PROF. GIBBS seems to forget that his pamphlet was specially announced as Arranged for the use of Students in Physics. When I wrote the remark which has called forth his recent letter, I was discussing the reasons for the comparatively slow progress of Quaternion Analysis in recent times. And, as it is precisely to students of Physics that I think we must look for such progress, anything which is calculated to divert their attention from Quaternions, or to confuse them in their use of Quaternion symbols, must be regarded as tending to retard the progress of the method. The Vector-Analysis supported by Prof. Gibbs involves a serious departure from the usage of ordinary Algebra, inasmuch as αβ is not regarded as a product, but merely as a “kind of product.” This is specially likely to confuse an ordinary student, and is undoubtedly artificial in the highest degree:— while one of the chief recommendations of Quaternions is their naturalness, i.e. the utter absence of artifice in their fundamental rules.