is right in most of, or even in any of, his assumptions, a
further expression of approval is due to him. Few engineers have the
time to show fully, by a process of _reductio ad absurdum_, that all the
author's points are, or are not, well considered or well founded, but
the writer desires to say that he has read this paper carefully, and
believes that its fundamental principles are well grounded. Further, he
believes that intricate mathematical formulas have no place in practice.
This is particularly true where these elaborate mathematical
calculations are founded on assumptions which are never found in
practice or experiment, and which, even in theory, are extremely
doubtful, and certainly are not possible within those limits of safety
wherein the engineer is compelled to work.

The writer disagrees with the author in one essential point, however,
and that is in the wholesale indictment of special reinforcement, such
as stirrups, shear rods, etc. In the ordinary way in which these rods
are used, they have no practical value, and their theoretical value is
found only when the structure is stressed beyond its safe limits;
nevertheless, occasions may arise when they have a definite practical
value, if properly designed and placed, and, therefore, they should not
be discriminated against absolutely.

Quoting the author, that "destructive criticism is of no value unless it
offers something in its place," and in connection with the author's
tenth point, the writer offers the following formula which he has always
used in conjunction with the design of reinforced concrete slabs and
beams. It is based on the formula for rectangular wooden beams, and
assumes that the beam is designed on the principle that concrete in
tension is as strong as that in compression, with the understanding that
sufficient steel shall be placed on the tension side to make this true,
thus fixing the neutral axis, as the author suggests, in the middle of
the depth, that is, _M_ = (1/6)_b d_^{2} _S_, _M_, of course, being the
bending moment, and _b_ and _d_, the breadth and depth, in inches. _S_
is usually taken at from 400 to 600 lb., according to the conditions. In
order to obtain the steel necessary to give the proper tensile strength
to correspond with the compression side, the compression and tension
areas of the beam are equated, that is

1 2 _d_
---- _b_ _d_ _S_ = _a_ x ( ----- - _x_ ) x _S_ ,
12