lb.

The matter of brakes is coming up for more attention in these days of high speed, heavy cars and crowded roads, and the total available braking power, which has hitherto been but partially taken advantage of, must be fully utilized. I refer to the fact that many of our wheels in six-wheel trucks have gone unbraked where they should not. As the height of cars and length of trucks cannot well be increased for obvious reasons, it is necessary to keep the size of the wheels within the limits that will enable us to get efficient brakes on all of them that carry any weight. This is not easy with a 42 in. wheel in a six-wheel truck, which is usually the kind that requires most adjustment and repairs after long runs. The Pullman Co. has recognized this fact, and is now replacing its 42 in. wheel with one 38 in. in diameter.

A 42 in. wheel with 4 in. journal has a greater leverage wherewith to overcome the resistance of journal friction than the 38 in. wheel with the same journal, and even more than the 36 in. and 33 in. wheels with 33/4 in. and 31/2 in. journals respectively, but the fact remains that the same amount of work has to be done in overcoming the friction in each case, and what may be gained in ease of starting with the large wheel is lost in time necessary to do it, and in the extra weight put into motion.

A large wheel increases the liability to bent axles in curving on account of greater leverage unless the size and weight of the axle are increased to correspond, and the wheel itself must be made stronger. A four or six wheel truck will not retain its squareness and dependent good riding qualities so well with 42 in. wheels as with 33 in. ones. Besides the brakes, the pipes for air and steam under the cars interfere with large wheels, and as a consequence of all this 42 in. wheels have been replaced by 36 in. ones to some extent in some places with satisfactory results. On one road in particular so strong is the inclination away from large wheels that 30 in. is advocated as the proper size for passenger cars.

On the other hand, there is no doubt a car wheel may be too small, for the tires of small wheels probably do not get as much working up under the rolls, and therefore are not as tough or homogeneous. Small wheels are more destructive to frogs and rail joints. They revolve faster at a given speed, and when below a certain size increase the liability to hot journals if carrying the weight they can bear without detriment to the rest of the wheel. Speed alone I am not willing to admit is the most prolific source of hot boxes. The weight per square inch upon the bearing is a very important factor. I have found by careful examination of a great many cars that the number of hot boxes bears a close relation to the weight per square inch on the journal and the character of lubrication, and is not so much affected by the size of wheel or speed. These observations were made upon 42 in., 36 in. and 33 in. wheels in the same trains. We find, furthermore, that while a 3-3/8 in. journal on a 33 in. wheel is apt to heat under our passenger coaches, a 33/4 in., even when worn 3-5/8 in., journal on a 36 in. wheel runs uniformly cool. In 1890 on one division there were about 180 hot boxes with the small wheel, against 29 with the larger one, with a preponderance of the latter size in service and cars of the same weight over them.

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.

[1]

A NEW INTEGRATOR.¹

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 præterea 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.

A NEW INTEGRATOR.

Before I turn to its claims to be considered new, I must first remind you of the importance of an