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and not to repeated reflections from the surface of drops of water, as some physicists have supposed.
As can readily be seen, the aqueous lines of the solar spectrum present a very wide field for investigation, but one which can only be cultivated under peculiar atmospheric conditions. This paper is only intended to open the subject. I hope to be able to continue the study on every favorable opportunity, and shall take pleasure in communicating any future results to this Academy.
Professor Charles W. Eliot exhibited to the Academy a dynamometer invented by Mr. S. P. Ruggles, the Curator of the Museum of the Institute of Technology.
“ This new and admirable invention accomplishes two objects ; — first, it measures the exact amount of power which is being consumed in driving a single machine, or any number of machines, at any instant of time, indicating every change in the force required, as the work done by the machines varies from instant to instant ; secondly, the apparatus adds up and registers the total amount of power which has been used by any machine, or set of machines, during a day, a week, a month or any desired time. The apparatus may be thus described. The pulley, from which the power is taken, is attached to the shaft by the intervention of a spiral spring. One end of this spring is secured to the shaft, and the other end to the hub of the pulley. The lateral motion of the pulley upon the shaft is prevented by a collar on either side of the pulley. On the inside of the hub is cut a screw of about threeinch pitch, that is, a screw which makes a complete turn within a distance of about three inches measured on the axis of the hub. A rectangular slot is cut out of that part of the shaft which lies within the hub of the pulley, and in this slot slips backwards or forwards a piece of metal which precisely fits the slot. From each side of this small piece of metal there projects beyond the surface of the shaft a small portion of the male screw which exactly fits into the screw cut in the interior of the hub of the pulley. If there be no resistance at all to the motion of the pulley, the shaft, spring, and pulley will all start together, and revolve together. But if a resistance be offered to the motion of the pulley, the shaft, and with it the piece of metal which slips in the slot, will start first, and the pulley will move only when the strain caused by the twisting of the spring is sufficient to overcome the resistance applied to the circumference of the pulley. But if the piece of metal in VOL. VII.
the slot begin to turn while the hub of the pulley is stationary, the piece must move laterally within the slot, being forced by the screw. If the pulley start a quarter of a turn later than the shaft, the piece will move laterally three quarters of an inch; if the pulley start a half a turn later than the shaft, the piece will move laterally an inch and a half. The lateral motion of the piece in the slot is proportional to the retardation of the pulley, and this retardation is proportional to the strain upon the belt which passes over the pulley, and conveys the power to be used. To the movable piece in the slot is connected a small round rod, which runs out through the centre of the main shaft and projects some little distance beyond it. On the end of this rod is a circular rack of teeth, in which plays a pinion, on whose shaft is a hand moving over a dial-plate. By applying strains, measured by standard scales, to the belt which passes over the pulley, - as a strain of ten pounds, fifty pounds, one hundred pounds, -- it is easy to graduate the dial-plate into pounds, so that the number of pounds of strain upon the belt may be read off at any instant by a mere inspection of the dial. The mode of operation of this part of the apparatus is then as follows :— when no power is being conveyed from the pulley, shaft and pulley start simultaneously ; there is no lateral motion of the piece within the slot and its connected rod, and the hand on the dial points to zero. But the moment that power begins to be expended in driving the machinery, the strain upon the belt will be first felt by the spring s which connects the pulley to the main shaft, and the spring will yield in proportion to the strain ; the effect is to let the sbaft make a small part of a revolution in the hub of the pulley, before the pulley begins to turn and keep pace with the shaft; the rod within the end of the shaft is thus drawn in a little, the hand moves over the dial-plate, and points to the exact number of pounds of power which the belt is conveying from the pulley at the instant of observation.
The registering of the total amount of power delivered from the pulley is effected by means of two small belts running over the round rod, which projects beyond the end of the main shaft and carries the index hand above described. These two small belts communicate the motion of the shaft to two parallel and equal wheels, one of which bears a dial-plate, and the other an index hand which moves over the dial-plate. When there is no strain upon the main belt going over the pulley, the two wheels revolve at the same rate, — neither gaining upon the other, and the hand remains constantly over the same figure on the dial-plate ; but when a strain is put upon the belt and the round rod moves laterally, as above described, the lateral motion brings a conical enlargement of the rod under the little belt which moves the wheel bearing the dial. The dial-wheel now goes faster than the wheel carrying the hand, and begins to count up the power used. The greater the lateral motion of the rod, or, in other words, the greater the power transmitted to the working machines, the larger the diameter of the cone which comes under the belt of the dial-wheel, and the greater the gain of the dial upon the hand. The wheels of both dial and hand are constantly revolving in the direction opposite to that of the motion of the hands of a watch. The belt of the band-wheel runs always upon the rod, where its diameter is constant, and as the rod moves laterally under the little belts, guides are necessary to keep the belts themselves from moving laterally also. The proportions of the cones on the rod, and of the two wheels which carry the dial and the hand, can be so adjusted as to make a difference of one complete revolution between the motions of the hands and of the dial indicate a delivery of ten thousand footpounds, or of ten million, or of any other convenient number, and, by a system of gearing analogous to that used in gas-metres, any desired amount of power could be consecutively registered. It is obvious that the registering apparatus takes account of both the strain and the speed, while the simple index first described measures only the strain.
This instrument is at once elegant in design, simple and therefore cheap in its construction, easily verified and proved at any moment when in operation, and of very easy application to any machine, or set of machines, driven by hired power, whether the power used be constant or variable in amount. The instrument admits of a great variety of forms: the one described above is meant for the end of a shaft ; another form is so arranged as to be attached at any part of a running shaft, while in the proportions and dimensions of the several parts there would be the same variety as in common scales, which are large or small, coarse or fine, according as they are meant to weigh coal or pills, hay or coin. The instrument meets a pressing want. Tea and sugar are sold by the pound, gas by the thousand feet, cloth by the yard, but steam-power and steam and air engines are sold by guesswork, or by rough and uncertain rules, on whose application buyer and seller can seldom agree.
Hereafter steam-power can be sold by the thousand or million footpounds.
Mr. Ruggles does not patent his valuable invention.
Notes on the Cells of the Bee. It is more than a century and a half since Maraldi studied the form of the cells of the hive bee, and described them as hexagonal prisms with trihedral bases, each face of the base being a rhomb, the greater angles of which were 109° 28', and the lesser 70° 32'.* Twenty-five years later, Reaumer, the most admirable of the observers of insect life, with the view of ascertaining how far such a form was an economical one, proposed to Koenig the following problem, —"Of all hexagonal cells, having a pyramidal base composed of three equal and similar rhombs, to determine that which can be constructed with the least amount of material.” † It is a part of the history of this subject, that Koenig's results differed from those of Maraldi by two minutes in each of the angles, the former having made them 109° 26' and 70° 34'. It has recently been stated that the table of logarithms used by Koenig had an error which would exactly account for the difference.
Admitting an error of two minutes in each of the angles, still the close correspondence between the results of Koenig and the measurements of Maraldi was well fitted to excite the wonder and admiration of all, and from that time to this the belief has prevailed, that the instinct of the bee enables it to construct such a cell as that sought in Reaumer's problem, if not in all cases, at least in the larger portion of them, without sensible error. It were unjust to keep out of sight the fact, that, however correct the measurements of Maraldi may have been, he has left no record of his method of making them, and furthermore, the possibility of measuring the angles of such a structure as the cell of the bee, without liability to an error of one or two degrees in each angle, is denied by competent authorities, since the angles of the cell are nowhere sharply defined and the surfaces are not strictly planes. I The mineralogist, treating the cell as a crystalline form, would not expect a closer approximation to exact measurement than that just stated.
* Mem. Acad. des Sciences, 1712. † Memoires pour servir à l'Histoire des Insectes, Tom. V. p. 389. Paris, 1740.
The first person who appears to have called Maraldi's measurements in question was Father Boscovich, “who had supposed that the admeasurement of the angles was too nice to be accurately performed, and that the coincidence of M. Maraldi's measurements with theory could only arise from his assuming that the angle of inclination of the rhomboidal plane was the same with that of the hexagon, viz. 1200, from which, no doubt, it would follow that the angles of the rhombuses should be 109° 28' and 70° 32' respectively." - Lord Brougham, Nat. Theol., p. 35).
Lord Brougham, who, of later writers, has written the most elaborately on the subject, in his essay entitled Observations, Demonstrations, and Experiments upon the Structure of the Cells of Bees, after having himself solved Reaumer's problem, after having obtained solutions of it through others, and after having himself measured the cells, asserts positively that they are constructed in accordance with the form deduced from calculation, and are therefore exact. Having compared the sides of the cell by measurement with a micrometer, he says, “I certainly can find no inequality.”* Again, “ She [the bee) works so that the rhomboidal plate may have one particular diameter and no other, always the same length, and that its four angles may be always the same”; † and he still further adds, “ The construction of the cell, then, is demonstrated to be such that no other which could be conceived would take so little material and labor to afford the same room.” 1
We have looked carefully through Lord Brougham's essay, for a recognition of the existence of irregularities in the cells, but have found none, except of such as are of microscopic size. “ The lines,” he says, “ may not be exactly even which the bee forms; the surfaces may have inequalities to the bee's eye, though to our sight they seem plane; and the angles, instead of being pointed, may be blunt or roundish, but the proportions are the same : the equality of the sides is maintained, and the angles are of the same size, that is, the inclination of the planes is just. .... Now, then, the bee places a plane in such a position, whatever be the roughness of the surface, that its inclination to another plane is the true one required. ” $
Lord Brougham's answer to L'Houillier's criticisms may be cited to the same effect. When the latter speaks of the conditions re
* Natural Theology, London, 1856, p. 224.
Ibid., p. 191.