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Page 4
I do not know that there is any more tendency for a large wheel to
slide than a small one under the action of the brakes, but large
wheels wear out more brake shoes than small ones, if there is any
difference in this particular.
My conclusions are that 42 in. is too large a diameter for steel
wheels in ordinary passenger service, and that 36 in. is right. But as
steel-tired wheels usually become 3 in. smaller in diameter before
wearing out, the wheel should be about 38 in. in diameter when new.
Such a wheel can be easily put under all passenger cars and will not
have become too small when worn out. A great many roads are using 36
in. wheels, but when their tires have lost 3 in. diameter they have
become 33 in. wheels, which I think too small.
There are many things I have left unsaid, and I am aware that some of
the members of the club have had most satisfactory service with 42 in.
wheels so far as exemption from all trouble is concerned, and others
have never seen any reason for departing from the most used size of 33
in.
One more word about lightness. A wrought iron or cast steel center, 8
or 9 light spokes on a light rim inside a steel tire, makes the
lightest wheel, and one that ought to be in this country, as it is
elsewhere, the cheapest not made of cast iron.
* * * * *
A NEW INTEGRATOR.[1]
[Footnote 1: A paper read before the University College Engineering
Society on January 22.--_Engineering_.]
BY PROFESSOR KARL PEARSON, M.A.
As I fear the title of my paper to our Society to-night contains two
misstatements of fact in its three words, I must commence by
correcting it. In the first place, the instrument to which I propose
to draw your attention to-night is, in the narrow sense of the words,
neither an integrator nor new. The name "integrator" has been
especially applied to a class of instruments which measure off on a
scale attached to them the magnitude of an area, arc, or other
quantity. Such instruments do not, as a rule, represent their results
graphically, and we may take, as characteristic examples of them,
Amsler's planimeter and some of the sphere integrating machines.
An integrator which draws an absolute picture of the sum or integral
is better termed an "integraph." The distinction is an important and
valuable one, for while the integraph theoretically can do all the
work of the integrator, the latter gives us in niggardly fashion one
narrow answer, _et pr�terea nil_. The superiority of the integraph
over the integrator cannot be better pointed out than by a concrete
example. The integrator could determine by one process, the bending
moment, from the shear curve, at any one chosen point of a beam; the
integraph would, by an equally simple single process, gives us the
bending moment at all points of the beam.
In the language of the mathematician, the integrator gives only that
miserly result, a definite integral, but the integraph yields an
indefinite integral, a picture of the result at all times or all
points--a much greater boon in most mechanical and physical
investigations. Members of our Society as students of University
College have probably become acquainted with a process termed "drawing
the sum curve from the primitive curve." Many have probably found this
process somewhat wearisome; but this is not an unmixed evil, as the
irksomeness of any manual process has more than once led to the
invention of a valuable machine by the would-be idler. Thus our innate
desire to take things easy is a real incentive to progress. It was
some such desire as this on my part which led me, three years ago, to
inquire whether a practical instrument had not been, or could not be,
constructed to draw sum curves. Such an instrument is an integraph,
and the one I have to describe to you to-night is the outcome of that
inquiry. It is something better than my title, for it is an integraph,
and not an integrator.
[Illustration: A NEW INTEGRATOR]
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