the first end 38 of the bulkhead member 32 c an annular female cone member 70 defining a conical bore 72 surrounding a portion of the optical fiber 20a and of the longitudinal strength member 22 the conical bore 72 of the female cone member 70 having an inner surface 73 which tapers from a larger diameter d 2 at a first end 74 of the conical bore 72 to a smaller diameter d 2 at a second end 76 of the conical bore 72 the first end 74 of the conical bore 72 of the female cone member 70 lying when the connector assemblage 10 is assembled nearer to the bulkhead member 32 and the second end 76 of the female cone member 70 being more remote from the bulkhead member 32 the larger diameter d 2 of the conical bore 72 of the female cone member 70 being about equal to the larger diameter d 1 of the male cone member 50 and the smaller diameter d 2 of the conical bore 72 of the female cone member 70 being about equal to the smaller diameter d 1 of the male cone member 50 and the lengths of the male 50 and female 70 cone members being selected so that when juxtaposed the male and female cones at least approximately mate the male 50 and female 70 cone members when so juxtaposed having a terminal portion 22t of the strength member 22 extending therebetween the terminal.