Suppose a telescope, fixed to a mural circle, to revolve on an axis, as in Fig. 21; point it horizontally at a star; turn it up perpendicular to another star. Of course the two stars are 90° apart, and the graduated scale, which is attached to the outer edge of the circle, shows a revolution of a quarter circle, or 90°, But a perfect accuracy of measurement must be sought; for to mistake the breadth of a hair, seen at the distance of one hundred and twenty-five feet, would cause an error of 3,000,000 miles at the distance of the sun, and immensely more at the distance of the stars. The correction of an inaccuracy of no greater magnitude than that has reduced our estimate of the distance of our sun 3,000,000 miles.
Fig. 21.—Mural Circle.
Consider the nicety of the work. Suppose the graduated scale to be thirty feet in circumference. Divided into 360°, each would be one inch long. Divide each degree into 60', each one is 1/60 of an inch long. It takes good eyesight to discern it. But each minute must be divided into 60", and these must not only be noted, but even tenths and hundredths of seconds must be discerned. Of course they are not seen by the naked eye; some mechanical contrivance must be called in to assist. A watch loses two minutes a week, and hence is unreliable. It is taken to a watch-maker that every single second may be quickened 1/20160 part of itself. Now 1/20000 part of a second would be a small interval of time to measure, but it must be under control. If the temperature of a summer morning rises ten or twenty degrees we scarcely notice it; but the magnetic tastimeter measures 1/5000 of a degree.
Come to earthly matters. In 1874, after nearly twenty-eight years' work, the State of Massachusetts opened a tunnel nearly five miles long through the Hoosac Mountains. In the early part of the work the engineers sunk a shaft near the middle 1028 feet deep. Then the question to be settled was where to go so as to meet the approaching excavations from the east and west. A compass could not be relied on under a mountain. The line must be mechanically fixed. A little divergence at the starting-point would become so great, miles away, that the excavations might pass each other without meeting; the grade must also rise toward the central shaft, and fall in working away from it; but the lines were fixed with such infinitesimal accuracy that, when the one going west from the eastern portal and the one going east from the shaft met in the heart of the mountain, the western line was only one-eighth of an inch too high, and three-sixteenths of an inch too far north. To reach this perfect result they had to triangulate from the eastern portal to distant mountain peaks, and thence down the valley to the central shaft, and thus fix the direction of the proposed line across the mouth of the shaft. Plumb-lines were then dropped one thousand and twenty-eight feet, and thus the line at the bottom was fixed.
Three attempts were made—in 1867, 1870, and 1872—to fix the exact time-distance between Greenwich and Washington. These three separate efforts do not differ one-tenth of a second. Such demonstrable results on earth greatly increase our confidence in similar measurements in the skies.
A scale is frequently affixed to a pocket-rule, by which we can easily measure one-hundredth of an inch (Fig. 22). The upper and
Fig. 22. lower line is divided into tenths of an inch. Observe the slanting line at the right hand. It leans from the perpendicular one-tenth of an inch, as shown by noticing where it reaches the top line. When it reaches the second horizontal line it has left the perpendicular one-tenth of that tenth—that is, one-hundredth. The intersection marks 99/100 of an inch from one end, and one-hundredth from the other.
When division-lines, on measures of great nicety, get too fine to be read by the eye, we use the microscope. By its means we are able to count 112,000 lines ruled on a glass plate within an inch. The smallest object that can be seen by a keen eye makes an angle of 40", but by putting six microscopes on the scale of the telescope on the mural circle, we are able to reach an exactness of 0".1, or 1/3600 of an inch. This instrument is used to measure the declination of stars, or angular distance north or south of the equator. Thus a star's place in two directions is exactly fixed. When the telescope is mounted on two pillars instead of the face of a wall, it is called a transit instrument. This is used to determine the time of transit of a star over the meridian, and if the transit instrument is provided with a graduated circle it can also be used for the same purposes as the mural circle. Man's capacity to measure exactly is indicated in his ascertainment of the length of waves of light. It is easy to measure the three hundred feet distance between the crests of storm-waves in the wide Atlantic; easy to measure the different wave-lengths of the different tones of musical sounds. So men measure the lengths of the undulations of light. The shortest is of the violet light, 154.84 ten-millionths of an inch. By the horizontal pendulum Professor Root has made 1/36000000 of an inch apparent.