shows that 



the angle that determines the direction of motion as affected by the 



earth's rotation varies only with the time and is entirely inde|)endent 



of the kind of frictional resistance ; it is the same for any force that acts 



in the direction of the path, and holds good for locomotives, steamshij)S, 



moving animals, &c. If the frictional resistance is in dn-ect proportion 



to the velocity, but in other respects the moving body is impelled by its 



own inertia, then the orbit is a spiral turning with the sun and can bo 



expressed hy the following equation : 



a 6 



r =.roe — -. 



2 w sin ^ 



We therefore arrive at a remarkable confirmation of the assumption 



with which Guldberg and Mohn commence their investigations. [Z. 0. 



G. M., XIX, p. 41.) 



258. F. Roth, in reference to his development of the path of moving 

 bodies on the earth's surface, controverts the position taken by Professor 

 Brniis to the effect that theoretical and mathematical investigations 

 have but little practical interest for the progress of meteorology uidess 

 every detail is considered instead of the approximate solutions frequently 

 given; the fact, however, is that Bruns' effort to introduce the consid- 

 eration of friction can scarcely be called very successful, as he ceitainly 

 has made no greater progress than did Finger in his memoir of 1877. 

 However, Roth finds in Bruns' work a confirmation of the correctness 

 of his own previous assumption, namely, that the eaith is a sphere to 

 whose surface the observed force of gravity is iierpendicular. Taking 

 complete account of the side forces introduced by frictional resistance, 

 Roth shows that it is not immaterial in which direction a bodj^ moves 

 on the earth's surface, but that the deviating force is for a motion to- 

 wards tke east greater than one towards thu west. He gives also tbo 



