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The 400 MeV LINAC1 of the proposed eRHIC collider1 is the first acceleration stage of the 18 GeV electron accelerator. The second acceleration stage of the electron accelerator is the Rapid Cycling Synchrotron (RCS), which can increase the energy of the electron bunches to 18 GeV and subsequently extract transfer and inject the 18 GeV electron bunches into the 18 GeV electron Storage Ring (SR) to collide with the hadron bunches of the existing (Relativistic Heavy Ion Collider (RHIC)) accelerator. This paper describes the beam optics of the transfer line between the 400 MeV LINAC and the RCS accelerator (LtRCS). The function of the LtRCS line is twofold, first to transfer the electron beam from the exit of the 400 MeV LINAC to the injection point of the RCS1 and second to rotate the stable spin direction of the polarized electrons from the longitudinal direction to the vertical. A detailed description of the constraints to be satisfied by the LtRCS transfer line will be given. A section will also be devoted to discuss the spin rotator2. [ABSTRACT FROM AUTHOR]