The present work is constructed on the same plan as the author's treatise onPlane Trigonometry, to which it is intended as a sequel; it contains allthe propositions usually included under the head of SphericalTrigonometry, together with a large collection of examples for exercise. In the account of Napier's Rules of Circular Parts an explanation has been given of a method of proof devised by Napier, which seems to have been overlooked by most modern writers on the subject. Considerable labour has been bestowed on the text in order to render it comprehensive and accurate, and the examples have all been carefully verified; and thus the author ventures to hope that the work will be found useful by Students and Teachers.