Since due recognition is now being more and more widely given to the importance of Vector Analysis for three-dimensional work in mechanics, geometry and mathematical physics, the time is opportune to consider the place which that subject merits in a University degree course. A student who undertakes anything like research work in applied subjects is considerably handicapped if he has had no training in Vector Analysis; but the need for it is felt much earlier than the stage at which research is generally begun. Every University course contains subjects which are less useful than Vector Analysis; and on the ground of utility alone there is no question that the latter deserves a place in the curriculum. It will, however, be found quite unnecessary to displace anything else, because the time occupied in teaching the essential parts of vector algebra and calculus will be saved, even during a three years’ course, by the application of this method to the three-dimensional parts of mechanics and mathematical physics.