consulting the column marked Fall, we find that the original level is reached between the instants +60 and +70, by interpolation at 611, so that the whole time of its flight has been 1·111. Also, in the columns marked Hor. Distance, we find 6984 for that covered during the rise, and 4726 for that passed over during the fall, making the total horizontal range 1.1710. The velocity with which the ball strikes the ground is seen to be 7777, while the impact is at an angle of 39°19'. The squares of the initial and final velocities are nearly in the ratio of 55 to 7; that is to say, of the work done by the gunpowder in putting the ball in motion, 48 parts are spent on the air, and 7 parts only remain to represent the destructive effort. Thus we can readily compute the range, the time of flight, and the incidence of the ball. A table of these, such as the following, forms a convenient adjunct to the fundamental table :— In order to apply these results to business, we must ascertain the values of the tabular units in terms of the actual units of time and distance. This is easily done if the terminal velocity be known. As an example, let us take a bullet whose terminal velocity is 800 feet per second, in which case the tabular velocities must all be multiplied by 800. A heavy body falling freely acquires velocity at the rate of 32 feet per second for each second of time, and would acquire this velocity of 800 in 25 seconds, wherefore all the tabular times must be multiplied by 25. Lastly, the unit of distance is described with the unit velocity in the unit of time, wherefore 800 x 25 20000 feet is the actual linear unit of the = tables as applied to this particular projectile. The above example, therefore, expressed in English feet and in seconds of time, becomes VOL. IX. 4 Q If the same ball be shot from the same gun, but at another inclination, the shape of the path is changed and the details thereof must be sought for in another table. We search among the various tables for that one in which the given initial velocity is found opposite the proposed angle of elevation; if the tables be constructed for values of V sufficiently close, we shall find this either directly or by an easy interpolation; and then, proceeding as above, we can get all the desired information. Similarly, if the initial velocity and the horizontal range be given, we convert these into the corresponding tabular numbers, and search among the various tables for that one in which these two are found together; the angle of inclination, the time of flight, and all the other quæsita of the problem are then to hand. It has been stated that three data suffice to determine the path. When the terminal velocity is one of these, the solution is obtained by simple inspection; but when that velocity is one of the quæsita, the operation becomes indirect. Suppose that the velocity communicated to a given shot by a specific charge of gunpowder has been ascertained, say, by help of the ballistic pendulum, we may discover the terminal velocity of that shot by observing the angle of elevation and the horizontal range. For this purpose we assume some terminal velocity, thence compute the corresponding tabular initial velocity, and thereby obtain the corresponding horizontal range. If this come out too much, we must reduce the assumed terminal velocity, and continue our trials until the computed agree with the measured distance. If the time of flight have also been carefully noted, we get a corroboration of the accuracy of the result. Not only so, we may dispense altogether with the ballistic pen dulum, and determine both the initial velocity and the resistance by accurate observations of the angle, the range, and the time of flight, For the purpose of facilitating the solutions of the various problems which may arise in practice, auxiliary tables may be derived from the fundamental ones. When a shot is fired in a steady breeze, the direction in which the ball meets the air is not the apparent direction of the gun, it is that of the resultant of the two motions, and the computations have to be made as for that resultant. Thus if AZ (fig. 5) represent the horizontal direction of the gun, and AB the initial velocity of the ball projected on the horizontal plane, while bB represents the velocity of the wind, Ab will be the horizontal direction in which the ball meets the air. Since the vertical motion is not affected, the tangent of the elevation of the gun must be changed in the ratio of Ab to AB in order to get the tangent of the true angle of elevation in relation to the air, and Ab multiplied by the secant of that elevation is the true initial velocity. If we now, using these corrected arguments, compute the hori zontal distances corresponding to equal intervals of time, measure those along the prolongation of Ab and from the successive points draw parallels cC, dD, &c., multiples of bB, we shall have the horizontal projection of the ball's path, that path being a line of double curvature. As an example of the variety and completeness of the information conveyed by such tables, we may cite the path detailed in the preceding table and represented by fig. 3. The ball is projected from A with the velocity of 2·18, and at once encounters a resistance 4 times greater than its weight. The speed is rapidly lessened, and the path is deflected to become horizontal at V, where, in the present instance, the resistance is just equal to the weight. On account of this resistance the speed is still slackened, but gravity now comes to accelerate the motion downwards, and, at about the fifth interval from V, has overcome the retardation, thereafter the velocity slowly increases, and tends ultimately to reach the limit 1.00. Those cases in which the characteristic angle A of fig. 4 is obtuse have little or no application to gunnery; in them the path is never horizontal, but is inclined downwards all along. The analysis of these motions is complex, and the calculations thereon following are tedious, but the results, when tabulated, are of easy application. The theory would be uninteresting to those engaged in the actual business, just as the mode of construction of trigonometric and logarithmic tables is scarcely ever thought of by the navigator or surveyor. What we have at present to consider is the advantage to be gained by the compilation of a series of tables such as those sketched out. 3. On some Physical Experiments relating to the Function of By David Newman, Glasgow. Communi the Kidney. cated by Professor M'Kendrick. (Abstract.) This paper treats of the physical influences which promote the secretion of urine, as far as can be demonstrated by experiments upon animal membranes and the kidneys of animals recently killed. Before going on to consider the subject I may be permitted simply to mention the theory held regarding the means by which the kidney performs its function, and also say a word or two in connection with the structure of that organ. As regards its histology the kidney may be said to be composed of two elements-(1) the bloodvessels, and (2) the tubuli uriniferi. (This is leaving out of account the lymphatic arrangement.) The kidney receives its supply of blood from the renal artery, which, as it passes into the substance of the kidney, penetrates the cortical portion and gives off branches. The uriniferous tubules in this part of the kidney end in globular dilatations called the capsules, or Malpighian bodies; it is into these that the branches of the renal artery pass to form convoluted coils, the glomeruli. The branches of the renal artery which pass into the glomeruli are called the afferent vessels, and the vessels that are formed by the reunion of the branches of the glomeruli are called the efferent vessels. After the efferent vessels emerge from the capsule of the Malpighian body they again subdivide to form true capillaries, most of which go to form a closely meshed network round the tubuli uriniferi. They finally unite to form the radicals of the renal vein. To make use of the description of Mr Bowman, "it would be difficult to conceive a disposition of parts more calculated to favour the escape of water from the blood than that of the Malpighian body. A large artery breaks up in a very direct manner into a number of minute branches, each of which suddenly opens up into an assemblage of vessels of far greater aggregate capacity than itself, and from which there is one narrow exit. Hence must arise a very abrupt retardation to the velocity of the current of blood." But besides this arrangement, by which a large volume of blood is exposed to circumstances the most conducive to free filtration of its fluid constituents, we have a condition, namely, the secondary capillary system on the distal side of the glomerulus, which, by its resistance to the onward flow of the blood, subjects the blood inside the Malpighian body to considerable pressure. It is now generally supposed that the excretion of urine takes place by filtration of a dilute solution of the soluble constituents of the urine through the glomerulus into the capsule of the Malpighian body. This weak solution then passes along the tubuli uriniferi, where it comes into close contact with the blood it has just left. It is then supposed that an interchange takes place between the blood in the capillaries surrounding |