HOW CELESTIAL DISTANCES ARE DETERMINED, AND HOW THE SUN IS WEIGHED I will not do my readers the injustice to suppose that they will be alarmed at the title of this Lesson, and that they do not employ some "method" in their own lives. I even assume that if they have been good enough to take me on faith when I have spoken of the distances of the Sun and Moon, and Stars, or of the weight of bodies at the surface of Mars, they retain some curiosity as to how the astronomers solve these problems. Hence it will be as interesting as it is useful to complete the preceding statements by a brief summary of the methods employed for acquiring these bold conclusions. The Sun seems to touch the Earth when it disappears in the purple mists of twilight: an immense abyss separates us from it. The stars go hand in hand down the constellated sky; and yet one can not think of their inconceivable distance without a shiver. Our neighbor, Moon, floats in space, a stone's throw from us: but without calculation we should never know the distance, which remains an impassable desert to us. The best educated persons sometimes find it difficult to admit that these distances of Sun and Moon are better determined and more precise than those of certain points on our minute planet. Hence, it is of particular moment for us to give an exact account of the means employed in determining them. The calculation of these distances is made by "_triangulation_." This process is the same that surveyors use in the measurement of terrestrial distances. There is nothing very alarming about it. If the word repels us a little at first, it is from its appearance only. When the distance of an object is unknown, the only means of expressing its apparent size is by measurement of the angle which it subtends before our eyes. We all know that an object appears smaller, in proposition with its distance from us. This diminution is not a matter of chance. It is geometric, and proportional to the distance. Every object removed to a distance of 57 times its diameter measures an angle of 1 degree, whatever its real dimensions. Thus a sphere 1 meter in diameter measures exactly 1 degree, if we see it at a distance of 57 meters. A statue measuring 1.80 meters (about 5 ft. 8 in.) will be equal to an angle of 1 degree, if distant 57 times its height, that is to say, at 102.60 meters. A sheet of paper, size 1 decimeter, seen at 5.70 meters, represents the same magnitude. In length, a degree is the 57th part of the radius of a circle, _i.e._, from the circumference to the center. The measurement of an angle is expressed in parts of the circumference. Now, what is an angle of a degree? It is the 360th part of any circumference. On a table 3.60 meters round, an angle of one degree is a centimeter, seen from the center of the table. Trace on a sheet of paper a circle 0.360 meters round--an angle of 1 degree is a millimeter. [Illustration: FIG. 80.--Measurement of Angles.]