CHAPTKH 111. 



OTHKK IN'SriUMI'.XI'S Fdi: hHSKIM INC IIOIMZONTAI, M(i\ KMKNT 



§ 80. J/./v-- fnr U, rn/L 



I'khii \vli;it luis lifcii <;ii(l in ^ J^ I") niul ]ll i( will lie iilivimi- tli;it ;ui\' 

 inctllDil liv wliich :i iiiLi--; i:\n If .-li|>|i<ii'tiMl willi niir (nr two) di'^ri'i'- dl' fVci'dmn 

 t<i innvc liiirizi>nt;iliy, :iinl in ncntial ur CccMy -(:ilil<' (■i|uililiriiiiii with r('s]i(ii id 

 .-Hell niDVemi'iUs, ciiii 1«' :>(lii|il(il in llif di-itiu ni' a limizuntal <ri-niiinii't<T, tlu' 

 ccntri' of jicrcu.-siiin of tln' nia-s rrlati\i' lu \l> axis {nv |i(iini i nf -iippMii IciiiL;- 

 lakfn as the staiulanl nf ri'st. 



One nii'tliiul of su|)|i()i't, in wliirli the ( (|iiililiiiiini ran \'r made a-^ t'rrM\- 

 ^tal)lc' as may lie desired, is <^iven «Inn a mas- nsts liv mean- ci' a rnr\rd liti-e 

 "n aimtlier plane or cnivi-d snifacr lixid I rldw it, the ma-s having IVerdom In 

 lull. Tile steadiness of the instantaneous axi- may lie increased li\- sn|i|iortinii- a 

 -ecund nia.-s there, with appiojiriate freedom of motion relatixcK- lo liie first m;iss. 



In llie li^inie, let J'<l lie a poiiion of the liase of 

 the lolling;- mass, \\ho^e ci'iitre <.f eia\itv is at '/. and 

 J'<^' a portion of the fixed snrfaee on which the nja-s is 



free to I'oll. Let nn<l ' >' III' till' ies])ee(i\e centies i,f 

 eni\atni'e. In the initial po-ition of eijiiililn imii the 

 lilU' 00' is SU] posed to he verlieal and thel-efore eon 



tains G. Now let the mass hedi-plaeed fhroni;h a small 

 are I'(l and let l'</ he made eipial to /''>. Th,. di>- 

 plai'emenl hrinir- (_' into eontaet with <)'. and ean-es the 

 radius (iO to foim a prolon<;ation of the ladins O'O' ■ 

 Tfeni-e a line (I I,', (hawn so that the anele < >(>l! is eipial 

 to VCt'il' , will he \ertieal ill the new pM^ition. 'flu' 

 i-i|llililiriniii, W ilh respect to the a — limed ili-plaeement, 



will tiierefore he .sfalile if '^Z is liel.,\\ /,'. nenlial ^' if loineidi- uilh /,', ami 



iiiistahle if ^/ is ahove /.'. 



Writing; i- ami r' for the radii of <iii\ aline <>l' and "/'' ii-pecti\ el\ , and 



8 for the are thron^li which the point of contai't iiio\cs, we have in the tri inuh' 



out I 



, ,, • * • / « " \ 



Ol; : r = .«in : sin I ■ I. 



r V ;■ ( ' 



= r : r | ,•', 

 if we :L>'«iinie .v to In- execediiij^ly small compared with thi' ladii 

 llei PI! : r — ,' : ,■ -f ,', 



