12 



Mr. F. P. Purvis on Amsler's Planimeter. 



to A B, and resting at its circumference on the paper. That n is 

 given by the circumferential motion of this wheel may be seen 

 by considering again the elementary motion of the bar from A B 

 to a. /3 : while the bar moves from AB to xy, the wheel turns 

 through the normal distance from 7 to A B ; while the bar 

 turns about the point y, the wheel remains stationary. 



If instead of centring the wheel at C we centre it at any 

 other point D, distant m from C, its circumferential travel for 

 the elementary motion will be the normal from z to A B( = fi?n) 

 — mdO, and for the whole motion from A B to a b will be n—m6 } 

 where 6= the inclination of ab to AB. 



If a retrograde motion be now given to the instrument, bring- 

 ing it into the position a'b', the product nl will still equal the 



area included between A a a', Bbb ! , and the two straight lines 

 A B and a'b ! , part of that area being, in the case shown, negative ; 

 nl=Aaa! IB — lbb 1 . If instead of allowing B to take any path 

 b b l we constrain it to move only along the line already traced, 

 while A traces out a new line a «', the negative area will be nil, 



and the product nl will equal the area A a o'5'B. If this motion 

 be continued, B being always kept in the path bb'B until AB 

 occupies its initial position, the product nl will equal the area 

 A a a' A, whatever be the nature of the line B V b. Also for the 

 whole motion = 0; so that the circumferential travel of the 

 wheel at D~?i } entirely independently of the value of m, 



