The principle involved is very crudely illustrated in the following experiment: Let the reader consider himself aboard ship lying at anchor—say a full-rigged ship, so as to insure a foremast of good height. Lower the dinghy and take along a sextant.
We start with a series of measurements to determine the angle, as read from the sextant in the dinghy, between the truck and the waterline about the vessel. As a result of these measurements, we discover that this angle becomes smaller as the distance from the vessel increases.
Carrying our tests farther, suppose when the sextant shows the altitude of the fore truck above the waterline to be 70°, that the distance to the vessel be determined. With this distance as a radius and the foremast as the center, we row in a circle around the vessel, the sextant will continue to read 70° all around the circle.
It is thus demonstrated that a circle surrounds that foremast upon which the altitude of its truck is everywhere 70°—a circle of equal altitudes.
Not being quite sure of this interesting fact, perhaps, another angle is selected by moving a little farther from the ship. The sextant shows the fore truck to have an altitude of 50°; the distance to the vessel is established, whereupon the dinghy is rowed around the vessel with this distance as a radius. Again the sextant reveals no change from 50° and it is clearly shown that we have moved about on a circle of 50° elevation of the truck.
We can continue experimenting in this way until the distance from the ship becomes so great that some physical condition prevents our reading the angle of the truck’s altitude.
These investigations show that there is a system of concentric circles of equal altitude about every elevated object like the little undulations we have seen so many times produced by the splash of a stone thrown into a pool.
These circles of equal altitudes surround not only elevated terrestrial objects but also celestial bodies, as will now be shown. As the sun is the most convenient body for this illustration, let us substitute it for the fore truck of the foregoing experiments, while for the waterline of the vessel we will use the point on the earth touched by a plumb-bob suspended from the center of the sun.
This point will fall on the equator on the 21st of March or thereabouts, as the sun coming up from his southern declination crosses the equator into north declination at this time. The instant of the transit is the vernal equinox. Now this point will be found an excellent one from which to study this problem, but, as this takes some time and the sun is ever on the move, we will imagine ourselves endowed with the power of Joshua to command the sun and moon, which will enable us to study this phenomenon while free from the restlessness of the Universe.
First of all, it must be understood that the sun shines on one hemisphere of the earth at all times; it matters not how the earth is tipped in relation to him, one half of the world is always enjoying sunshine. The center of the lighted area is the spot directly beneath the sun where the plumb-bob touches and about this point lies the system of concentric circles of equal altitudes of the sun.