applied at d, K will be the common center of gravity, and the bearing point H of the friction journal must be beneath the line nn', drawn through K and e, if the windlass is to be non-overhauling. The journal e will still be regarded as frictionless. Through e and G, the bearing point of the friction journal when the weight is being raised, draw the moment axis mm'; as e and G are the only points of support for the windlass this line is evidently the axis with respect to which the leverages of the power and weight must be reckoned. Putting w for the weight of the windlass, W+w will act downward at Kand. must have a moment about this axis equal to that of P acting upward at a. The lever arms of W+w and P are the dotted perpendiculars let fall from K and a upon this axis, but as they are proportional respectively to Kk and ap these lines may be used instead of the perpendiculars in forming the equation of moments. This equation is This last equation becomes evident by noticing that, as Kis the common center of gravity, W dJ = (W+w) KJ. Eliminating W by means of the equation of moments, the expression for the used energy becomes U. Subtracting this from the total energy, there remains for the amount wasted in friction, Comparing these expressions it is evident that if we take the diameter aa' of the power pulley to represent the total 100 per cent. of applied energy then the segments ap and pa', into which it is cut by the moment axis, will correctly represent the percentages of used and wasted energy, and the segment corresponding to the used energy will be that one at the end of which the power is applied. It follows therefore that, with the power at a, pa', the wasted energy, is less than fifty per cent., while with the power applied downward at a' that wasted would be ap and more than fifty. Further with the power applied upward at n, or downward at n', none would be wasted, while if applied downward at m' or upward at m all would be lost, i. e. the power, no matter how great, would simply cause the journal to bear with more or less pressure at G without producing any motion of the weight. Finally, with the power at r or r', fifty per cent. of the energy would be wasted. This model is instructive inasmuch as it shows no connection between the velocity ratio aa' ÷ df and the percentage of energy wasted, that ratio remaining the same for all positions of the power pulley from nm' to mn'. Conversely also, the efficiency may be retained constant while the velocity ratio is changed. Thus, if the power pulley be changed not only in position but also in diameter, and so that the latter is always contained between the lines ea and ea', the velocity ratio will be changed without changing the percentage of energy wasted. Experiments upon the model show that when the friction is such as to make it non-overhauling, a power of 1.55 lbs. will raise a weight of 5 lbs., the velocity ratio being 5 but one pound is needed to raise the weight and the remaining .55 lb. is necessary to overcome the friction, so that the percentage of lost energy is 100 × .55 ÷ 1.55 35+. A diagram, similar to Fig. 104 has been drawn with as good measurements as can be made from the model, which is of wood, and it shows that about 30 per cent. should be lost. DISCUSSION. Mr. Oberlin Smith.-Mr. President: I would say, in connection. with this subject, that two or three years ago I made sketches of a device embodying this idea applied to a crane, which I showed to some of my friends, but I never actually built anything exactly on this principle. My idea was to make a very small pinion, having as few teeth as possible, driving a large gear on the drum shaft, and then put very large journals, so that the shaft should be a good many times larger in diameter at the journals than the pinion itself. This, I thought, would work just as a worm. gear does, stand wherever it was put and not "overhaul," as Professor Ball terms it. But on studying it a little, I found that it might have just the same features as worm gear in regard to power wasted in friction, because the journals had to be so very large. It then occurred to me to take advantage of the principle that Professor Webb has explained, of lifting the shaft at the point of greatest friction, by the action of the power against the load. I think if I had put another shaft carrying the crank or pulleys by which the power was applied, so placed as to lift the friction shaft from its bearings, thus making it double-geared, things might be so proportioned and arranged that such lifting would relieve a great deal of the friction, and very likely a practical crane might be made out of it. Professor Webb.-I would say in reference to this paper that a copy was sent to Professor Ball, but, it being sent rather late, there was not time to get any remarks from him upon the subject. I offered, however, to put into this discussion, when printed, anything that he would send. In reply to Mr. Smith, I will say that I am no stranger to his powers of invention, having spent many enjoyable hours with him in planning new devices, and I have no doubt he might succeed in making a very good crane upon this principle. The following communication* has been enclosed in a letter me, dated Oct. 21, 1888, as a part of the discussion upon this paper: "NOTE submitted to the American Society of Mechanical Engineers,' by Sir ROBERT BALL, Royal Astronomer of Ireland, * Added since the meeting. relatively to the paper CCCXXVIII. on the 'Overhauling of a Mechanical Power,' by Mr. J. Burkitt Webb, of Hoboken, N. J. "I am indebted to the kindness of Mr. J. Burkitt Webb for the privilege of adding a few remarks to his paper, and I return him my thanks for his courtesy. "Considering that my book on 'Experimental Mechanics' has been largely used by students and teachers for seventeen years (a new edition of it has been placed in my hands this very day) it would indeed have seemed strange that it should have contained a serious blunder which had never been pointed out till Mr. J. Burkitt Webb honored the work by his notice. Of course there is no such blunder. Mr. Webb does not seem to be aware that it is of the essence of A MECHANICAL POWER that the power employed shall be a small fraction of the load raised. The instances he gives consist of contrivances in which to raise a small load a gigantic power must often be exerted. If he will have the goodness to consider an inclined plane which is really capable of use as a mechanical power, he will find that the principle is verified with all the accuracy of which any statement with regard to friction is capable. "But I am glad of this incident to take the opportunity of laying before so eminent a body as the American Society of Mechanical Engineers the brief theoretical demonstration of that useful, practical principle in which Mr. Webb does not believe. For the full details of the numerous experiments by which the principle has been practically verified I must refer to my work already mentioned. "The mechanical powers on which I have experimented may be broadly grouped under three heads. 1st. Those produced by winches or wheel-work; 2d. Those produced by screws in any combination; 3d. Those produced by pulleys of any type. It "I select for discussion here the last-mentioned group. includes all forms of ordinary blocks as well as the differential pulley, the epicycloidal pulley and many patent hand-hoists and ingenious contrivances in which ropes or chains are used. The following theory comprehends the action of every mechanical power of this kind: "Let n be the velocity ratio of the machine, i.e., the number of feet through which the power must be moved in order to raise the load one foot. "Let P be the actual force which it is practically necessary to apply in order to raise a load R.. "To raise R one foot n P units of work are required, and since only R of these units are usefully expended, units of work must have been expended in overcoming friction. "Let the power P be removed, then, since the upper block supports a smaller weight, the friction is diminished at that block, though remaining sensibly the same at the lower block, if there should be one. The entire friction is not therefore diminished in a greater ratio than that of R to P + R. Hence the number of units of work necessary to overcome friction in the descent of the weight is not less than R 3 But by the descent of the load only R units of work can be accomplished, and therefore the block will not overhaul if In the case, for example, of a differential pulley block in which = n 16 I found that a power of 46.09 lbs. was required to raise a load of 280 lbs. In this case and, as this is less than the observed value of P, it follows that the differential pulley block of this type cannot overhaul, a fact that everybody knows. On the other hand if the block will certainly overhaul. Take a 3-sheave block in which n = 6; I found that for a load of 228 lbs., the power was 56 lbs., but |