Abstract: The incremental system for measuring lengths comprises a scale member that is provided with a measuring scale and is accommodated in a tubular projective housing, on which the scale member is held at one side edge of the scale member. A scanning unit is guided on the scale member to be movable parallel to the longitudinal direction of the scale member and comprises a light source for illuminating photoelectric receivers with light which is transmitted by a condenser, scanning gratings, the measuring scale and the scale member. A compact structure is obtained in that the scale member extends with an inclination of 45.degree. in the cavity of the carrying housing. The photoelectric receivers are provided on that side of the scale member which is opposite to a slot formed in the housing. The cone of light emitted by the light source is deflected by a reflector disposed between the light source and the condenser.