Maech 12, 1920] 



SCIENCE 



271 



The trustees of Cooper Union, New York 

 City, have authorized the organization of a 

 four-year day course in industrial chemistry 

 to be started in September of the present year. 

 This course will aim to train men as analysts, 

 research chemists, foremen and superintend- 

 ents in manufacturing plants, and sales 

 agents. Mr. Maximilian Toch, has been ap- 

 pointed adjimct professor of industrial chem- 

 istry. 



Dr. H. E. Roaf has been appointed to the 

 university chair of physiology tenable at the 

 London Hospital Medical College, and Pro- 

 fessor T. Swale Vincent to the university 

 chair of physiology tenable at the Middlesex 

 Hospital Medical School. 



DISCUSSION AND CORRESPONDENCE 



AN ODD PROBLEM IN MECHANICS 



To THE Editor of Science: The following 

 statements are intended to throw light on the 

 questions raised by Dr. Hering in his letter 

 entitled " An odd problem in mechanics " in 

 Science for January 9, 1920. 



The statements in the second paragraph of 

 the letter are correct: a body travelling east- 

 ward on the ground along the equator will 

 exert less pressure on the ground than one at 

 rest relative to the earth's surface, and still 

 less pressure than a body travelling westward. 

 The correctness of this statement was verified 

 experimentally in connection with observa- 

 tions to determine the intensity of gravity at 

 sea by determinations of the boiling point 

 compared with readings of the mercury 

 barometer. In the spring of 1909 the Eussian 

 government placed a war ship at the disposal 

 of Professor Hecker, who was engaged in this 

 work, and tests were made in the Black Sea 

 by comparing the gravity obtained when the 

 ship was rimning east with gravity at the 

 same point when the ship was running west. 

 The correction in question is of the order of 

 0.100 dyne for a vessel of fair speed, and 

 the reality of the expected effect and the 

 necessity of applying a correction for it were, 

 of course, verified. It should be mentioned 

 that the rolling, pitching and lifting of the 

 ship, which occur on all courses, were such 



that the total effect of the ship's motion did 

 not necessarily reverse in sign when the ship's 

 course was reversed. 



In the third paragraph it is assumed that 

 the " gyroscopic tendency (of a rotating hori- 

 zontal flywheel) to get into the vertical plane 

 has been counteracted and may be neglected." 

 But the forces Dr. Hering has been describing 

 in this paragraph are exactly the gyroscopic 

 forces themselves that tend to make the axis of 

 the flywheel parallel to the earth's axis. At the 

 equator, since the celestial pole is in horizon, 

 the plane of the flywheel would tend to become 

 vertical. If the gyroscopic tendency is coun- 

 teracted, there is, of course, no shifting of the 

 axis of rotation. 



In the cases supposed in the fourth para- 

 graph, there are gyroscopic forces arising from 

 the earth's rotation that Dr. Hering has not 

 considered. When the plane of rotation is 

 north and south, that side of the disk which is 

 descending will tend to move eastward, and 

 the side that is ascending will tend to move 

 westward, thus tending to turn the plane of 

 the disk out of the meridian into the prime 

 vertical, so that its axis shall be parallel to lihe 

 axis of the earth. The apparatus will there- 

 fore not be dynamically balanced as Dr. Her- 

 ing states. At the equator there is no twisting 

 effect due to the horizontal motion of the par- 

 ticles on the edge of the disk, for this effect 

 varies as the sine of the latitude. At the 

 equator, when the plane of the disk is east and 

 west, its axis is parallel to the earth's axis, and 

 the apparatus is dynamically balanced. 



The nature of the general question raised 

 may be stated in a few words as follows. For 

 a body at rest on the earth, it is sufficient to 

 consider only the attraction of the earth and 

 the centrifugal force due to the earth's rota- 

 tion. For a body in motion relative to the 

 earth, there are additional apparent forces to 

 be considered, the so-called gyroscopic forces, 

 or compound centrifugal forces. These ap- 

 parent forces arise from the fact that our axes 

 of reference are not fixed in direction in space, 

 but are rotating. These forces are all propor- 

 tional to the product of the earth's angular ve- 

 locity of rotation by a comiwnent velocity 



