The transformations of volume integrals into surface integrals, and of surface integrals into line integrals, are usually established first for a small parallelepiped and parallelogram. These elements are not, however, very convenient, or indeed altogether satisfactory, for the extension of the theorems over finite domains. If arranged in straight rows and plates, the elements cannot be fitted to a general boundary; and if they are arranged in curved rows and shells like the stones of a vault, there will be, in general, between various elements of the first order, spaces of the second not represented. This inconvenience disappears if tetrahedra and triangles are taken as elements. In Quaternions, the theorems are easily proved for such elements.