Naturally we begin with the sun, and the oldest and most important problem which the study of this body offers is the determination of its distance from the earth in terrestrial units of measure. This distance is important because the knowledge of all the phenomena of all the heavenly bodies, except those of the moon, depend directly or indirectly on its value. The problem of the sun's distance is difficult because the data given for determining it are insufficient to enable the astronomer to apply the principles of trigonometry directly to it. He is, therefore, compelled to use indirect methods of solution, which, at best, give only approximations to the true distance, arising chiefly from small errors in observation, which, at the present time, seem unavoidable. A familiar illustration will make our meaning clear. The knowledge we have of the sun's distance depends on the accurate measurement of a small angle formed by drawing two lines from a point at the sun to the extremities of the earth's radius. That angle is called the sun's parallax. Ptolemy thought that this angle was 3' of arc, but we now know that its value is very near 8.80" of arc, and that the error of this amount from the true angle probably is not more than 0.02". To measure this small angle has been the astronomer's great trouble since the time of Aristarchus, and he does not yet know its value accurately. His problem is like that of a surveyor attempting to measure a ball, whose real diameter is one foot, at the distance of 4.4 miles nearly; and unless he can determine the diameter of the ball so that he shall not be uncertain in his measure to the amount of 0.03 of an inch, his work will not add anything useful to present knowledge. If we suppose the angle of parallax to be known, the computation of the distance of a celestial body is easy. Multiply earth's radius by 206,265 (seconds of arc in the unit radius), and divide the product by the angle of parallax in seconds of arc. The mean equatorial radius of the earth, as given in Clark's Geodesy, is 3963.3 English miles. The sun's distance for a parallax of 8.78" would be 206,265" × 3963.3 ----------------- = 93,108,000 miles. 8.78" For parallax of 8.80" = 92,897,000 miles. For parallax of 8.82" = 92,686,000 miles. The range of error in parallax, as here given, is 0.04", and the change of the distance of the sun in allowing for this error is nearly half a million of miles. If 8.80" be the assumed parallax, with ± 0.02" as probable error, then the uncertainty of the sun's distance is still nearly a quarter of a million of miles.