The next elements of accuracy must be perfect time and perfect notation of time. As has been said, we get our time from the stars. Thus the infinite and heavenly dominates the finite and earthly. Clocks are set to the invariable sidereal time. Sidereal noon is when we have turned ourselves under the point where the sun crosses the equator in March, called the vernal equinox. Sidereal clocks are figured to indicate twenty-four hours in a day: they tick exact seconds. To map stars we wish to know the exact second when they cross the meridian, or the north and south line in the celestial dome above us. The telescope (Fig. 21, p. 61) swings exactly north and south. In its focus a set of fine threads of spider-lines is placed (Fig. 23). The telescope is set just high enough, so that by the rolling over of the earth the star will come into the field just above the horizontal thread.
Fig. 23.—Transit of a Star noted. The observer notes the exact second and tenth of a second when the star reaches each vertical thread in the instrument, adds together the times and divides by five to get the average, and the exact time is reached.
But man is not reliable enough to observe and record with sufficient accuracy. Some, in their excitement, anticipate its positive passage, and some cannot get their slow mental machinery in motion till after it has made the transit. Moreover, men fall into a habit of estimating some numbers of tenths of a second oftener than others. It will be found that a given observer will say three tenths or seven tenths oftener than four or eight. He is falling into ruts, and not trustworthy. General O. M. Mitchel, who had been director of the Cincinnati Observatory, once told one of his staff-officers that he was late at an appointment. "Only a few minutes," said the officer, apologetically. "Sir," said the general, "where I have been accustomed to work, hundredths of a second are too important to be neglected." And it is to the rare genius of this astronomer, and to others, that we owe the mechanical accuracy that we now attain. The clock is made to mark its seconds on paper wrapped around a revolving cylinder. Under the observer's fingers is an electric key. This he can touch at the instant of the transit of the star over each wire, and thus put his observation on the same line between the seconds dotted by the clock. Of course these distances can be measured to minute fractional parts of a second.
But it has been found that it takes an appreciable time for every observer to get a thing into his head and out of his finger-ends, and it takes some observers longer than others. A dozen men, seeing an electric spark, are liable to bring down their recording marks in a dozen different places on the revolving paper. Hence the time that it takes for each man to get a thing into his head and out of his fingers is ascertained. This time is called his personal equation, and is subtracted from all of his observations in order to get at the true time; so willing are men to be exact about material matters. Can it be thought that moral and spiritual matters have no precision? Thus distances east or west from any given star or meridian are secured; those north and south from the equator or the zenith are as easily fixed, and thus we make such accurate maps of the heavens that any movements in the far-off stars—so far that it may take centuries to render the swiftest movements appreciable—may at length be recognized and accounted for.
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Fig. 24. |
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Fig. 25.—Measuring Distances. |
We now come to a little study of the modes of measuring distances. Create a perfect square (Fig. 24); draw a diagonal line. The square angles are 90°, the divided angles give two of 45° each. Now the base A B is equal to the perpendicular A C. Now any point—C, where a perpendicular, A C, and a diagonal, B C, meet—will be as far from A as B is. It makes no difference if a river flows between A and C, and we cannot go over it; we can measure its distance as easily as if we could. Set a table four feet by eight out-doors (Fig. 25); so arrange it that, looking along one end, the line of sight just strikes a tree the other side of the river. Go to the other end, and, looking toward the tree, you find the line of sight to the tree falls an inch from the end of the table on the farther side. The lines, therefore, approach each other one inch in every four feet, and will come together at a tree three hundred and eighty-four feet away.
The next process is to measure the height or magnitude of objects at an ascertained distance. Put two pins in a stick half an inch apart (Fig. 26). Hold it up two feet from the eye, and let the upper pin fall in line with your eye and the top of a distant church steeple, and the lower pin in line with the bottom of the church and your eye. If the church is three-fourths of a mile away, it must be eighty-two feet high; if a mile away, it must be one hundred and ten feet high. For if two lines spread one-half an inch going two feet, in going four feet they will spread an inch, and in going a mile, or five thousand two hundred and eighty feet, they will spread out one-fourth as many inches, viz., thirteen hundred and twenty—that is, one hundred and ten feet. Of course these are not exact methods of measurement, and would not be correct to a hair at one hundred and twenty-five feet, but they perfectly illustrate the true methods of measurement.
