Centrifugal force and gravitation : a lecture / by John Harris.

  • Harris, John, 1942 May 3-
Date:
1873
    III! i 04 TKKUr.STIUAI^ OKAVITATION. G^ TIIK KOTATION OF THE KAHTII (OR DTTIER IM.ANKT) AS INFI.rKN('IN(J TFHKIvSTKlAL (INTFKNAI.) (JCAVITATION. All iiitpiirciit <linicnlty iiiiiy ho flms Htutcd. Let l''iir. is n'prcsrjif liiilti»ftli<'cjirtirs sjdicn": E, E, E ))oiiiff 11 srrti(»ii ;i< (he ('(|iiii(<>r, iiiid !* the jdaco of one of tlio l»(»lcs. Tlic rjirtli is ii>tii(iii<r in tlic diirction of the iirr(»\\ s, iiinl a Ixxly on Hie siir'arc at \\, is tiicrcfort'rc- vol\iiiiX with dial siirtiuM'. around llit- crntrc of llic //7 rartli at tlic rale of al)oii( KMMl miles an lioiir. A liody on llu' surface at or near I'. is ('4>iii|)arati\eiv nnintliieii- eed liv this rotatoi'N niolioii. \^-_ An arirniiient to liie tollow- ^^^ar iiii; eileet is lliere(l»re likely to siiiryest itsell' to llie stii- tleiit : (I) A ltod\- re\ olviniraronnd a eeiitre of irravitalion (oreeiilral |)oiiit ) at the rate of a thousand miles an hour iiiiisi develojte a xery eonsideraltle eeiitrifnual force. (•-') This centrifugal tor«'e oj)j)(»ses the attractive force from the centre, and must therefore (:>)'»<'•'• deductitui iVom I he a|t|>areiil i:ra\ ity or \veii>ht of the l)od\'. Hence (i|iicry), is the (apparem) weiyhl of the same l>od\ coii- sidciahly <:reater in the jtolar reuioiis than near the e(|i!a- ior ;' or is there any st'iisilde dillerence in the (ajtpareiit) weight ottlie same iiody it'removed t'roiu the one to the other situation .'' 'I'lie (|iies|ion as to t.ict is answered iii the ne':ati\e:—where is the explanation .' The i:ieal stnmhlinu hlock in this case, is the s.iiiie alr»Md\ retcired to as the prohaide oriuin ot' the error in Kepltv's iliird law; \ i/.., the neulect.to discriminate
    TEKUESTIMAL (iliAVITATION. 65 between angular and areal velocity. It is true the body on the surface near the e(]uator lias an actual areal velocity in the circle of rotation of about lOUO miles an hour; never- theless the motion is correctly represented by tiie hour- liand of a watch, vvliich likewise [tasses throu<,di the circle once in 24 hours; and if the hour-hand were extended and made about -iOOO miles in len^tli, tlu; extremity of the hour-hand would also then move with u velocity of about 1000 miles an liour. .*-',j soon as this (iict is correctly appreciated the dilliculty will ju-oltably be in a irreat mea- sure removed, because it will be understood that theaiiiin- lar velocity as observed in the honr-liand of the watch or clock is not sullicient to develope iiiiy very apju'ecialde amount of centrifugal force. The ditlicnlty may, however present itself in a diHerent form, and one in which tlm solution is not so readily apjtarent. A body revolvin<r at a short distance from the surface around the earth with such velocity as to make a ccmiplete revolution in a little less than 11 hours would not fall to the earth but continue to revolve in its orbit at that distance i^- the same manner as tlie moon. (Note. This is of course discanling the earth's atmosphere ;—i.<:. supposing the earth to be without an atmosphere; which would resist and im[iede the motion of the body.) But then, if the revolution performed in i | hours is sufficient to neutralize and overcome entirely the attractive force ; nmst not: a revolution of IM hours, which represents nearly one half the velocity, havifat least some considerable influence in reducintr the efii-ct of the central gravitating force ? To explain this case, if is proper in the first place to point out that the tenn, ceiitrifugal force, is strictly speaking a misnomer. It is one of those names which contains within itself a definition, and that defini- tion is mischievous because it is false. The force (and the motion out of which the force is devehtped) is not centri- fugal, but tangential. The teaching on thi.s sultject au- thorized at the present time would, directly, or indirectly, leadthestuilent to the conclusion that the attractive force, acting on a body in motionat right anirles to the direction \i
    TiG TERRESTRIAL GRAVITATION. in which the body is moving, conibint'S with, interferes with, increases or retards tlie motion of the body, and so be"-oineapartially or wholly inoperative in the direction of the centre whence it proceeds. It has been sliown in the earlier part of tliis lecture that sudi t(^acliing is unsound and therefore unt«'nal)le. In fact the sjravitatincr (or attractive force) is not interfered witli nor (hniinished l)y tlie taiiirential motion of thi' revolvinir body ; for examph', the 1. <»■'!! is constantly acted upon with the full force of terrestrial <rravitation, and the elli'ct of that force is to canst' the moon to constantly deviate from the tnnsrential direction of motion. ('onse((uently if a body revolvi's round the earth near tlie surface at the e(|uator, it is sub- ject to tlie full attractive force of <:ravitiition ; and if it falls to llie earth, so soon as it reaches llie uround its inde- pendent motion iiMist cease, and its gravity or weiyht is the sjune as at any otiier place on the sudiu'e. The qnes- lion as to wlit-lher a body revolvinir near the surface can escapecontact ....d continue to revolve.isevidently dej)end- ent ujion equality l>et\\een tlie Acised sine of the arc throuuh w hich the l»ody moves v: a definite time, and the distance thnninh which the gravitation would move the liodv towards the centre in the snme definite time; ]»e- cause the latter measures the tbrmer and, if e(|Ual, causes no more than tlie deviation from the taiigt-ntial direction, which is re(|nired to prodiu'e tlie arc, and in that case jh«' bodv will continue to revolve ; but if the deviation is in any degree greater than re(|uisite for the versed sine of the arc. then must the Ixidy fall to the e;irtli. ]\y taking the e(|iiivalent to a thousand miles at the ecpiator cm a circh', the case mav V»e illustrated,—as in fig. li>, where the angular divisions I 2 3 4 f> (> are each equivalent to about 1000 miles ; and the body A, near the surface of the earth is supposed to be moving in the tangential direction AD, with a velocity of about 3C)h miles in 1 minute; (which would carry it through a space equal to the circumference of the earth in about 10 hours and ;j7 miinites.) Tlio •effect of terrestrial irravitation actiim freelv on h bodv
    near tlie surfjico is known to equal in efl'ect an approach Unvards tlie centre (or space fallen throngli) of 57,!)(»u feet in aniiiniTc. Tliis would be therefore the deviation from the tanj-ential line of motion caused in the body A by the attractive force; viz, (about) MSfi feet in 52SiO feet, (ecpial to about tiOO miles in 2000 miles.) The body A, would ^ conseinientlytia- velL>OOU miles in o45 minutes, and ^ *^ arrive at IJ, hiiv- ing in that same time uiiderir( lie a deviation of its motion ti(tm ilie I C tangential line AD, measured by the verse 1 sine AE, of a^out 60) miles. And since the distance J)F, is «'qual to the distunco AE the body A, will revolve continually in an orbit at that dis- tance. (The velocity, however, should be a little increased to e(|iialize the dillc'rence in the radial distance of CA greater than CK ; (e g, if AK=I0 niilrs; then CA : CE: : 4010: 4000 mih's.)* THE TIDKS. Dirtr's MdiDiiiJ (if Asfrononiu. Paire 7^. *' InjKj l'> jiJati; VI, let Z represent tiie moon, K the €)^ earth. Now ihe moon attracts every particle of the earth': rmd ilie wat(>r i)eirig free to move, will tend towards her at o : it will be higli tide, therefore, to those idaces situated at o and its neiuhbourhood, which have •Tlie puppositioii ff mcli iiioroa.ep is inclmlod in the nssurnjjtion above that the (liHiuiici' iih\ iiroiimil to the diHtunccAL;. I-
    the inoon on the meridian; but since the quantity of water remaiiiiM the same, tlie place? at n and s, 90° dis- tant from 0 will supply the rise at p; with them there- fore and down the line n R s it will be low water. As the earth turns round with her diurnal motion, other places will advance towards the moon, or will have her in the meridian ; it will therefore be liigh tide to them at that time. So far the matter is clear; but the pecu- liarity is, tliat when it is high tide at o it will be also high at q, diametrically opposite, or with those places on whose inferior meridian the moon is situated. To render our explanation of tliis fact more lucid, let us investigate the operation of attraction on three bodies, at ditlerent dis- tances from the attractive body (Fig 1'2). The etfect of a { \ h' z. ^ a •eo liody Y, operating on three others r, z, x, in the same line would be to increase their mutual distances; for rwould be drawn to w, tiirough th(> space rw ; z, being further oil' from Y, would be drawn through a less spac;', in t!ie proportion Yi^: Yz-, viz., to v, zv being less than rw; X would be still less operated upon, and would pass through a less space towards the attracting body ; viz. xt. The result will be, that the distance of tlie two bodies r and x, from z, will l)e increased; vw and vt, tlieir new distances being greater than zr and zx, their original distances. Let the waters on either side of the earth R, in fig. 4o, pi. vi, be considered in the same circumstances as the two bodies x and r with respect to z in fig 12. The operation of the attrac- tion of the moon z, upon them and the earth will be to raise the waters at p, and to draw the earth, as it were away from the waters at r, causing a simultaneous rising of the tides at o and ([." The explanation here given is that *he moon attracts the water on the earth's surface, at i4<