A seat of the abovementioned type is known, for example from Swiss Pat.  No.  529 537.  The back of the seat is on the chair rotatably supported about a front swivel bearing, while the back member is connected swingably through a lever to the seat carrier.  The connection between the back member, namely the lever of the back member, and the seat member occurs through a control member, so that during an inclination of the back member, the seat member is lowered a specific amount.  A similar arrangement is known for Gebrauchsmuster No.  84 17 429.  Here the difference lies only in the lever of the back member being rotatably connected directly with the seat member, while the control member is arranged between the lever and the seat carrier.  Here too an inclination of the seat member is obtained with a specific back inclination. 
A chair is known from German A No.  1 33 16 533, in which also upon a swivelling of the back member there occurs a seat back inclination.  In this embodiment, the control, according to the Gebrauchsmuster No.  84 17 429, has been replaced with a sliding guide, which, on the one hand, determines the coupling of seat and back in a predetermined relationship and, on the other hand, effects the balance in view of the different fulcrum points of seat and lever of the back. 
All of these known chairs have the disadvantage, that the support for the back in the lumbar vertebra area can be constructed at an optimum only for a very specific seat back inclination, while the support for a seat back inclination which is changed for this, be it with a steeper or with a flatter positioned seat back, is insufficient. 
The basic purpose of the invention is to provide a chair of the abovementioned type so that the support of the lumbar vertebras in the region of the user's back by the seat back is changed with the change in the inclination of the back of the chair such that the support is optimal during each seat back inclination. 
Thus in the inventively constructed chair, there is arranged a main control member extending parallel to the lever, to which the back member is secured and which engages at the same time the seat member.  The lower end of the control member is hinged either to the seat carrier or to the seat member.  The upper end of the control member is hinged to the lumbar vertebra area of the back of the chair.  The lever which carries the back member and the control member are rotatably connected with one another, so that in the case of a change in the inclination of the back member, there occurs additionally a swivelling of a part of the back member in an opposite sense.  As a result, during a large back inclination, the support in the lumbar vertebra area becomes greater, while the support is reduced accordingly during a steeper more upright back inclination, so that a suitable support is provided during each back inclination. 
Since the lower hinged connection of the lever and also of the control member must lie spaced from one another, or otherwise a suitable change in the form of the back member cannot be obtained, and since the control member and lever are rotatably coupled with one another, the relative movement between the control member and the lever must be balanced in order to obtain a balance of the different fulcrum points.  The balance of the relative movement can be obtained either through a connecting link guide, or through an intermediate, or additional, control member, either of which connects the lever and the main control member with one another, or in the alternative connects the main control member to the seat carrier.  By selecting the hinge points for the main control member on the lever or the seat carrier and by selecting the length of the additional control member and as well as its hinged location on the seat carrier or by selecting the location of the connecting link guide between the two control members, the magnitude of the change of the form of the user's back in the lumbar vertebra region is determined. 
In an advantageous embodiment of the invention, the additional control member, or in the alternative the connecting link guide, is arranged between the main control member and the lever to facilitate an adjustment of the chair to different body sizes by adjusting the length of the control member or, in the alternative, the inclination of the connecting link guide.