110 Canon Moseley on the Descent of a Solid Body on an 



and the third of equations (11), and observing that because of 

 the small difference of a x from a, and the exceeding smallness 

 of the factors 



w sin (cj) + 1) , w; sin ((f) — i) 

 2E cos cj) 2E cos <j> 



we may consider 



we have 



w sin (cj) + C) _w sin (<£ -f 1) 

 2E cos </> a "~ 2E cos f Qy 



wsin {4> — t) . _ wsin (4> — t) . 

 ~2Ecos<£ 1_ ~2E^cos^ ' 



ia2 =(l +Wl )(i-H){i + ^i^«} 



f, wsin (<6 + t) "I 

 L 2Ecos$ S 



whence, by reduction, 

 1 « 2 =«(1 + / 1 X)(1-/ 2 X) 



f / n z^ff sin A 2 /wa tan d> cos A 2 "1 



K 1+ hje )-(— m— )j 



^2=^(1 + / 1 X)(l-^ 2 \) 



r / ?/•« sin A /wa tan cos A 2 1 



or, approximately, 



i« 2 =fl(i + >s (l-x* 2 )(l + — ^— J, 



^^fltl+Xyfl-X^l ^— J. 



(13) 



IV. 



Case III. — TF/^?2 no point in t lie plate is mechanically fixed. 



Since X (fig. 1) is a point so taken that if the plate were cut 

 asunder there, the resistance of the part X A to being thrust 



