ON AMSLER S PLANIMETER. 



409 



the wheels R &c, will make a further 4 inches of circumferential movement, 

 equal 2 revolutions, indicating 20 square inches. If, now, the tracer T be 

 moved from A to B, there will clearly be unwoimd from all the wheels E &c. 

 the amount of motion that was put into them in ti'aversing from C to D, 

 and thus the wheels E. &c. will all be left with the double revolution indicative 

 of 20 square inches. The only side remaining to be passed over is that from 

 B to C ; and if this traverse were devoid of effect on the wheels R &c., as the 

 traverse from B to C was in the cases of figures 3, 4, and 5, then the imple- 

 ment on arriving at C, at the end of the circuit, would record double the 

 proper area, or 20 inches instead of 10 ; but in the outset of this paragraph 

 it was shown that the journey from B to C in fig. 6 would unwind exactly 

 one revolution of the wheel R, leaving therefore one revolution remaining, 

 indicating, as it should do, 10 square inches for the area of A B C D. 



The next step is to show the ability of the implement to give the area 

 correctly of figures which are not rectangular. Assume, as in figure 7, it be 



Fig. 8 

 A 



B C 



a=T=^r 



-7?B 



Q 



3^sR' 



required to find the area of the triangle BCD, and let it be imagined that 

 in lieu of the straight line for the hypotenuse B D the boundary of the figure 

 on that side were made by a number of extremely small steps, as sketched ; 

 if then the tracer T be made once more to traverse from C to D, the wheel R 

 will have a certain amount of revolution given to it ; and if it then be made 

 to rise through the space D 1, it wiU have a " rate " of revolution equal to the 

 length of the line C D, and a " quantity " equal to the height D 1 ; if it then 



