¥ivl&M(^ m SijniboHcal I^^^ Hi/i 



and V as ' sides,, and 7 is at right angles to the plane ^ or ti at 

 parallelogram ; hence it follows, that the line which sipnboUcaUy 

 represents uv is equal numerically to the area of the paralleloyram 

 uv, and is drawn at right angles to its plane. 

 io ?!tiim iU.tBfiJ a'iJ85q<(F» Hi jbomxijoo uu^ iXu^yi- ^di moil 



' " Th^e ^riii^dlfA^s '^feMffi^ieilt td #Me m tii ^a;()^lf ^^^ip^ 

 bolical system here proposed to a variety of cases of considerable 

 importance. Among others the following may be mentioned as 

 interesting, because of its connexion with the problem of the 

 pendulum as a means of exhibiting the earth's rotation; :'^fi.^Js 



as follows. 



tinn VM 



IP-. 



^'*If we calculate the indtioh of a particle relatively to the eai. 

 rorgetting to allow for the earth's rotation, we may complelte' 

 correct the error by supposing the accelerating force, '"^ 



dsdt Ik 81 Mi hm { fioitfil?i\ <?/ "^ i.j^baB '.buiixi^Bm ab-isg^'i 



. , Jj'jrrrhb -^rf bfjQff 



to act on the particle ; o) denotnig a line equal numerically to 



the earth's angular velocity and parallel to the polar axis, and u 



the distance of the particle frdm the darth's centre; -j- being 



mio': . . ' . dt ■,. 



t^^oOn the supposition that the earth is fixed. This is the 

 ixViQ centrifugal force J —(o{ci)u) represents the ordinary statical 

 centrifugal force in magnitude and direction, and the additional 



fffitf^r^^Sii -TT arises from the motion of the particle relatively to 



to «lB&»'iq'*i doidw (f) nm- di %} ndi :)d ot «ioo! sd xLoidw 

 »^;LBy means of this result the trtle equationsdf m6tion'of a' pm- 

 dulum are obtained with great facility ; they are as follows : — 



flfr a dt 



'" ' d\j a ^ . ^ dx 



-^ .^.,-.^ dt^ a^ dt ..,:>,.;..., .rff 



fere X and y are the coordinates of the projection of tli^^^^^r 

 ting particle on the horizontal plane referred to two horizontal 

 axes, one of which always lies in the meridian plane, n denotes 

 the earth's angular velocity, and X the latitude. ' ' " ' 



It is obvious from these equations, that the effect produced by 

 the earth's rotation on the pendulum is proportional in every 

 respect to sin X. .^ ^iufe.ui, y/o7. 



[To be continued.] 

 fid /!i3cp)"ig y«iii )orjj ft io iHniJ&ham^ odT * 



