November 29, 1901.] 



SCIENCE. 



853 



Presque Isle I investigated, but they proved to 

 be unfounded. Who can tell how this African 

 snake found its way to the shore of Lake Erie 

 and how long it had found subsistence there ? 



e. l. moseley. 

 Sandusky, Ohio, 



Oct. 27, 1901. 



SHORTER ARTICLES. 



THE TJNHXPLAINED SOUTHERLY DEVIATION OP 



PALLING BODIES. 



The formula published by Mr. Eoever, of 

 Washington University (Science, July 12, 1901, 

 p. 70), giving the southerly deviation of falling 

 bodies due to the earth's rotation, is of special 

 interest, because it marks a fresh attack upon 

 a problem which in my * History of Physics,' p. 

 75, I call an unsolved problem. The difficulty 

 lies in a wide discrepancy between the theoret- 

 ical and the observed results. The latter are 

 over 1,000 times greater than the former. 



1. Experiments. — When Robert Hooke under- 

 took to verify experimentally Newton's predic- 

 tion of an easterly deviation of falling bodies, 

 due to the earth's rotation, he reported also a 

 small southerly displacement.* 



When in 1791 G. B. Guglielmini again under- 

 took to verify Newton's prediction by a series 

 of experiments from a tower at Bologna, a 

 southerly deviation was again observed. He 

 found H ('height' or distance fallen through) 

 = 241 Paris feet (78.3 m.), E. D. ('easterly de- 

 viation ')= 8.375 lines (18.894 mm.), S. D. 

 ('southerly deviation ') = 5.272 lines (11.894 

 mm.).f 



In 1802 J. F. Benzenberg experimented from 

 the St, Michael's tower in Hamburg. H = 235 

 feet (76.3 m.); E. D.= 3.99 lines (9.00 mm.) ; 

 S. D.= 1.5 lines (3.4 mm.).'| 



*See Ball, ' An Essay on Newton's Principia,' pp. 

 146, 149, 150, 



tSee Gilbert's Annalen, Vol. XI., p. 172; Vol. 

 XII., 1803, p. 372 ; Vol. XIV., p. 222. Eosenberger, 

 in his * Geschichte der Physik,' Vol. III., p. 96, refers 

 to Guglielmini's book, ' De diurno terras motu, 

 experimentis physico-mathematicis confirmato,' 

 Bologna, 1792, but as early as 1803 the book is spoken 

 of as being very rare. 



t Gilbert's Ann., Vol. XIV., p. 222. Rosenberger 

 refers to Benzenberg's book, ' Versuche iiber die 

 Gesetze des Falles,' Hamburg, 1804. 



In 1804 Benzenberg experimented in a shaft 

 of a coal mine at Schlebusch. H. = 260 ft. (84.4 

 m.). An E. D, was noticeable, but on selecting 

 from the total number those experiments which, 

 in his judgment, were made under the most 

 favorable conditions, there seemed to be no in- 

 dication of a S, D,* 



In 1831 F. Reich experimented in a mine- 

 shaft at Freiberg, H, =158.5407 m., E. D. = 

 28.396 mm., S. D. =4.374 mm. These results 

 are deduced from six series of experiments. 

 Altogether 106 balls were dropped. Reich's 

 are the most carefully conducted experiments 

 on the subject which have been made. Yet 

 they differ much among themselves, though not 

 as much as those of Benzenberg.f 



In 1848 W. W, Rundell published experi- 

 ments made in the shaft of a Cornish mine.f 

 Balls were dropped through a distance of one- 

 fourth of a mile and a S. D. of 10 to 20 inches 

 (25 to 51 cm.) was noticed. From the account 

 of the experiments it is difficult to convince 

 oneself that sufficient precautions were taken 

 against disturbances from air-currents. 



All observers experimented with metallic 

 balls. Are these observed southerly displace- 

 ments due wholly to experimental error? 

 Though we may incline to that opinion, we can- 

 not deny the force of Benzenberg's remark: 

 ' Sonderbar bleibt doch diese Tendenz der Feh- 

 ler nach Siiden.' 



2. Theory. — Mr. Roever is not the first to de- 

 rive a formula for S. D., due to the attraction 

 of the rotating earth. This was done in 1803 

 by Gauss § and by Laplace. || 



Neglecting the resistance of the air, G^auss 



obtained 



Yi.Tf . ^= y = \ cos <p gnt^, 

 S.D. = a; = \ cos <p sin (p gnH*, 



where ic is the angular velocity of the earth, 

 the latitude. Applying this to Benzenberg's 



* Gilbert's Ann., Vol. XVIII., p. 381. 



tSee Poggendorff's Ann., Vol. XXIX., 1833, p. 494. 

 Rosenberger refers to Reich's book, 'Fall versuche iiber 

 die Umdrehung der Erde,' Freiberg, 1832. 



X Robertson's Mechanic's 3Iagazine, London, Vol. 

 XLVIII., p. 485. 



I Gauss, ' Werke,' Vol. V., 1877, p. 495. 



II Bull. d. sciences par la Soc. Philomath., Plairial an 

 11 (1803). 



