344 Mr. C. V. Boys on an Integ rating-Machine. 



will always be so. Instead of the middle wheel an open band 

 may connect the two outside wheels, with the same result. In 

 the same way another arm may carry a third wheel, c, con- 

 nected with b by an open Fio . 2 

 band, as shown ; then what- 

 ever motion is given to the 

 wheel a or to the arms, lines 

 on a and c, if ever parallel, 

 will always be so. To apply 

 this principle the wheel a is 

 mounted on the fixed centre 

 B, and its rotation is equal 

 to that of the rod A B. A 

 pair of arms hinged at H 

 connect B with that part of 

 the cart corresponding to 

 the head of a bicycle, while 

 the handles are replaced by the wheel c ; the wheel b is mounted 

 on the hinge H, and a single band goes round all three 

 wheels, as shown. The wheel b and the arms are balanced 

 about B by the counterpoise W. Thus, as A traces out any 

 given curve, the front wheel of the cart has its plane always 

 parallel to A B ; and as the connexion between the cart and 

 B in no way interferes with its vertical motion, the front 

 wheel must describe the required curve. As the ascent in 



i r 



this curve is equal to -j- 1 y dx, all that has to be done is to 



measure the ascent, multiply by k, and the product is the 

 area required. If A is taken round any closed curve, the 

 ascent can be measured immediately by a rule and multiplied 

 by h as before. 



In the instrument shown, k can be made either one, two, 



77" 



three, 7r, or — inches. If the one-inch constant is used, the 



inclination of the rod A B is with large ordinates so great and 

 the motion of the cart so nearly at right angles to the direction 

 in which it is pushed, that there is danger of its being upset. 

 This difficulty is in great measure avoided by inclining the 

 board in the direction e e ; and then, as the inclination of 

 A B becomes greater and the power of the instrument to drive 

 the cart becomes less, the action of gravity on the cart in- 

 creases, and it can be moved with equal ease in all directions. 

 As the model works exceedingly well, I have no doubt that 

 a carefully-made machine would give results as accurate as 

 any other planimeter. As an aid in teaching physics to 

 pupils not familiar with the principles of the integral calculus, 



