We have anticipated in some measure a few observa tions, that would more properly have fallen under the head of Construction; but we were anxious to furnish our readers with the remarks of the distinguished Pro fessor of the College or Naval Architecture, on Chap man's t icws relative to the resistance of fluids, in order to place every step of so difficult and mysterious a sub ject, in a candid and explicit point of view, It may not be amiss, however, to allude more parti cularly to the expetiments with which Mr. Chapman D" says his formula of resistance C' x , (n BC ) D CZ 2 C X , (n w) is found to agree.
In a large and deep pond, says he, were placed a hun dred feet from each other, two poles A, B, and two piles C, D, Fig. 5, Plate CCCCXCI. to which were fitted two copper gullies, and through these were reeved ropes to support the weights, as represented in the figure. The lines E and G were attached to the body employed in the experiment. On the line E, a weight was placed, to give motion to the body in the water; and on the other line G, there was also a weight, but less than the first, to keep the body in the straight line from which it would have deviated without it. To the line E were tied two small pieces of red cloth 1, K, at the distance of 74 feet from each other. To measure the time, a stop watch showing seconds was used. When the mark ar rived at L, the stop watch was let go, and when the mark I was come to the same point, the watch was stopped. It then showed the number of seconds which the body F took up to pass over the space of 74 feet. The bodies with which the experiments were perform ed, were of wood, and 28 inches in length. The trans verse sections under the water were circular. Their diameters at the greatest breadth were 4 of the length, or 3 inches, and the water lines either straight or conic parabolas, and the vertex of the parabolic curve was at the greatest breadth. As the bodies were lighter than water, lead was run in, until their specific gravity was nearly equal to that of sea water, so that they only just floated, having their axes parallel to the surface of the water. The weight attached to the line E, to put the body in motion, was varied according as it was required to increase or diminish the velocity ; but the retarding weight was always the same. The bodies employed were the following: Fig. 6, Plate CCCCXCI. having its greatest breadth at the middle, and its extremities formed by parabolic lines.
Fig. 7, having its greatest breadth at 4 of its length from the point 13. The extre mities also were parabolas.
Fig. 8, having its greatest breadth at 4 of the length from the point D, the extremi ties still parabolic.
Fig. 9, having its greatest breadth at the mid dle. The extremity F parabolic, and the other G conic.
Fig. 10, having its greatest breadth at of the length from the point IL The extre mity 11 parabolic, the other conic.
Fig. 11, having its greatest breadth at 4 of the length from the point 0. The extre mities conical.
Fig. 12, — wholly conic, having its greatest breadth equal to that of the other bodies, and its length twice and a half the breadth.
The results of the experiments performed with these bodies, are recorded in the following table : To understand the nature of these experiments, let the example of Fig. 7 be selected, in which the moving weight was equal to that of the entire body; and the retarding weight, half the same quantity. It may then be remarked, that with the extremity 13 forward, the body will pass over 74 feet in 14 seconds; but with the sharper end C in a similar situation, the body will pass over the same in seconds. In like manner, with the body represented in Fig. 10, and the same conditions of the moving and retarding weights, when the parabolic extremity of the body was moved forward, the time of describing 14 feet was 15 seconds ; but with the conical extremity under the same circumstances, the same space was described in 16 seconds.
Each of the experiments recorded in the table, Chap man informs us, was repeated six times, with consider able uniformity. The velocities, he venial ks, do not present the proportionality we might be led to expect from a consideration of the weights,—a circumstance, however, which he attributes to a division of the fluid too near the surface. The number of pullics over which the line passed, rendered the experiments less exact, on account of friction. The friction, however, beMg the same for all the experiments, the variation in the velo city ought to be the same.
The inferences Mr. Chapman draws from his experi ments are the following : First, That when the motion is slow, the body has a greater velocity when the sharper end is forWord, than the full. Secondly, That when the velocity is increased to a certain degree, the body passes over the same space in equal times with either extremity forward. Thirdly, That when the velocity becomes still greater, the body takes a less time to pass over the same distance when its obtuse end is Thus, says he, it is the -velocity of the body which should determine the place of the greatest breadth, to render the resistance the least—a conclusion, however, we would add, that implies the inadmissible supposition of a variable posi tion of the greatest breadth.