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Log. mean daily sid. mot. 3.0358738
Time of revolution 11934 sidereal days. “ The following are the results of the comparison of this orbit with observation :
Three hundred and sixth Meeting.
March 7, 1848. MONTHLY MEETING. The PRESIDENT in the Chair.
The Corresponding Secretary read letters of acceptance from the Hon. Capt. W. H. Smyth, President of the Astronomical Society of London, and from Professor Spencer F. Baird, of Carlisle College.
Dr. M. Wyman, from the Committee, appointed at the October meeting, to make experiments for testing the value of the principal kinds of ventilating apparatus now in use, made a report, of which the following is an abstract.
“ The apparatus used in most of the following experiments consists, 1st, of a machine for producing and maintaining a constant and equable blast of air; 2d, of an arrangement for measuring the velocity of the current produced by this blast.
“The air is put in motion by means of a revolving fan of four blades or vanes, each 21 inches long by 10 inches wide, placed upon the extremities of radii 13 inches in length. These blades revolve within a cylindrical case, nearly concentric with the axis of the blades, to which the air gains admission by two circular openings 13 inches in diameter, one in either end of the case. From one side of this case, the air, put in motion by the blades, enters a trunk 3 feet in length, and at its commencement 21 inches wide by 18 inches deep, which is gradually contracted until, at its farther extremity, its cross section becomes a square of 100 inches area. To the mouth of this trunk another is fitted, also 10 inches by the side and 3 feet in length. This last was added to avoid any interfering or unequal currents which might be produced by the converging sides of the first. Upon the axis of the blades is fixed a pinion of sixteen leaves, which engages a wheel of eighty teeth, driven by a handle ; consequently the blades revolve with five times the velocity of the handle, or 300 times per minute when the handle makes one revolution per second. This is the velocity always used in the following experiments, unless otherwise stated.
“ To measure the velocity of the blast, a toy marble, .62 inch in diameter, is suspended by a silken thread, to which it is fastened by a little sealing-wax. This thread is 3 feet in length, and the point of suspension, over the mouth of the trunk, is such that the marble hangs as nearly as possible in its centre. The handle is made to revolve accurately once a second, and the deflection of the marble from the point of rest, under the influence of the blast thus produced, observed. The marble is then protected from the blast, and the effect of the blast upon the thread alone observed and deducted from the first result. To ascertain the value of this deflection, the following method is adopted. Into a large cylindrical vessel, filled with water, a pipe, an inch in di. ameter and bent into the form of an inverted syphon, is so placed, that, while one of its branches rises in the centre of the vessel, an inch above the surface of the water, the other branch rises along the side of the vessel, over which it is bent nearly horizontally. Another and similar vessel 15.5 inches in diameter at the top, 14 inches at the bottom, and 8.25 inches in depth, is inverted upon the surface of the water in the first. By pressing down this second vessel the contained air is made to issue from the open extremity of the pipe ; and as the areas of the vessel and pipe are both known, we have but to note the time required to empty the second vessel to learn the velocity of the escaping air. The marble is now suspended by the same thread; the point of suspension being so situated that the marble falls against the mouth of the pipe, and would, if allowed to move freely, hang as far within it as the marble, deducting the effect upon the thread, was de. flected by the blast. The second vessel is now depressed with such velocity that the marble is just made to swing clear of the mouth of the pipe, by which its deflection becomes precisely that produced by the blast which is to be measured.
“In the case under consideration, the deflection of the thread and marble together was 2.5 inches; that dependent upon the thread alone, .95 inch. The time occupied in depressing the vessel until it rested upon the top of the inverted syphon, in several successive experiments, was 12.25 seconds. The contained air was compressed .25 inch to produce this velocity, and, as the pipe rose 1 inch above the surface of the water, 1.25 inches were deducted from the depth of the vessel, leav. ing an available depth of 7 inches. The mean diameter, that at the top being 15.5 inches, and at the bottom 14 inches, is 14.75 inches. As the areas of circles are to each other as the squares of their diameters, we have these areas in the proportion of 217.56 to l. This number multiplied by the depth in inches, 7, gives the whole expenditure in 12.25 seconds, the time required to empty the vessel ; from which
we obtain a velocity of 124.32 inches, or 10.36 feet, per second, 7.06 miles per hour. This, therefore, may be assumed as a near approximation to the velocity of the blast, when not otherwise mentioned.
“ The velocity of the induced current being the true measure of the practical value of different forms of ventilating apparatus, it becomes necessary to ascertain this value as accurately as possible. The inconvenience attending measurements in which time is involved as one of the elements, and also, probably, the difficulty of determining the instant when a current has passed through a certain space, have led to the adoption of other means, by which the velocity of the current is not directly measured, but inferred. The mode which has been repeatedly adopted, of measuring the efficiency of a ventilator by its power of sustaining a weighted Alap or valve, or a head of water, or by some other statical effect, is decidedly objectionable. Such a measure gives the correct value of the initial force or tendency to establish a current in a chimney in which there is no actual movement; but it does not indicate the velocity of the current which will be the final result of the action of the ventilator, nor is it any measure of this final velocity when ventilators of different construction are compared together. Mechanics and engineers are familiar with the difference between the statical and dynamical effects of a force. They are aware that the former may be greatly increased by the mechanical powers, so that, through the medium of a pulley or a lever, a single pound may be niade to sustain and raise a hundred times its own weight. But the dynamical effect is not correspondingly increased, for in order to raise one hundred pounds through the height of a foot, the one pound must in all cases fall one hundred feet; so that the loss of height precisely balances the gain in weight. In the same way, the dynamical effect of different springs is not to be measured by their strength alone ; it is not simply dependent upon the amount of weight which they will sustain, but equally upon their length, or rather upon the distance through which they move in restoring themselves to equilibrium. The archer's bow is a good instance of this assertion, which any one can try for himself, and he will find, that, with a given exertion of strength, he is able to throw the arrow farthest and highest with that long bow of which he can draw the string to his full arm's length, and not with the strong bow which he can hardly move. But an example more nearly allied to the case under consideration is derived from the air-pump, in which the dynamical value of any amount of exhaustion is equal to the power required to produce it, and is, therefore, proportioned to the magnitude of the receiver when other circumstances are the same; whereas its statical power or its power to sustain a head of water is wholly independent of the magnitude of the receiver, and proportioned solely to the tension of the air within it. In all these cases, there is a striking difference between the operations of using the statical and dynamical effects, which deserves the most careful consideration, because it is essential and characteristic. The statical effect may be used for any length of time without being impaired, and the reason is obvious ; it manifests itself in a state of rest, when there is no change of condition. The dynamical, on the contrary, can be used once and but once. The one pound can balance the hundred pounds as long as the materials of the pulley and lever will endure ; a compressed spring may sustain its weight, or the expanded air its head of water, as long as we choose, without any diminution of effect. But when work is to be done, a change to be effected, a weight to be raised, a velocity to be produced, the result can only be obtained by a corresponding change in the opposite direction, an undoing of work, a falling of a weight, a consumption of power once and for ever. In the present case, in which the object is to obstruct or divert the motion of the wind in such a way that part of its velocity may be communicated to the air in the chimney, and thus produce a current, the amount of this communication and transfer of velocity cannot be measured when it does not take place, - when, on the contrary, the mouth of the chimney is entirely stopped up, so that it is impossible to produce any current within it. It would be just as proper to weigh a water-wheel by the weight which will just reduce it to a state of rest, instead of that smaller weight which reduces it to its usual working velocity, and which is universally adopted by experienced engineers as the correct measure of the power of the wheel. It should also be borne in mind, that there are resistances offered to air in motion by the tube through which it passes. These resistances are not constant; they increase as the perimeter and length of the tube directly, and also as the square of the velocity ; these, it is obvious, cannot be measured where they do not exist.
“ The plan, therefore, which has been adopted in these experiments, is to measure directly the velocity of the current produced, and it will not be surprising, after what has preceded, if some striking differences should be observed between the results thus obtained and those derived from any statical measure.