TY - JOUR
AU - Butcher, J. G.
AB - 174 Mr. J . G. Butcher on the Quaternion Forms of [Dec. 14, in which Z vanishes. (" Messenger of Mathematics," Vol. v., p . 156.) I n this case (y) reduces to d?z dz _ dxdxj dx the solution of which is known to be z = 2 - .(" Messenger of Mathematics," Vol. vi., p. 41). On the Quaternion Forms of some General Propositmis in Fluid Motion. By Mr. J . G. BUTCIIER, B.A., Fellow of Trinity College, Cambridge. . [Mead December Uth, 1876.] 1. I propose here to prove some general propositions on the pure kinematics of a continuous medium by Quaternion methods. Let V denote, as usual, Hamilton's operator i -=- + j -7- + h -?-• dx dy dz Then, if a be any vector whatever, « a small vector displacement of a point (a;, 1/, 2), it is easily proved, as in Tait's " Quaternions," p. 216, (SJTV) a = -D <r, where D, denotes total differentiation in virtue of having passed from one end to the other of the vector it. Thus SirV is a scalar operation. If we perform it on a scalar func- tion P , we can write (Sn-V) 
TI - On the Quaternion Forms of some General Propositions in Fluid Motion
JF - Proceedings of the London Mathematical Society
DO - 10.1112/plms/s1-8.1.174
DA - 1876-11-01
UR - https://www.deepdyve.com/lp/wiley/on-the-quaternion-forms-of-some-general-propositions-in-fluid-motion-oM2Clv01oT
SP - 174
EP - 184
VL - s1-8
IS - 1
DP - DeepDyve
ER -