226 On the Transverse Strain, 
ceived theories, in which all the fibres (with 
the exception of those on the edge of a bent 
body) are conceived to be ina state of ten- 
sion: and next to adapt the investigations to 
the more general case, where part of the 
fibres are extended, and part contracted, and 
to seek experimentally for the laws that re- 
gulate both the extensions and compressions. 
PART I.—Theoretical. 
3. Suppose a beam ABCD, (fig. 1.) fixt 
firmly in a wall, and then broke by a weight 
W, suspended at one of its ends. 
When the fracture commences the fibres 
at ac separate the first; next, those imme- 
diately under them, and so on till the whole 
depth, ab, is broke; with the exception of 
the lowest stratum, b, which is supposed to 
be incompressible, and serves for a fulcrum 
to the bended lever Dba. It is evident then, 
that, whatever the extension of a fibre ata 
may be, the extension of one at z must be 
in proportion to it, as bx to ba: or the ex- 
tensions must vary as the distances from the 
fulcrum b. Let us then call the length 
Db=t, the depth ba =a; any variable dis- 
tance br = x, the breadth of the beam at bot- 
tom =b, any double ordinate de—y; the 
