4M)4 



REPORT 1872. 



absolute equality which would exist in A A' down to the absence of all rolling 

 motion which would obtain in the case of A A^. 



These preliminaries being stated, let it be inquired how they apply to the 

 action of the planimeter. Eor this purpose it will be well to refer to the 

 sketch, fig. 3. This sketch shows an imaginary elementary planimeter, used 



rig. 3. 



A" 



-5"- 



-Q 



iJB 



-B' 



m 



I ^ I 



o 



-N 



to ascertain the area of the rectangle A B C D, the length of each of its sides 

 A B, C D being 5 inches, and the length of each of its ends D A, C B being 2 

 inches, so that its area is 10 inches. Let M be a block carrying the pivot N 

 and capable of sliding in the straight groove in the bridge P, pinned down 

 over the paper, and let Q be a rod pivoted at N, and say, for the sake of 

 illustration, 5 inches long from the pivot N to the tracer T at its opposite 

 end ; and let it have on it, say at K, a wheel E, having a circumference of 

 exactly 2 inches ; and also, for the sake of a second illustration, let there be 

 similar wheels as R', E," free to revolve on the rod Q,, at distances greater 

 than the distance of the wheel R from the pivot N ; and let there be to one 

 of the wheels, say R, a pointer S, to enable the graduated divisions on the 

 circumference of R to be read off. 



