16 



wo liavo 



REPORT 1876. 



^.-cV'4.^-(,"0,-6)"^-,,--6"(u+*)"+^>-c%-26)"-J-g-c"Ca+2J)"-|.^^C, 

 = f I { Q 1 + Q, + Q5 • • . . + Qh-1 } 3m(c\")dx, if ,1 Ije even, 



smli -^— 

 



cosli-T^ cos , 



b 



2^«+Qi+Q.-... + Q.-.. 



- sin(c x")(h, if » Ijc 

 imeveii. 



The exponeuis on the left-liand side are always to be unmerically negative, viz. 

 they should be written - V{t-"«-"}, V \c""{(t—h)-"\, &c. The quaiitity c is redun- 

 daut, and may be put equal to uuity without loss of generality. 



Putting n=2 and c = l, we tind that 



^^•here 



Now 



■+'^"> -T-' f {/ (" T) +/ (f. -?) }- «'"'■. 



/•(-„ V ^ginb ;V3+8in 0;V2+2g) 

 -^ "^'^ ■'^ cosh^V2-cos(^V'2+2j)* 



f-.^-^ + fi-(.<-„)' + e-C..+«)^ -f &c.= ^ I 1 +2e" "'cos ?^* 



llf A 1 



+2e «-^cos^'' + &c. ; 

 a J 



whence, the notation being that of the aumdamenta NoAa,' it can be shown that 



^(?) = V\/(l) • r{f(^' ^ + -» +/ (^, - ..-i.) } sin^.., 

 ud therefore 



■w-hert 



e(.r)=\/(|). [ j/ («<,«)+/ (.^,-.)} 



sin fdt, 





Also it can be shown that 



where 



e('^-) =^(|) . J { ,^(«;, u)+<i>{uf, - u) I cos m, 



<h(p, „)_ -^i"h/>V2-sin (;)V2+ 29) 

 coshpV'2— cos 0V2+2y)" 



On Parallel Motion. By "W. Hatden. 



lu this paper the author noticed several cases of approximate three-bar paraUel 

 motion, founded upon certain numerical coincidences. 



