Pedometer

“ On that occasion I had fastened a Catel’s pedometer by a hook to the waistband of my trousers and the silken cord which runs down the thigh to a curved hook of steel at my knee, so that the three indexes on one dial (of which the first marks a hundred steps, the second a thousand, and the third up to twenty thousand) were all moving just as I moved myself. At this moment I met a young lady, whom it was incumbent on me that I should see home. I begged her to excuse me, as I had a Catel’s pedometer on, and had already made a certain number of steps towards my measurement of the diameter of Hof. ”

“ Of course, when engineers go out in a party they measure every mile by a chain, and know just how far they have come. The old trappers used to allow three or four miles an hour for their pack-horses in a country like this. Sometimes an engineer carries what is called a pedometer in his pocket, which tells him how far he has walked. ”

“ The same pedometer will, by a proper application to the saddle, ascertain every pace a horse takes, and it may be made to change its performance in a second, should the horse in the course of measuring go from one pace to another. ”

“ In this ingenious contrivance motion is communicated from the traveller to the machinery of the pedometer, by means of a horizontal lever, which is furnished with a weight at one end and a pivot or axis at the other; under the lever is a spring, which keeps the lever when at rest close up to a regulating screw; the spring is so arranged as to be only just sufficiently strong to overcome the weight of the lever and to prevent its falling downwards. ”

“ The compass will give the course very nearly if he walks or rides; no instrument can be perfectly depended on. A pedometer will do for short distances, but when he becomes weary it counts his feeble steps just as it did his vigorous strides at the beginning, and thus shows more than the truth. If wheel carriages can be used, take a trochiameter, and contrive if possible to have the wheel on which it is fixed exactly five yards in circumference; it saves no end of trouble if there are no odd half inches to calculate. ”

“ A Pedometer is an instrument cunningly devised to tell you how far and how fast you walk, and is, quoth the Doctor, a "perambulator in miniature." The box containing the wheels is made of the size of a watch-case, and goes into the breeches pocket, and by means of a string and hook, fastened at the waistband or at the knee, the number of steps a man takes, in his regular paces, are registered from the action of the spring upon the internal wheel-work at every step, to the amount of 30,000. ”

“ Well, this term, Animal Pedometers, is used here not for proving anything, but for the purpose of impressing on the mind of the reader the fact of certain patterns on the horse’s skin being intimately related to its locomotive life which, I hope I may assume, has been sufficiently demonstrated in this chapter. A pedometer is one of those works of men devised for his physical and mental advancement which are marked by a precision as well as purpose often absent from Nature’s handiwork. ”

“ A compass is of great value to keep one's course between observations on the sun; and an aneroid barometer and a thermometer make possible a more accurate correction for refraction. A pedometer, also, or some other form of distance meter, would be useful to estimate the distance traveled.
Although the methods of determining one's geographical position would be the same near either pole, there are slight differences in their applications; for instance, the solid land of the Antarctic continent precludes drift, and therefore this disturbance is absent. ”

“ The registration is effected by the fall of a heavy pendulum, caused by the percussion of each step. The pendulum is forced back to a horizontal position by a delicate spring, and with each stroke a fine-toothed ratchet-wheel connected with it is moved round a certain length. The ratchet communicates with a train of wheels which work the dial-hands. In using the apparatus a measured mile or other known distance is walked and the indication thereby made on the dial-plate observed. According as it is too great or too small, the stroke of the pendulum is shortened or lengthened by a screw. ”

“ An ordinary cyclometer is nothing but an arrangement for counting these revolutions, but it is graduated in such a manner that it gives at once the distance in miles. On the same principle depend a number of instruments which, under various fancy names, serve to measure the length of any curve; they are in the shape of a small meter chiefly for the use of cyclists. They all have a small wheel which is rolled along the curve to be measured, and this sets a hand in motion which gives the reading on a dial. ”

“ Measurement of Speed of Rotation.
To measure the speed of rotation, a tuning-fork, bearing on one prong a steel mirror, was used. This was kept in vibration by a current of electricity from five "gravity" cells. The fork was so placed that the light from the revolving mirror was reflected to a piece of plane glass, in front of the lens of the eye-piece of the micrometer, inclined at an angle of 45°, and thence to the eye. When fork and revolving mirror are both at rest, an image of the revolving mirror is seen. When the fork vibrates, this image is drawn out into a band of light. ”

“ 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. ”

“ In the present chapter it is our intention to describe such instruments as are usually employed for determining the weight of bodies. To attempt a description of the various machines which are used for the measurement of time, would lead us into too wide a field for the present occasion, and we shall, therefore, confine ourselves to an account of the methods which have been practised to perfect, to perfect that instrument which affords the most correct means of measuring time, the pendulum. ”

“ Hooded dials, brightly lighted push-buttons, a telephone headpiece and receiver combined, and switches all lay in easy reach. Here was the tachometer, that would give to a fraction the revolutions of each screw per minute; here the altimeter, to indicate height; here the air-speed indicator, the compass with reflector, the inclinometer, the motometers—to show the heat in each engine—and there, the switch to throw on the gigantic searchlight, with the little electric wheel to control its direction, as accurately as you would point a wand. ”

“ Fig. 81—A simple pendulum.
101. Definition of Terms. The center of suspension is the point about which the pendulum swings. A single vibration is one swing across the arc. A complete or double vibration is the swing across the arc and back again. The time required for a double vibration is called the period. The length of a simple pendulum is approximately the distance from the point of support to the center of the bob.
A seconds pendulum is one making a single vibration per second. Its length at sea-level, at New York is 99.31 cm. or 39.1 in., at the equator 39.01 in., at the poles 39.22 in. ”

“ For outside gearing that ratio is negative, because the wheels turn contrary ways; for inside gearing it is positive, because they turn the same way.
If the velocity ratio is to be constant, as in Willis’s Class A, the wheels must be circular; and this is the most common form for wheels.
If the velocity ratio is to be variable, as in Willis’s Class B, the figures of the wheels are a pair of rolling curves, subject to the condition that the distance between their poles (which are the centres of rotation) shall be constant. ”

“ Moreover, since the instrument is so constructed that of two vanes, on opposite sides of the wheel, one always presents a blackened and the other a lustrous surface to an incident beam, we should further expect to find in the motion of the wheel a differential phenomenon, due to the unequal action of the light on these surfaces. On the other hand, if the radiometer is a heat-engine, and the reaction takes place between the heated blackened surfaces of the vanes and the colder glass, it is evident that the total effect will be simply the sum of the effects at the several surfaces. ”

“ The usual way of experimenting is to put a dynamo meter car (see Dynamometer) between the engine and the train. This car is equipped with apparatus by means of which a continuous record of the draw-bar pull is obtained on a distance base; time indications are also made on the diagram from which the speed at any instant can be deduced. The pull recorded on the diagram includes the resistances due to acceleration and to the gradient on which the train is moving. ”

“ Pendulum clocks, if they are to run accurately, must have their pendulums automatically adjustable for variations in temperature, because the longer the pendulum the more slowly it oscillates. Many years ago a grid type of pendulum was invented in which various alloys were used, which reacted one against the other and preserved the center of gravity always at the same distance from the center of oscillation. The action of a pendulum movement is similar to that of a balance-wheel movement described above. The pendulum operates a pallet lever similar to that shown in Figure 29. ”

“ The transmission of power by a strap is familiar to every one in a treadle sewing-machine or an ordinary lathe. The driving force depends on the difference in the tightness of the two sides of the belt, and the power transmitted is equal to this difference multiplied by the speed; a power-meter must, therefore, solve this problem—it must subtract the tightness of one side from the tightness of the other side, multiply the difference by the speed at every instant, and add all the products together, continuously representing the growing amount on a dial. ”

“ The air-speed meter, whether of the Pitot type or pressure-plate type, will prove invaluable in flying through clouds or mist when the ground is obscured. Also the inclinometer is able to give the angle of flight when the earth is not visible, although the speed indicator usually is sufficient to give the angle of flight, for an increase of speed means downward motion and decrease of speed means upward motion. ”

“ If we make comparisons with different varieties of man-made records, we find that the swiftest human runner covers his mile at the rate of about twenty-one feet per second; the skater brings this up to about thirty-four feet; and the bicyclist attains the acme of muscle-motor speed with his eighty feet per second. In the case of the bicyclist, the wind-shield pace-maker on the auto-cycle plays an important part. But even so the cyclist would be left behind one hundred and thirteen feet each second by the flying automobile.
All these types of record maker, therefore, are quite outclassed. ”

“ A, let there be hung by a pair of links of lengths equal to the pendulum arms, a load, B, capable of sliding up and down the spindle, and having its center of gravity on the axis of rotation. Then the centrifugal force is that due to A alone, and the effect of gravity that due to A + 2B; consequently the altitude for a given speed is increased in the ratio A + 2B : A, as compared with that of a simple revolving pendulum; and a given absolute variation of altitude in moving the regulating-valve produces a smaller proportionate variation of speed than in the common governor. ”

“ Gear-wheels therefore form a convenient method of either simply transmitting motion or power, as when the wheels are all of equal diameter, or of transmitting it and simultaneously varying its velocity of motion, as when the wheels are compounded either to reduce or increase the speed or velocity in feet per second of the prime mover or first driver of the train or pair, as the case may be. ”

“ But in the ease of two elliptical wheels, if the follower stand still while the driver moves, which must happen when the motion is reversed if backlash exists, the pitch-curves are thrown out of contact, and, although the continuity of the motion will not be interrupted, the velocity ratio will be affected. If the motion is never to be reversed, the perfect law of the velocity ratio due to the elliptical pitch-curve may be preserved by reducing the thickness of the tooth, not equally on each side, as is done in circular wheels, but wholly on the side not in action. ”

“ 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. ”

“ Now rotate the lathe spindle any number of full revolutions that are required to cause the carriage to travel over the portion of the lead-screw that is being tested, bringing the line on the faceplate to the surface gage point. If the distance traveled by the carriage is not greater than one inch, the micrometer will indicate the error directly. For lengths of carriage travel greater than one inch, an end measuring rod, set to the number of even inches required, can be used between the micrometer point and lathe carriage. ”