of small balls, discharged at an elevation of 750 or 800, such accelerated velocities, as would, if true, be quite sufficient to do good service in the way M. Carnot suggests; but the fact is, that there can be no acceleration beyond a limit which, with small balls, is very much less than is generally imagined. "From the vertex of the curve, where all the vertical motion is lost, the ball begins to descend by an urging force which is nearly constant, viz., its own weight. This force would produce equal increments of velocity, in equal times in vacuo; but in air, the descent of the ball being resisted more and more as the velocity accelerates, the urging force will, at a certain velocity, be opposed by an equal resistance of air; after which, there can be no further acceleration of motion, and the ball will continue to descend with a velocity nearly terminal.” In considering this problem as applied to vertical fire, Sir Howard Douglas remarks that, M. Carnot has entirely overlooked terminal velocity; " and I shall show," says he, "from his own words, that this is the case. It is not necessary to exhibit here the investigations by which I have established the impotency of M. Carnot's vertical fire; I shall only state the results, not to embarrass the conclusions with abstruse matter. The solutions are computed, from the theorems given in Dr. Hutton's tracts; and although the results may differ a little from the truth, yet it is quite clear, that in the descent of the balls there can be no acceleration of motion beyond a certain limit;-that with small balls this velocity is very much less than persons who have not investigated this curious problem would imagine; and that M. Carnot has evidently overlooked this circumstance. "The velocity which a musket ball has acquired when the resistance becomes equal to the weight, or urging force of descent, is only about 180 feet in a second. The potential altitude, or the height from which the ball must descend in vacuo, to acquire a velocity equal nearly to the terminal velocity, is 523 feet. Hence, in the first place, it would be a waste of means to use the full charge; for a musket-ball fired upwards with the ordinary quantity of powder, would be pro jected to a greater height than 523 feet; and it is evident that all above this is unnecessary. "The indentation which a musket-ball, moving with a velocity of 180 feet per second, makes on a piece of elm timber, is about th of an inch this might, perhaps, be sufficient to knock a man down, if by great chance it were to fall upon his head; but in no other case would it put him " hors de combat." Now, as to the four-ounce balls. The diameter of a French four-ounce ball, is one inch, two lines, five points; which, reduced to English measure, is 1.28038 inches. Its content is 1.09909 inches. The weight is 4.72247 ounces, if made of cast iron, and 4.8624 if of wrought iron. The terminal velocity of the cast-iron ball, is about 201 feet. The terminal velocity of the wrought-iron ball, is about 204 feet. The potential altitude of the cast-iron ball, is about 631 feet. Ditto ditto wrought ditto ditto 650 "M. Carnot recommends that the balls should be made of hammered iron; but adds, that as the charge of powder for a mortar is small, balls of cast-iron may resist the explosion without breaking, and will answer as well. Now this observation shows that the author had not considered the effect of the air's resistance, nor doubted a sufficiency of force in his vertical fire for the weight of a ball of hammered iron, is greater than that of a ball of cast-iron of equal diameter; and the superior weight,, or urging force, of the former, would generate greater terminal velocity than a lighter ball, of the same size, could acquire; the momenta of the two balls in question, would be as 19 to 18. "Four-ounce balls, discharged at elevations even considerably above 45°, to the distance of 120 yards, would not inflict a mortal wound, excepting upon an uncovered head. They would not have force sufficient to break any principal bone; there would be no penetration, but merely a contusion. This certainly would not oblige the besiegers to cover themselves with blindages, as M. Carnot imagines; for a strong cap or hat, and a cover of thick leather for the back and shoulders, would be sufficient protection from the effects of his vertical fire with small balls. "As the quantity of balls required to feed mortars discharging 600 balls at a time would be very considerable, M. Carnot observes that cubes of iron, of 8 or 10 lines side, cut from square bars of this dimension, may be substituted. These, he says, may be fired from mortars, howitzers, or stone-mortars, and will produce the same effect as balls (page 491, Carnot.) "Let us consider this: 10 lines French are equal to 89523 inch English. "We have no experiments from which we can ascertain the terminal velocity of square shot; but from comparative experiments with round and flat surfaces, we know that the resistance of the air to the flat end of a cylinder is more than double the resistance to a ball of the same diameter. Thus, although the urging force of a ball and cube of the same weight be the same, yet the surfaces upon which the resistance acts (and very irregularly in regard to the cube) are very different: "From this, together with what has been said respecting the descent of balls, we know, and that is enough for our present purpose, that the terminal velocity of the cube must be much less than 185 feet per second; and, consequently, its effect or momentum inferior to that of a 3·08 ounce-ball. The motion of a cubical shot will, besides, be quite irregular, descending sometimes with an angle, then a face, then an edge foremost, tumbling over and over in oblique, irregular directions, without any certainty, excepting that the velocity and effect will be much less than those of a round shot of equal weight." ART. XIII. An Account of the good Effects of the white Oxide of Bismuth in a very severe Stomach Affection of a Gentleman far advanced in Years. By G. D. YEATS, M.D., F.R.S., Fellow of the Royal College of Physicians, &c., (communicated by the Author.) MANY years have now elapsed since Dr. Marcet published a very clear and explicit account of the good effects of the white oxide of bismuth in certain painful conditions of the stomach. Relying upon the recommendation of this medicine, as coming from so respectable an authority, other practitioners very soon made trial of it, and were much gratified in finding that it answered the expectations of the curative powers which had been attributed to it. Among those who have since more particularly called the attention of physicians to this subject, is Dr. Bardsley, of Manchester, who, in 1807, published some interesting and instructive cases in his Medical Reports. Some insulated cases have also been published in the medical journals, confirming the high character given to the medical virtues of the oxide of this metal. In reviewing the cases which have been presented to the public, I do not find the age of any one * As a practical exhibition of the doctrine of terminal velocity, Sir Howard notices the descent in the parachute, of which the aëronaut, detaching himself from his balloon, falls with accelerated speed until the resistance of the air to the expanded canopy becomes equal to the total weight of the descending body, after which it falls to the earth with uniform velocity nearly. To the man of science these illustrations may appear superfluous, and perhaps obtrusive; but the author knows from experience, that such familiar illustrations are necessary to convey his meaning to those who, like the theorists of no remote period, make no allowance for the resistance of the air, which is now known to be such that a 24 lb. ball, moving with a velocity of 2,000 feet in a second, would suffer a resistance of 800 lb. ucarly. patient to exceed fifty-five years; and, as the patient whose case I am about to relate, had, for a long period of years been afflicted with distressing pains of the stomach, was past seventy when the treatment was first commenced, and when the symptoms were so violent as justly to excite a suspicion of much organic mischief about the stomach, I am induced to believe that a detail of it will add considerably to the good opinion entertained of the bismuth; and will contribute to diffuse still wider the benefits to be derived from an exhibition of this valuable medicine. I am aware that the result of the operation of a medicine in an individual case can prove nothing decisively of its good effects; but, when such individual statement comes in confirmation of many other cases, it must have its weight in the recommendation of the adoption of a medicine not previously very generally resorted to. In this point of view, therefore, I trust the perusal of the following case will not be without its utility. January 21, 1816. PC, Esq., æt. 71, complained, at the beginning of winter, of pain about the pit of the stomach, attended with much eructation of wind, and costiveness. The appetite is rather deficient, but it varies; it is not accompanied by any morbid thirst; the tongue is foul; pulse full, slow, and soft; a wasting of the flesh has taken place; the urine is of the natural colour and quantity; there is nothing remarkable in the colour of the fæces. No uneasiness is complained of by pressure on the epigastric region. The pain is troublesome at various times during the day, but is most distressing between ten and eleven o'clock at night, when it comes on with intolerable violence, and to such an extent, as to cause vomiting, when the matters thrown up are very liquid, great in quantity, and extremely acid; some relief from pain is then obtained. Sometimes the pain returns in the night, so as to destroy rest. It occasionally shoots to the back, and produces a slight dyspnæa for a short time. The pain is not brought on immediately upon taking food, but he describes it as occurring about three hours after meals, by a kind of fermentation, and a sensation of weight, as if the food |