On Sal Nitnun and Nitro^ Aerial Spirit 53 



no other way than by approximating their convex and 

 concave surfaces. 



The third mode of bending a rigid body is that in 

 which the planes at its extremities are turned towards 

 each other and also elongated, while the concave and 

 convex surfaces retain their original length as in Plate 

 I., Fig. 6, in which let a^ c, b^ d^ be the bent rigid body 

 whose convex surface 3, d^ I suppose to be equal to the 

 line ?', 2, or what is the same thing to the length of the 

 rigid body before it was bent. Then the planes at its 

 extremities a^ b^ and c, d^ must be turned towards 

 each other and elongated as is clear from the figure. 

 For these end planes are inclined at the angle 3, z, e^ 

 and are elongated by as much as the plane 3, /, is 

 longer than the plane e^ i. 



Lastly, a rigid body can be bent by shortening its 

 concave surface while its convex surface and also end 

 planes remain of the same length as before ; as may 

 be seen in Plate I., Fig. 7, where let a^ c, 3, d^ be the 

 bent rigid body whose concave side «, <;, I suppose 

 before the inflexion equal to the line between the 

 extremities e, e. But now when the rigid body is bent 

 that surface is shortened by the difference between ^, ^, 

 and ^, c. But we suppose the convex surface 3, d^ to 

 retain its original length, or what is the same thing to 

 be equal to the line between the extremities ^, e. 



But these observations regarding the various modes 

 of bending a rigid body will be better understood from 

 the following example. At the ends of a flexible rod, 

 let two other shorter rods also flexible be fixed perpen- 

 dicularly, as in Plate I., Fig. 8. Then let a string 

 attached to the end of one of the rods be passed 

 through a hole in the end of the other, as is seen in 

 the same figure. Then the rod with the two small 

 rods and the attached string will represent the sides of 



