Pentameter

“ Whether the intensity of gravity is sought in absolute or relative measure, the most widely used instrument for its determination since the creation of classical mechanics has been the pendulum. In recent decades, there have been invented gravity meters based upon the principle of the spring, and these instruments have made possible the rapid determination of relative values of gravity to a high degree of accuracy. The gravity meter, however, must be calibrated at stations where the absolute value of gravity has been determined by other means if absolute values are sought. ”

“ The form of the earth has, however, a value confined not alone to those interested in horology—it furnishes us with a standard of weights and measures. In England and the United States, the pendulum is the unit of mensuration, or at least the common standard from which measurement is derived. It has been shown that, deducting the effects of nutation, the axis of the earth’s rotation is always in the same plane. Now, the mass being the same constant quantity, a pendulum oscillating seconds at the Greenwich Observatory, has been adopted by the English Government as its standard of length. ”

“ Although alternative methods of determining absolute values of gravity are now in use, the pendulum retains its value for absolute determinations, and even retains it for relative determinations, as is exemplified by the Cambridge Pendulum Apparatus and that of the Dominion Observatory at Ottawa, Ontario.
The pendulums employed for absolute or relative determinations of gravity have been of two basic types. The first form of pendulum used as a physical instrument consisted of a weight suspended by a fiber, cord, or fine wire, the upper end of which was attached to a fixed support. ”

“ Everything that we have said assumes that there is a mass depending from such a fine line that the mass of the line shall not be considered; but if we examine the pendulum of some clocks we see that the rod is of steel, and that its weight or bob is elongated, and consists of a long cylinder of glass filled with mercury, and carried in a sort of stirrup of steel; this is very different from our simple pendulum—it is a compound pendulum. ”

“ Hence one of the best methods of determining the magnifying power of a telescope is to measure the diameter of the emergent pencil of rays, after the telescope has been adjusted to focus upon a star, and to divide the diameter of the object-glass by the diameter of the -emergent pencil. If we desire to utilize all the parallel rays which fall upon an object-glass it is necessary that the full pencil of emerging rays should enter the observer's eye. ”

“ We have unquestionable authority for saying, that the mercurial pendulum of the usual construction, that is, with a steel rod and glass cylinder, is not affected by a change of temperature simultaneously in all its parts. Now, the pendulum of which we are treating being formed throughout of the same material in a single piece, and in every part of the same thickness, it is presumed it cannot expand in a linear direction, until the temperature has penetrated to the whole interior surface of the glass, when it is rapidly diffused through the mass of mercury. ”

“ Figure 13.—This drawing accompanied John Goldingham’s report on the work done in India with Kater’s invariable pendulum. The value of gravity obtained, directly or indirectly, in terms of the simple pendulum, is called “absolute.” Once absolute values of gravity were established at a number of stations, it became possible to use the much simpler “relative” method for the measurement of gravity at new stations. Because it has only one knife edge, and does not involve the adjustments of the convertible pendulum, this one is called “invariable.” ”

“ At Greenwich, Oxford and several other observatories, instead of measuring the distances of the star’s image from the opposite sides of the 5 mm. réseau-square by means of a spider-line micrometer, a glass scale, on the plan shown in fig. 16, is employed in the common focus of the objective and the eyepiece. The image of the star is set upon the intersections of the lines of the central cross, and the positions of the réseau-lines are read off by estimation to 1/10° of a division on the glass scale. ”

“ Figure 14.—Vacuum chamber for use with the Kater pendulum. Of a number of extraneous effects which tend to disturb the accuracy of pendulum observations the most important is air resistance. Experiments reported by the Greenwich (England) observatory in 1829 led to the development of a vacuum chamber within which the pendulum was swung.
While the British were engaged in swinging the Kater invariable pendulums to determine relative values of the length of the seconds pendulum, or of gravity, the French also sent out expeditions. ”

“ A metallic barometer is a new kind, in which the air presses on a curiously contrived ring or band of brass, and according as it presses more or less, it moves an index like the hand of a watch, which is placed on the face of it. It was such an instrument as this that the two students had, on Vesuvius.
The way in which you use such an instrument to measure the height of a mountain is this: You look at the instrument when you are at the bottom of the mountain, before you begin your ascent, and see how it stands. There is a little index like the hour hand of a watch, which is movable. ”

“ A pendulum, therefore, is a means of learning the force of gravity at a given place, and without sacrifice of accuracy it is well that it should be as small as possible. In 1890, Professor T. C. Mendenhall, then superintendent of the United States Coast and Geodetic Survey, designed a pendulum one fourth the length of those previously used, and of admirable precision. Afterward pendulums were built of dimensions further reduced to about two and one half inches in length, with periods of oscillation of one fourth of a second. ”

“ At the present day we designate more peculiarly by the name of metrology that part of the science of measurements which devotes itself specially to the determining of the prototypes representing the fundamental units of dimension and mass, and of the standards of the first order which are derived from them. If all measurable quantities, as was long thought possible, could be reduced to the magnitudes of mechanics, metrology would thus be occupied with the essential elements entering into all phenomena, and might legitimately claim the highest rank in science. ”

“ When the standard quantity is greater than that to be measured, we often adopt the first mode, and subdivide the unit until we get a magnitude equal to that measured. The angles observed in surveying, in astronomy, or in goniometry are usually smaller than a whole revolution, and the measuring circle is divided by the use of the screw and microscope, until we obtain an angle undistinguishable from that observed. The dimensions of minute objects are determined by subdividing the inch or centimetre, the screw micrometer being the most accurate means of subdivision. ”

“ Greenwich Observatory has been here selected for tracing the progress of accurate measurement. But there is one instrument of great value, the heliometer, which is not used at Greenwich. This serves the purpose of a double image micrometer, and is made by dividing the object-glass of a telescope along a diameter. Each half is mounted so as to slide a distance of several inches each way on an arc whose centre is the focus. The amount of the movement can be accurately read. ”

“ The barometer, or measurer of the weight of the air, consists of a glass tube about thirty-three inches in length, hermetically sealed at one end, and containing mercury that has been carefully boiled within it, and being perfectly filled the tube is inserted in a cistern of clean mercury, when it gravitates to a height equal to the pressure of the air, leaving a space at the top called the torricellian vacuum. ”

“ The dividing of the tube so that an equal volume of mercury may occupy the same number of degrees at the various parts of the tube is called the calibration of a thermometer, and on the perfection of this work, if it is attempted at all, largely depends the value of the thermometer. As Pernet has remarked, the labor of determining the errors of a thermometer is much increased by having to determine the errors the maker has introduced in the imperfect calibration of its scale. ”

“ Suppose there is a known source of carbonic acid: the determining the amount of it in a room can also be used for measuring another element, which would otherwise defy calculation—I mean the amount of ventilation of a closed space of definite construction. Imagine to yourselves a room with its walls, windows, and doors, its numberless penetrable places through which the air holds ingress and egress. It is impossible to measure the velocity of the air at each crack, to measure each little hole, the diameter of each pore, even if one had the means of measuring such minute velocities and sections ”

“ It is, however, difficult to measure correctly the distance a body will fall in one second. We have, therefore, been obliged to resort to other means for determining the force of attraction of the earth at the equator and other accessible parts of its surface. The methods adopted are founded on the pendulum, which is, perhaps, the simplest and certainly one of the most useful of philosophical instruments. The ideal pendulum is a small and heavy weight suspended from a fixed point by a fine and flexible wire. ”

“ The water-meter which is the subject of the patent consists of two parallel horizontal cylinders, each traversed by two pistons, connected together by a connecting-rod of such length that when one piston is at one end of the cylinder the other is at a sufficient distance from the other end, to leave the requisite space to be filled with the quantity of water to be measured at each stroke. ”

“ In rough work, such as carpentry, it does not, indeed, matter if measurements are the hundredth of an inch or so out. But when we have to deal with scientific instruments, telescopes, measuring machines, engines for dividing distances on a scale, or even with metal turning, the utmost accuracy becomes needful; and a number of instruments will be much more alike in all dimensions if compared individually with a common standard than if they were only compared with one another. Supposing, for instance, a bar of exact diameter is copied ”

“ Every increase in the number of lenses is attended with one drawback, from the circumstance that a certain portion of light is lost by reflection and absorption each time that the ray enters a new medium. This loss bears no sensible proportion to the gain arising from the increased aperture, which, being as the square of the diameter, multiplies rapidly; or, if we estimate by the angle of the admitted pencil, which is more easily ascertained, the intensity will be as the square of twice the tangent of half the angle. ”

“ In this way the scale can be viewed by a microscope of much higher magnifying power than can be employed for the photographed spectrum. Indeed, if the scale were subdivided to 1/10 mm. the power employed might only be limited by the sharpness of the division-lines. But for refined work this would imply the investigation of too many divisions of the scale; it is therefore more usual to divide the scale into single millimetres or half-millimetres and to provide a micrometer which subdivides the millimetre into 1000 or, by estimation, into 10,000 parts. ”

“ If we project the point-rows to any point in the plane, we obtain two projective pencils having the same center. At most two pairs of self-corresponding rays may present themselves. Such a ray is clearly a line joining two corresponding points in the two point-rows. The result may be stated as follows: The system of rays joining corresponding points in two protective point-rows has at most two rays in common with any pencil in the plane. For that reason the system of rays is called a pencil of rays of the second order. ”

“ Since the rate of a pendulum has a known relation to the intensity of the earth’s attraction, we are enabled, by this instrument, not only to detect certain variations in that attraction in various parts of the earth, but also to discover the actual amount of the attraction at any given place. ”

“ The dip angle is always referred to a horizontal plane, and hence vertical beds have a dip of 90°. The device for measuring this angle of dip, the clinometer, is merely a simple pendulum which serves as an indicator and is centered at the corner of a graduated quadrant. A home-made variety is easily constructed from a square piece of board and an attached paper quadrant (Fig. 28 c) , but the geologist’s compass is always provided with a clinometer attachment to the dial. ”

“ But is nothing else than the weight of the mass , and we thus find that the kinetic energy of the meteorite is the product of its weight multiplied by the radius of the earth. Adopting the engineer's unit of energy as the metre-kilogram, and the mass unit as that mass which weighs 9.81 kg., we must take the radius of the earth in metres, and shall get the velocity in metres per second. ”

“ Consequently, when the vernier is set to the mercurial column, the difference shown by the vernier from the tenth on the scale is the hundredths to be added to the inches and tenths of the scale.
A little practice will accustom a person to set and read any barometer quickly; an important matter where accuracy is required, as the heat of the body, or the hand, is very rapidly communicated to the instrument, and may vitiate, to some extent, the observation. ”

“ Some makers, designing to improve upon the simple construction just described, have engraved the outer circle of feet on a movable ring encircling the dial, so that when an observer is at any locality whose height is known, he may bring the proper mark of the altitude scale against the index pointer. Then if the observer travels about over a section of country, the pointer will indicate with fair approximation for some hours the altitude of the new positions. ”