I was led to the present subject by observing that every one, almost without exception, is interested in astronomy, yet from lack of learning spherical trigonometry very few of those who have passed through an ordinary school and college course of mathematics can understand a book of physical astronomy, or at least any other than a very elementary and popular exposition of this royal science. The ordinary well-educated man cannot only not predict an eclipse, but he has no idea of the method followed in the prediction. His astronomy is all taken on faith or on authority; he knows only results, nothing of processes. The work of Kepler is as much a mystery to him as a theological dogma. If he possess a telescope, he can use it little better than a toy; he has no power of adding anything to the sum of astronomical knowledge. Now this seems a pity: I think it is not necessary, for my experience tells me that spherical trigonometry is not much harder than plane trigonometry.