measured the pulleys on the frames and counter-shafts, and found no appreciable difference in the size. There were two counter-shafts between the loosing frame and the line-shaft, requiring three belts to transmit the motion. I puzzled over the matter for some time, but was unable to account for the loss, and finally let the matter drop. The difference in speed was nothing unusual, however, as in my previous experience I had found it. an exception, rather than a rule, to find two frames running the same speed.

Twelve or thirteen years passed by, until one hot day in summer, when I was travelling in the cars, having on a straw hat with an elastic string attached, I found myself winding this string around my finger, and noticing that one inch of it was sufficient to stretch several times around according to the tension I put upon it. I conceived the idea that here was the solution of the mystery of the difference of the speed of the frames, being well aware of the great amount of elasticity of a leather belt. (For the benefit of those that have not given this subject much thought, nail one end of a belt to the floor, and pull on the other. By so doing, you can see how accommodating a belt is, whether old or new; new being the most pliable according to the soundness of the leather. Let it be about one inch wide, as you may not have strength to stretch a wide belt.) Now, supposing this to be the case, we will imagine this to be a driven pulley, and this the driver of equal diameter. Then suppose the driven pulley is carrying a machine which acts as a brake of about one-horse power in resistance to motion of belt; this resistance all on the upper side, as shown by the straight line (in practice, to get the best results from a belt, the sag should be on top). The resistance of the driven to that of the driver creates a stretch of the belt, of, say, one-half inch in twelve, making twenty-four inches of belt twenty-five inches long: this stretched belt passes on to the driver pulley, and remains in this condition until it is about to leave the pulley, when it contracts itself to its natural condition, namely twenty-four inches long on the sag side, which passes on to the driven pulley in its unstretched condition; it will readily be seen by this, that the driver will have to perform twenty-five turns to the driven twenty-four. In other words, suppose we put on an elastic or rubber string that will stretch, by a suitable resistance, one inch into two: we then have two turns of the driver to one of the driven. As I have

before stated, there were three belts between the line-shaft and the frame: this being the case, we find it necessary to multiply the half-inch stretch by three, which gives us in round numbers twenty-five turns on the line-shaft to twenty-two on the frame, supposing all the pulleys alike in size.

Engineers that have figured on the speed of machinery from the first motion find themselves invariably come short of the result sought for, unless their long experience has taught them to look out for what they would naturally call slip of belts, and take it for granted that there lies the cause of deficiency. I would here suggest, that a belt might be made non-elastic by cementing on its back a non-elastic substance.

Professor WHITAKER. The stretching and shrinking of a band or belt undoubtedly affect the relative number of turns of the two pulleys which it connects, as Mr. Birkenhead has inferred. The ordinary theory is correct enough for most practical purposes. It assumes that the inner surface of the belt, or the surface which touches the face of the pulley, is flexible, but not elastic; in other words, that this surface bends, but does not stretch or shrink: the belt is supposed not to slip on either pulley. It follows that the face surfaces of both pulleys and the inner surface of the belt run with the same speed, and that the number of turns of the driver divided by that of the follower equals the diameter of the follower divided by that of the driver.

Again, if an unstretched band or belt be laid upon the face of a pulley, its outer surface is stretched, and its inner surface is compressed or shrunken in length, while about half way between the outer and inner surfaces is a layer of fibres which are neither stretched nor shrunken. This may be called the neutral layer. An approximate rule, that is more correct in some cases than the one just cited, assumes that the straight parts of a band or belt run with the same speed as the neutral layer, and that, no matter how much the band or belt is stretched, the neutral layer is still half way between the outer and inner surfaces. Whence the rule that the number of turns of the driver divided by that of the follower equals the sum of the diameter of the follower and the thickness of the band or belt, divided by the sum of the diameter of the driver and the thickness of the band or belt.

When the elasticity of the band or belt is taken account of,

the resulting rule becomes more complicated. If two lines be drawn across the inner surface of an elastic belt, square with the length of the belt and near to one another, these lines will be nearer to one another when they are both on the slack side, than when they are both on the tight side of the belt. For the slack side, being under less tension than the tight side, shortens on account of the elasticity of the belt. When the two lines touch the face of either pulley, their distance apart is least when they are nearest to the slack side of the belt. The belt then creeps on the surfaces of the pulleys, and produces that polishing of the faces that has been observed so often. It is evident that the belt creeps backward upon the surface of the driver, and forward upon the surface of the follower, in both cases toward the tight side of the belt; and we may conclude that, on account of this creeping, the surface of the driver gains a little upon that of the belt, while the surface of the belt gains a little upon that of the follower; still more, then, does the surface of the driver gain on that of the follower.

But there is still another way in which the elasticity of the belt enables the driver to gain upon the follower. The friction between the pulleys and the belt hinders the belt, to some extent, from shrinking upon the driver, and from stretching upon the follower. It results that the same portion of the belt will measure a longer distance upon the face of the driver than upon the face of the follower, or that the driver must turn more times than the follower to carry the belt around.

Then both the elasticity and the degree of tension of a band or belt affect the ratio of the number of turns of the driver to that of the follower; and if any two spindles of a ring-frame make exactly the same number of turns per minute, it is only by a strange coincidence that they do.so.

Mr. ATKINSON. In considering the effect of the first starting of the frames in the morning, I have assumed, that, if the spindles stick from the chilling or want of fluidity in the oil, the strain will come upon the band next the wheel, and the whole power will be concentrated on one side of the band, which, if then damp, will be at once stretched to its utmost.

Mr. DRAPER. I have been requested to make the following motion, which I do now make: that, in order to meet the expenses of the coming year, the Board of Government be, and they hereby are, authorized to lay such an assessment upon the

members of the Association as in their opinion is required, not exceeding in amount ten dollars, as limited by the by-laws.

This motion was carried without dissent.

Mr. DRAPER. This matter of banding spinning-frames as a practical thing has been forced upon me, and I have given it as much attention for the last ten or twelve years, perhaps, as any other man. I have had a very deep interest in it, and as far back as seven or eight years ago, being greatly perplexed with the contradictory tests of the dynamometer with regard to the different spindles, I made up my mind that it was just as utterly impossible to compare one with another from any tests we could get, without knowing the tension of the bands, as it would be to try that friction-machine by the different results which have been set out here. In fact, taking a Sawyer spindle-frame, and banding it one way and banding it as it was banded in the mill where it was found, it would vary thirty-six per cent in the power required to drive the spindles. Now, I said seven years ago, I was going to find out some way to ascertain the tension of the bands. I have asked a great many men here, and a great many elsewhere, "How much lateral pull is there to the band in the spinning-frame? How much in your practice?" I never found one who would make an estimate. One of my sons had been to the School of Technology here, and I thought I would give him a practical question. So I said to him, "There is some way by which we can ascertain the tension of bands; I want you to find it out." He went to work and took a bolster and step out of a frame, drilled a hole through the spindle above, put a wire through the spindle, and then applied a springbalance to bring it to the point where it belonged. That was a practical test. Then we tied the bands with different tensions, and we very soon found that the difference in the different bands was simply astounding. I thought the matter over, talked about it, and finally Mr. Sawyer, the inventor of the Sawyer spindle, taking that idea, went to work and constructed something by which you can ascertain the tension of every band on each frame in a few minutes; ascertain it just as well as you can weigh a pound of butter. It is to have that whorl [exhibiting an implement] fixed the size of the whorl on the frame, and slip the band off; put this straddle of the spindle and slip the band on this whorl, and then pull on this scale until the sides of the whorl are together, just the same as when you weigh with