■ THE SUN.

3

conditioned triangle. This involves that the distance of theplaces of observation from one another must not he, as theyare in Fig. II., very small compared with their distances fromthe object. In such a case the formulae fail to give anyaccurate or useful result.

Now, if we attempt to apply the above method to thedetermination of the Sun’s distance, it is easy to see that we

Fig . I.—A well-conditioned triangle.

shall not only have an ill-conditioned, but an exceedingly ill-conditioned triangle to deal with.

The utmost distance, ab, measured in a straight line,between any two stations that we can select upon the Earth ,is equal to the length of its diameter, which is rather under8,000 miles. And this is less than the TiWi part of the

Fig. II.—An ill-conditioned triangle.

distance, as or bs, from any such station to the Sun, orvery nearly in the ratio of one inch to a thousand feet.

It may, however, be remarked that if the above-describedsurveying method could be used, the trigonometrical formula}involved would equally well determine, either the long sides ofsuch a triangle, corresponding to the Sun’s distance, or thevery small angle between them. This angle (asb in Fig. II.)is evidently that which is subtended at the Sun by the straightline joining the two points of observation ; or, in the mostfavourable case possible, by the length of the Earth ’s diameter.