318 Mr Hart, On two models of parallel motions. [Dec. 8, 1879. 



AD : BG :: PA : PG 

 :: PE : FC, 



that is AD = const., 



so that if the bars JEB, FC be connected by a sixth bar 

 .J. BG.PE 

 ^^-~PC~' 

 the angles at E and F will be equal, and consequently since 

 PE.EB = PF.FG 

 PB'-PG^ = constant, 



or P describes a straight line perpendicular to BG. It may also 

 be shewn that PD^ — PA^ is constant, so that P describes also a 

 straight line relatively to AD. 



The following particular case is of special interest. Let the 

 links be so chosen as to satisfy the conditions 



{PE + EBf + BG' = {PF+ FGf, 



PE = EB, and consequently PF=FD*. 



By the former of these conditions we see that when PEB (and 

 therefore PFG) is a straight line, PBG and PDA are right angles, 

 and therefore since P moves perpendicularly to BG and AD, they 

 are always so. 



The second of these conditions further shews that PE, PF 

 have tram motions relatively to BG and AD, that is, if PE, PFhe 

 produced to Q and R, so that E, F are the middle points of 

 PQ, PR respectively, PQ moves, so that P always lies on one fixed 

 straight line PB, and Q on that perpendicular to it, viz. BG ; 

 similarly w^ith regard to PR. 



Thus considering the six-bar linkage 



(1) P describes a straight line and any point in PE or PF an 

 ellipse according as we fix BG or AD. 



(2) It is further evident that if we fix PE, since B describes a 

 circle and BG is always perpendicular to PB, any point on BG 

 describes the lima^on, and for a similar reason if we fix PF any 

 point on AD describes the same curve. 



The two models were exhibited at the meeting. 



(4) Mr J. B. Kearney, M.A., On some results in the Theory 

 of Equations. 



This paper related to Fourier's and Sturm's theorems, and 

 Professor Sylvester's researches. 



* It will easily be seen from these conditions that BC- CD and BA —AD. 



