CORRESP ONDENCE. 



749 



we are disposed to overlook inaccuracies 

 such as tliese, lying merely on the surface. 

 It is otherwise wkh anything that betrays 

 confusion of thought in regard to the funda- 

 mental elements of the problem. This, it 

 seems to me, the writer has done in ascrib- 

 ing to centrifugal force a primary place in 

 the causation of tides. It is only as the 

 waters upon the earth's surface have free- 

 dom of motion are acted upon, therefore, 

 as independent of the earth's mass that 

 tides are possible. On the other hand, only 

 in so far as the waters take up by friction 

 and cohesion of their particles the motion 

 proper to the portion of the solid earth un- 

 derlying them, wUl they acquire the in- 

 creased tangential momentum which consti- 

 tutes the so-called centrifugal force. When 

 it is understood that the force in question 

 operates only in this indirect manner, it be- 

 comes plain that it ought not to be classed 

 with gravitation as a primary cause of the 

 tides, but rather with the rotation of the 

 earth as an important secondary factor, 

 necessary to be studied in tracing out the 

 actual operation of their real cause. 



The new mode of explaining the ob- 

 served phenomena is, however, on the whole, 

 quite intelligible and satisfactory in its ap- 

 plication to the solar tides. It requires a 

 greater effort of the imagination to see ex- 

 actly how the same principles operate in the 

 causation of the lunar tides. It is easy to 

 understand how centrifugal force will pre- 

 dominate on the side of the earth opposite 

 the moon, and how the waters on the nearer 

 side will tend to insphere themselves about 

 the centre of gravity of the rotating system, 

 a point only 2,687 miles from the earth's 

 centre. There is some difficulty in taking 

 on trust the statement that the earth will 

 feel on the side facing the moon a centripe- 

 tal force equal to the centrifugal force which 

 is said to cause the tide on the opposite 

 side, when we remember that the moon it- 

 self is a part of the rotating system, and 

 must itself claim a share, however small, of 

 the forces, centrifugal and centripetal, whose 

 balancing equivalents are to be sought on 

 the remote side of the earth. And it is far 

 from clear to the tyro in mathematics why 

 high tide should occur directly under the 

 moon, where centrifugal force, acting in a 

 direction away from the earth's centre, is 

 but slight, while centripetal force, acting in 

 the oppo&ite direction, is at its maximum so 

 far as it is dependent on proximity to the 

 centre of rotation. Although the explana- 

 tion of this latter apparent paradox is by 

 no means difficult, it will certainly prove to 

 many a fertile source of perplexity. 



The interest I have myself taken in ap- 

 plying Prof. Schneider's hypothesis to the 

 numerous practical problems which arise 

 the moment we pass in our study from hy- 

 pothetical tidal waves to the actual move- 

 ment of the waters of existing oceans, has 



led me to jot down the above points in the 

 way of friendly criticism. For the rest, I 

 would rather listen to some abler critic. 

 A. B. Lyons, M. D. 

 Detroit, June 27, 1877. 



THE NEW IDEAS ABOUT SPACE. 



To the Editor of the Popular Science Monthly. 



Dear Sir: The letter of Prof. G. B. 

 Halsted, of Johns Hopkins University, in 

 your number for July, 1877, in regard to 

 the imaginary geometry of Gauss, Loba- 

 tchewsky, and Beltrami, brings to my mind 

 the fact that there is no necessary truth in 

 many things that we have regarded (at least 

 we mathematicians) as necessary truths. 



Sir George Airy investigated the condi- 

 tions under which perpetual motion might 

 exist (Cambridge "Philosophical Transac- 

 tions," 1880, vol. iii., pp. 369-372). 



Newton's notion of negative density 

 (" Principia," book ii., sec. ii., prop, x.) is 

 another ease. 



Laplace, in the "Mecanique Celeste," 

 has indulged in a remarkable speculation as 

 to what the laws of motion would have been 

 if momentum, instead of varying simply as 

 the velocity, had been a more comphcated 

 function of it. 



These things seem to overturn current 

 metaphysics, and that is about all the good 

 in them. Yet Reid, in what he calls the Ge- 

 ometry of Visibles, chapter xli. of his "In- 

 quiry," raised a question of like nature. 

 Hamilton, as noticed by George Lewes 

 (" Problems of Life and Mind," vol. ii.. Ap- 

 pendix), has avoided any comment. 



By reason of the superb contempt which 

 this extraordinary man affected for mathe- 

 matics, I presume he thought it beneath his 

 notice. Your obedient servant, 



Lewis Kennon, M. D. 

 Fort Bataed, New Mexico, Jnly 29, 1S77. 



THE WOODEUFF SCIENTIFIC EXPEDI- 

 TION. 



We give below an important letter from 

 Prof. W^ilder, of Cornell University, on the 

 Woodruff Scientific Expedition, and would 

 call the attention of those interested to the 

 assurances it contains concerning the op- 

 portunities for study and the facilities for 

 original work which the expedition is expect- 

 ed to afford. Prof. Wilder is a member of 

 the faculty of scientific instructors, and also 

 one of the trustees of the expedition. The 

 letter, as will be seen, is in response to our 

 inquiries : 

 To the Editor of the Popvlar Science ifonihly. 



Sir : In answering your inquiry as to 

 the nature and extent of scientific work to 



