Mudgis Free Efcnpemmt. ma 



fpring V, by a£ling on the pallet q, and is detained by a projc(flion, after liavlng carried it, 

 through an angle of 27°, cxaiflly as in the former cafe. The arcs pafled through by th? 

 arms G o and I o, and marked in the figure, are alfo denoted by the fame letters on the 

 rim of the balance. 



The cffe£l of this efcapement may be thus explained : Let the balance be in the qui- 

 efcent ftatc, the main fpring being unwound, and the branch or crank in the pofition re- 

 prefented in the figure. If the qulefcent points of the auxiliary fprings coincide with that 

 of the balance fpring, the arm Go will juft touch the rod LM, and in like manner the 

 arm lo will juft touch the rod W Z ; the two arms G o and loin this pofition are pa- 

 rallel to the line CO. -This pofition of the balance and auxiliary fprings remains as long 

 as the main fpring of the machine continues unwound ; but whenever the a£lion of the 

 main fpring fets the balance wheel in motion, a tootli thereof meeting with one or other 

 of the pallets p or q, will wind up one of the auxiliary fprings; fuppofe it fliould be thfr 

 Ipring u. The arm G o being carried into the pofition G h, by the force of the balance 

 wheel ading on the pallet p, remains in that pofition as long as the tooth of the balance 

 wheel continues locked by the prcjedion at the extremity of the pallet p ; and the balance 

 itfelf not being at all affeded by the motiofi of the arm G o, nor by the v/inding up of 

 the fpring u, remains in its quiefcent pofition : confequently no vibration can take place, 

 except by the afiiftance of fome external force to fet the balance in m.otion. Suppofe an 

 impulfe to be given fufficient to carry it through the femi-arc OB, which is about i35« 

 in Mr. Mudge's conftrudion. 



The balance, during this motion, carries with it the crank AX YD, and the affixed 

 rods LM, ZW. When the balance has dcfcribed an angle of about 27" = the angle 

 o C h, or o G h, the rod L M meets with tlie arm G H, and by turning the axis T R, 

 and the pallet p in the diredlon of the arc oh, releafes the tooth of the balance wheel 

 from the projedion at the extremity of the pallet p : the balance wheel immediately re- 

 volves, and the lower tooth meeting with the pallet q, winds up the auxiliary fpring v, 

 and carries the arm lo with a circular motion through the angle oik, about 27^', in 

 which pofition the arm I o remains as long as the tooth of the balance wheel is locked by 

 the pallet q. While the fpring v is winding up through the arc ok, the balance defcribes. 

 the remaining part of the femi-arc hB, and during this motion the rod LM carries round, 

 the arm Gh, caufing it to defcribe an angle hCB, or h G B, which is meafured by the 

 arc h B = 108^. When the balance has arrived at the extremity of the femi-arc OB = 135", 

 the auxiliary fpring u will have been wound up through the fame angle of 135", that is 

 to fay, 27°, by the force of the main fpring ading on the pallet p, and 108° by the ba- 

 lance itfelf, carrying along with it the arm Go, or G h, while it defcribes the arc hB. , 

 The balance therefore returns through the arc B O, by the joint action of the balance 

 fpring and the auxiliary fpring u; the acceleration of both fprings ceafing the inftant the 

 balance arrives at the quiefcent point o. When the balance has proceeded in its vibration 

 about 27° beyond the point O, to the pofition Ck, the rod Z W meets with the arm Ik, 

 and by carrying it forward releafes the toothy of the balance wheel from the pallet q. The 

 balance wheel accordingly revolves, and the upper tooth meeting with the pallet p winds 

 up the auxiliary fpring u, as before. Tlie balance with the crank proceeding to defcribe 

 Vol.. II.— May 1798. 1 the 



