Among the most useful results of quaternion or vectorial algebra we may count the identities and transformations worked out by Hamilton and Tait and their all too few followers. It is not merely that a vector identity is equivalent to three scalar identities—a fact which aids us greatly to condense our calculations in respect to bulk. Yet more important is the greater fruitfulness of a vectorial relation in giving rise to derived relations which we would be less likely to perceive from a purely scalar analysis.