u 



The multiiilying; lever coasists of a liffht wooden rod </ rigidly lixwl to B-. 

 bv a bridge b, and tiieref'ore forining a prolongation of (/. At the top of this a 

 light arm of straw i is jointed (with freedom of motion about a horizontal axis), 

 and stands mit horizontally with its end (steel-tipjK>d) resting on a fixed or 

 revolving smoked-glass ])late, «f whicl; a portion is shown at j in fig. -"»O. 



When its equilibrium is nearly neutral the duplex jiendnlum forms an 

 exceedingly sensitive level. If the line joining the upper witii tlie lower point 

 of sii|iport is not perfectly vertical a very large deflection of the pointer results. 

 It is ca.sy to show mathematiealiv that if the e<(uilibrium were exactly neutral 

 when the line joining the supjiorts was vertical, tlie ap])aiatus would be imstable 

 shotdd anv deflection of this line from the verti<-al take place, and that when 

 there is some small stability the effect of sue!» a deflection is to cause a large 

 displacement of the lH)bs. Tlie same characteristic is, however, shared by other 

 neutral or nearly neutral ei|uilibrium seism« >nu'ters, such as the rolling sphere or 

 the horizontal peniliiliim. 



§ 42. Duplex Pendnhnn irilh n sinylc bob. 



The two bobs of the duplex pendulum may be united to form a single bob, 

 jirovidcd we make one (pf thi' sup])orting pieces, ])rcferably that of the upper 

 ])endulnm, extensible. This idea has been carried out in the instnuiient shown 

 in Plate X, which was de.'^cribed to the Seisniological Sncictv of Ja]:au on Feb. 

 l.ith. ISK:^. by the present wiit-jr. 



Figs. .■)] and ."52, I'late X, give scctior.al cli'vations of tlie in.-trument, ia 

 ]i]anes at right angles to each other. Tiie bob is a cast-iidii ring li, jiartially 

 supported by the stirru];-shaped piece n, at the bottom of wliicii there is a steel 

 P'in h standing in a tup of ngate in the lower sup.]~ort .«^. The weight of B is 

 does not all con)(> on (his fi ot stc]- : tiie rcn;aindcr is borne by the spiral spring 

 r- whi<'h is .stretched veitieally between tiic u|)]ier support .«, and the middle of a 

 bar II which crosses the upper surface of the b.ob. 



The apparatus is, in fact, a common and an inverted pendulum conibine<l in 

 one, and its relation to the duplex ]-en<liilum is at once evident if we conceive of 

 the bo!) /)' as consisting of two parts; one borne by the tension of the spring, 

 tile other by the upwar<l thm.st of the footstep. Thc.-^e correspond to the two 

 liobs Z?, and ]>., of the last article. The condition giving neutral equilibrium in 

 small displacements is that the thrust of the footstep A\a]\ bear to the pull of 

 the spring the same latio as the length of the inverted jiendnlum bears to the 

 length of the spring. In other words, the weiirht of the bob must be shared 

 between its two su])jH)rting jiieccs in jiroportiou to their respective lengths. In 

 jiractice, to give feebly stable equilibrium, the tension of tiie spring mn.st bc 

 somewhat increased. It is adjustable by the screw (/ and luit e. The initial 

 strain of the sjiring is so considerable that any actual displacement scarcely 

 increases the pull it exerts. 



To regi.-ifer the motion, an ujiright multiplying lever /", carried by a gimbal 



