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erally but a few hundredths, and were very much closer than either of the other methods. Does this look as if the formula was very inaccurate?

We have tried Unwin's method and found it very tedious, but Rankine's is so rapid that, when the inconvenience of laying out full-size cones, perhaps 8 or 10 feet apart, is taken into consideration, we believe that there is still a place for this formula. We designed by this method a set of cones with extreme diameters of 38" and 11", and about 12 feet apart. Afterwards, measuring with a tape-line, we found no practical difference in length of belt between extreme steps.

Mr. C. A. Smith.*-I am sorry if I have given credit to the wrong man for having first used the method illustrated in Fig. 48. Iu looking up the data on this point, I followed the reference given by Prof. Sweet in the American Machinist, Sept. 17, 1881, viz.: "This method was illustrated some months ago in the American Machinist, and in the American Artisan for February, 1874." After spending a great deal of time in searching through the back numbers of the American Machinist, I finally found the article, by Mr. Fuchs, to which reference has been made, and as it was given as original, and as I did not have access to the American Artisan for reference, I concluded that possibly the latter publication was by the same author. This illustrates the importance of giving references in full and complete when given at all, giving name of author and date of publication as well as the other important information. As Prof. Sweet has now explained that he is the one who first used the method, Fig. 48, I hope it sets the matter all right on this point.

In regard "to lumbering up our minds with so much," I will simply say this: If Prof. Sweet will examine impartially the method described in this paper, he will find that all that has been added to his own method to make the new one is an arc of a circle, Fig. 36, struck from the center, G, and touching the belt line. In some exceptionally few cases it may require two such arcs as shown in Fig. 41, when the extreme belt angles are greater and less than 18°. The extra work required is to multiply the center distance by a constant, then lay off the point G and describe the circle. The extra time required to do this will not exceed five minutes.

As I have already stated in the paper, it always takes more time to describe any method fully, and seems more complicated than it

* Author's closure, under the rules.

really is in practice. The present paper may seem all the more so to a superficial observer, from the fact that it is so profusely illus trated and described in detail for the purpose of making every step perfectly clear.

The next point raised by Prof. Sweet is that his method "is sufficiently accurate for all practical purposes." Is it? When the practical man makes use of any formula, rule or method of practice, and it fails to give him the desired result in a single instance, his confidence in it will be gone forever afterwards, because he never knows when and to what extent he can depend upon it. I admit that Prof. Sweet's method is practically as good as the new one in certain cases, and for certain proportions of pulleys and line of centers the two methods are identically the same.

Taking Example 1, represented by Fig. 53, and designing the pulleys by Prof. Sweet's method, the belt, when cut so that it will be just the right length for the first step, will be over nineteen inches too long for the eleventh step. Granting that this may be called an imaginary case, yet we can feel confident that the method which will hold good in this case will not fail in any other case.

When the diameters of the first pair of pulleys, Di, d1, Fig. 36, and the line of centers are such that the belt line, HI, will pass through the point G, then the two methods will become one and the same, because the radius, R, of the directing circle will then reduce to zero, the circle becoming a point. This condition of things is approximated to in Example 4, in which we would expect practically no difference in the two methods.

Example 3, as calculated by Prof. Sweet's method, gives a difference in the length of belt of nearly one-quarter of an inch against .007" by the new method. Perhaps, however, Prof. Sweet considers this "within practical limits."

Example 2 gives a difference in the length of belt of nearly three-quarters of an inch by Prof. Sweet's method. This example comes so far within practical dimensions that it can not be called an "imaginary case," but, perhaps, the " variation in the length of the belt would be considered within practical limits if the workman can cut "two or three inches off the belt" to take up the slack caused by changing it from one step on to another. But this latter expression was evidently meant as a figure of speech. Certainly no good practice would admit a variation of " on a lathe where the belt is in a vertical position.

In regard to Prof. Denton's criticism, I would simply say that

the tables to which he refers are not practical, for the reason, already mentioned in my paper, that the ratio of the pulleys is a datum usually used, and not the difference of their diameters, nor the height of the steps, nor the ratio of a pulley to the line of centers. Neither of these data would be of any value in the solution of any of the examples given in the paper. If graphical methods have been published which are "absolutely exact," and an approximation which is "exceedingly simple" and comes within the requirements of good practice, Prof. Denton should have done their authors the justice of giving us references to their publications.

CCCXXI.

AN ACCOUNT OF CERTAIN EXPERIMENTS UPON SEVERAL METHODS OF COUNTERBALANCING THE ACTION OF THE RECIPROCATING PARTS OF A LOCOMOTIVE.

BY GAETANO LANZA, BOSTON, MASS.

(Member of the Society.)

WITH EDWARD H. DEWSON, GEORGE F. REYNOLDS, AND EDWARD M. SMITH.

THE object of this paper is to give an account of the experimental work that has been done in the Laboratory of Mechanical Engineering of the Massachusetts Institute of Technology in regard to the effect of different methods in use for counterbalancing the throw of the reciprocating parts of a locomotive; and also as to how to counterbalance the horizontal throw and prevent nosing.

These experiments have formed the subject of the graduating theses of the following three students, viz.: Edward H. Dewson, '85; George F. Reynolds, '86; and Edward M. Smith, '88. They made use of a model of an eight-wheel Hinkley Passenger Locomotive, one-eighth scale, which was suspended by four wires, one at each corner, and set in motion by steam. The following are some of the dimensions of the locomotive:

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The latter includes box, sponge box, saddle and brass. Ten per cent. of the last three weights should be deducted for finish, which will give

Weight of finished wheel...

.2,895 lbs.

From the weights of the locomotive on the drivers and truck, the center of gravity of the entire machine is found to lie 9′ 7′′ back of the center of the truck, and 1' 6" forward of the center of the main driving axle.

From these and other data an eighth scale model shown in the ent (Fig. 55) was constructed by Mr. Dewson and afterwards slightly modified in some particulars by the other two.

Particular attention was paid to making all the parts, which affect in any way the disturbances of the reciprocating parts, exactly one-eighth scale. The following changes were made for convenience in construction, and it will be seen that they can have no effect on the subject under discussion. The frame is made of a single piece of cast iron, to which the driving axle boxes are rigidly attached.

The wheels are also made of one casting, and without spokes, with two circular, slots, diametrically opposite each other, one to admit the fastening on of the counterweights, and the other to compensate for the loss of metal in cutting the first. Instead of placing the steam chests on top of the cylinders they were placed on the inside, the valve moving in a vertical instead of a horizontal plane. Also certain changes were made in the main rod and the parallel rod for the sake of convenience of construction, as follows: The main rod was split, and the cross-head placed between the two parts, and the piston rod projects through the cross-head, and ruus in a fixed bearing, fastened to the frame. The model, as thus far described, weighs seventy-four pounds, whereas, in order to correspond to the weight of the locomotive, it should weigh 156 pounds. Hence a bar of iron of eighty-two pounds was fastened to it in such a position that the forward end when supported at the center of the truck should weigh 58.6 lbs., thus bringing the center of gravity

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