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 praeterea 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.