18 
The N.Z. Journal of Science and Technology. 
[Feb. 
of the word “ theoretic ” is a very careless and ignorant one. In addition 
to a bending-stress the leaves, or at any rate the tapered “ overhang ” 
of each leaf, have also to withstand a shearing-stress, and this the pointed 
ends are quite unable to do. The whole basis of the design therefore falls 
to pieces, and a fuller theory is called for. 
Considering any consecutive square-ended leaves of a spring, it is evident 
that they are in parallel contact at the rigid (sensibly) buckle, and are also in 
contact at the extremity of the lower shorter leaf. Here, however, the upper 
plate has a certain bending-moment and consequent radius of curvature, so 
it is springing up and away from the lower leaf, which is not under any 
bending-moment at the point. They are not in contact anywhere between 
Fig. 3. 
that point and the buckle, and in most springs (save those where the over¬ 
hangs are tapered off to a very flexible point) the various plates gape every¬ 
where else. The photograph reproduced in fig. 3 shows this fact in a very 
striking manner. Each leaf is therefore a cantilever loaded at the end and 
flexibly supported by the point of the leaf below at an intermediate point. 
The ordinary formulae for deflection can now be applied. The general 
case for the wth and (w-j-l)th leaf is indicated in fig. 4. Considering the 
(w-hl)th leaf at section X-X we ,can calculate the deflection y as 
follows:— 
1 d 2 y M 1 ( ) 
R ~~ dx 2 ~ El — El 1 Wn + 1 + 1 ~ ^ ~ w ~ ^ f 
Integrating 
