D992 Mr. A. G. M. Michell on the Limits of 
@ the angle between RO and the direction of F, and P is the 
allowable stress in the material. 
A more general class of frames satisfying the condition 
e=e, consists of those whose bars, both before and after 
the appropriate deformation, form curves of orthogonal 
systems. 
In such a system the test strains may be equal and of the 
same sign, or equal and opposite, in directions at right angles, 
without the strains in the bars being exceeded by those of 
any other lines in the field. In the first case the strain is 
evidently the same in all directions ; in the second, if A, —X 
are the strains in the principal directions, the strain in any 
direction at an angle @ to one of them is +A cos 20=N/, 
ey latin ae 
The condition that a two-dimensional orthogonal system 
shall remain orthogonal after equal and opposite extensions 
of its two series of curves, is that the inclination between 
any two adjacent curves of the same series is constant 
throughout their length. This is easily seen as follows :— 
Let / be the elementary length, ¢ the change of direction 
of the curve §,, between its points of intersection with two 
adjacent curves R,R, of the other series, and let m be the 
elementary length of R, between the two curves §,, 8S, of 
the S-series, m being taken small in comparison with J. 
Let the curves of the S-series be extended by the small 
fraction X of their length. 
If the element remains rectangular the change in the angle 
@ must be equal to the change in the inclination of the 
elements R,; and R, to each other, 
M—A(U+ = m) 
Bo éb= se Be =)¢. 
m 
Take now a new element, with sides of comparable length, 
1,n, formed by the pairs of curves R,R,, 8,S;. Let yr be 
