CHRISTOPHER T. RUSSELL Institute of Geophysics and Planetary Physics, Univ. of Calif., Los Angeles, Calif. 90024,U.S.A. Originally published in Cosmic Electrodynamics, 2, 184196, 1971. All rights reserved. Copyright 1971 by D. Reidel, Publishing Company DordrechtHolland. (Received 12 January, 1971; in revised form 26 March, 1971) Y Abstract. The use of a vectormatrix formalism to describe the transformation from onecartesian coordinate system to another results in simpletouse and easytounderstandrelationships. Furthermore, the required matrix transformations may be derived directly.The common coordinate systems in use in solarterrestrial relationships are described andthen the transformation matrices required to convert vectors in one system to another arederived. XLIntroduction ` hp x (#%'0*,.8135@8: