Vernier scale

“ Scales of Construction. —Scales of construction are intended to afford means of measuring more minute quantities than scales of distances. Of the former there are two kinds, known respectively as the Diagonal and the Vernier scale. The diagonal is the more frequently employed. Its construction involves no peculiar difficulty, as it consists simply of an ordinary scale of distances, with the addition of a number of parallel lines crossed by other parallel lines drawn diagonally from the smaller points of division. An example will best show the construction and mode of using this scale. ”

“ It is not desirable that the vernier should read nearer than one-hundredth of an inch. Two verniers and scales may be fitted one on either side of the mercurial column, so that one can denote the last reading, and thus show at a glance the extent of rise or fall in the interval. The scale and thermometer should be covered with plate glass. A cheap instrument has an open face and plain frame, with sliding vernier instead of rack-and-pinion motion. The barometer may or may not have a moveable bottom to the cistern, with screw for the purpose of securing the mercury for portability. ”

“ 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. ”

“ With the milled head set at the point which gives the appearance of the middle disk as shown, the eye of the observer is raised to the reading tube, K, and the position of the scale is noted. It will be seen that the scale proper is attached to the quartz wedge, which is moved by the milled head, and attached to the other quartz wedge is a small scale called a vernier which is fixed, and which serves for the exact determination of the movable scale with reference to it. ”

“ The steelyard uses counterweights, and so its measurements are independent of gravity. A spring balance depends entirely on gravity to record the weight of an object. It is therefore a spring balance (Verne: “peson”) that the professor needs to determine the reduced gravity on Gallia. ”

“ After the first hole is bored, the work is located for boring the other [Pg 38] to the edge of the auxiliary plate, and horizontal measurements y between the parallel and the plate. These measurements, if quite large, might be taken with micrometer gages, whereas, for comparatively small adjustments, size blocks might be more convenient.
Vernier Height Gage and Plug Method
When a vernier height gage is available, it can often be used to advantage for setting work preparatory to boring in a milling machine. One advantage of this method is that it requires little in the way of special equipment. ”

“ Procope and Timascheff demurely bowed their heads.
The professor resumed. "Upon a spring-balance, dependent upon mere tension or flexibility, the attraction will have no influence. If I suspend a weight upon it equivalent to the weight of a kilogram, the index will register the proper weight on the surface of Gallia. Thus I shall arrive at the difference I want: the difference between the earth's attraction and the comet's. Will you, therefore, have the goodness to provide me at once with a spring-balance and a tested kilogram?" ”

“ Before they started, Professor Rosette requested that one of the men might be ordered to cut him a cubic decimeter out of the solid substance of Gallia. “My engineer is the man for that,” said the count; “he will do it well for you if you will give him the precise measurement.”
“What! you don’t mean,” exclaimed the professor, again going off into a passion, “that you haven’t a proper measure of length?”
Ben Zoof was sent off to ransack the stores for the article in question, but no measure was forthcoming. “Most likely we shall find one on the tartan,” said the orderly. ”

“ It is well known that attraction, or weight, is in proportion to the bulk, and in inverse proportion to the square of distances. Hence this consequence. If the earth had been alone in space, if the other heavenly bodies were to be suddenly annihilated, the projectile, according to Newton's law, would have weighed less according to its distance from the earth, but without ever losing its weight entirely, for the terrestrial attraction would always have made itself felt, no matter at what distance. ”

“ After the scale is thus leveled, if from any cause whatever, such as shifting the scale on a table, or shifting the table itself, the scale support is thrown out of level, the center of gravity of the poise and beam is shifted from the vertical line above the support, and its moment immediately becomes greater than the torsional resistance, and the beam tips out of balance, and cannot be used as a correct scale until the support is again leveled. ”

“ A deaf man would soon learn to hear perfectly."
"But won't this density augment?"
"Yes; according to a rather obscure law. It is well known that the weight of bodies diminishes as fast as we descend. You know that it is at the surface of the globe that weight is most sensibly felt, and that at the centre there is no weight at all."
"I am aware of that; but, tell me, will not air at last acquire the density of water?"
"Of course, under a pressure of seven hundred and ten atmospheres." ”

“ Of this rock here is a solid decimeter; let us get at its weight, and we shall have the key which will unlock the problem of the whole weight of Gallia. We have demonstrated that the force of attraction here is only one-seventh of what it is upon the earth, and shall consequently have to multiply the apparent weight of our cube by seven, in order to ascertain its proper weight. Do you understand me, goggle-eyes?"
This was addressed to Ben Zoof, who was staring hard at him. "No!" said Ben Zoof.
"I thought not; it is of no use waiting for your puzzle-brains to make it out. ”

“ Soon after the first graduating machine was put into use, the vernier caliper, reading to thousandths of an inch, was brought out by Mr. Brown; the first was made as early as 1851. In the following year he applied the vernier to protractors. A writer, in speaking of the invention of the vernier caliper, says, “It was the first practical tool for exact measurements which could be sold in any country at a price within the reach of the ordinary machinist, and its importance in the attainment of accuracy for fine work can hardly be overestimated.” ”

“ The result of these two assumptions is that if we collect a very large number of measurements of the different parts and proportions of some ancient building,—say an Egyptian temple,—whilst no assignable length is likely to be permanently unrepresented, yet we find a marked tendency for the measurements to cluster about certain determinate points in our own, or any other standard scale of measurement. ”

“ We had started at one, it was now, therefore, about eleven o'clock at night.
It does not require great knowledge of arithmetic to know that twenty-eight times two hundred feet makes five thousand six hundred feet in all (more than an English mile) .
While I was making this mental calculation a voice broke the silence. It was the voice of Hans. "Halt!" he cried.
I checked myself very suddenly, just at the moment when I was about to kick my uncle on the head.
"We have reached the end of our journey," said the worthy Professor in a satisfied tone.
"What, the interior of the earth?" ”

“ Hence it would be difficult, by mere observation, to prove that the law of error in any given case was not exponential; unless the statistics were very extensive, or the actual results departed considerably from the exponential form. (2) It is quite impossible by any graphic representation to give an adequate idea of the excessive rapidity with which the curve after a time approaches the axis of . At the point , on our scale, the curve would approach within the fifteen-thousandth part of an inch from the axis of , a distance which only a very good microscope could detect. ”

“ But, independently of this effect, this flattening ought to have a more curious and more personal effect, which we should perceive if we had mathematical sensibility.”
“What do you mean?” asked Bell.
“I mean that we are heavier here than at Liverpool.”
“Heavier?”
“Yes; ourselves, the dogs, our guns, and instruments!”
“Is it possible?”
“Certainly, and for two reasons: the first is, that we are nearer the centre of the globe, which consequently attracts us more strongly, and this force of gravitation is nothing but weight ”

“ The astronomer bit his lip, frowned, snorted, and cast at him a withering look, but did not take any further notice.
“Now, Captain Servadac,” said the professor, “take your pen again, if you please, and find me the volume of Gallia.”
The captain hesitated.
“Quick, quick!” cried the professor, impatiently; “surely you have not forgotten how to find the volume of a sphere!”
“A moment's breathing time, please.”
“Breathing time, indeed! A mathematician should not want breathing time! Come, multiply the surface by the third of the radius. Don't you recollect?” ”

“ Secondly, if an observer at rest in measure the radius and circumference of the rotating disc, he will obtain the same value for the radius as when the disc is at rest, but since, when he measures the circumference of the disc, the scale lies along the direction of motion, it suffers contraction, and, consequently, will divide more often into the circumference than if the scale and the disc were at rest. ”

“ A lath was then cut of this exact length and given to the engineer of the Dobryna, who was directed to cut out of the solid rock the cubic decimetre required by the professor.
The next business was to obtain the precise weight of a kilogramme. This was by no means a difficult matter. Not only the diameters, but also the weights, of the French coins are rigidly determined by law, and as the silver five-franc pieces always weigh exactly twenty-five grammes, the united weight of forty of these coins is known to amount to one kilogramme. [3]
“Oh!” cried Ben Zoof ”

“ It was quite true that the mercury, after rising gradually in the instrument, as long as our descent was taking place, had stopped precisely at twenty-nine inches. "You perceive," said the Professor, "we have as yet only to endure the pressure of air. I am curious to replace the barometer by the manometer." The barometer, in fact, would become useless as soon as the weight of the air was greater than that calculated as about the level of the ocean. ”

“ Now, at this distance, any objects sixty feet square would be perfectly visible.
"If, then, the penetrative power of telescopes has not been further increased, it is because that power detracts from their light; and the moon, which is but a reflecting mirror, does not give back sufficient light to enable us to perceive objects of lesser magnitude."
"Well, then, what do you propose to do?" asked the general. "Would you give your projectile a diameter of sixty feet?" ”

“ Lionel rose, Lucy rose; Lord Garle and Decima came forward, and Sibylla sprang towards him with a cry. Lady Verner was the only one who retained entire calmness.
"Papa! it cannot be you! When did you come?"
Dr. West kissed her, and turned to Lady Verner with some courtly words. Dr. West was an adept at such. Not the courtly words that spring genuinely from a kindly and refined nature; but those that are put on to hide a false one. All people, true-hearted ones, too, cannot distinguish between them; the false and the real. Next, the doctor grasped the hand of Lionel. ”

“ Every perceptive faculty that Lionel Verner possessed was strained upon the spot. He could make out a tall man; a man whose figure bore—unless his eyes and his imagination combined to deceive him—a strong resemblance to Frederick Massingbird's. ”

“ By degrees they dilate, and gain in huge size what they lose in number. Such is their ponderous weight that they cannot rise from the horizon; but, obeying an impulse from higher currents, their dense consistency slowly yields. The gloom upon them deepens; and they soon present to our view a ponderous mass of almost level surface. From time to time a fleecy tuft of mist, with yet some gleaming light left upon it, drops down upon the dense floor of grey, and loses itself in the opaque and impenetrable mass.
The atmosphere is evidently charged and surcharged with electricity. ”

“ That is, it being known from wide experience that the heights of any tolerably homogeneous set of men are apt to group themselves symmetrically,—the condition for the coincidence of the three principal kinds of mean,—the middle man of a row thus arranged in order will represent the mean or average man, and him we may subject to measurement. Moreover, since the intermediate heights are much more thickly represented than the extreme ones, a moderate error in the selection of the central man of a long row will only entail a very small error in the selection of the corresponding height. ”

“ The greatest danger to be guarded against in considering all scales as continuous rather than discrete, is that careless thinkers may refine their calculations far beyond the accuracy which their original measurements would warrant. One should be very careful not to make such unjustifiable refinements in his statement of results as are often made by young pupils when they multiply the diameter of a circle, which has been measured only to the nearest inch, by 3.1416 in order to find the circumference. ”

“ The inclination of our planet’s axis, or in other terms, the angle which its axis of rotation makes with the plane of its ecliptic is 66° 32′. A few degrees would thus bring the axis perpendicular to the plane of the orbit it describes round the Sun.
But—it is important to remark—the effort that the North Polar Practical Association was about to make would not, strictly speaking, right the Earth’s axis. Mechanically, no 71force, however considerable, could accomplish that. The Earth is not like a chicken on a spit, that we can take it in our hand and shift it as we will. ”