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with, cf. (1.2) on page 265 in B1, 
X1, …, XN a sample from a distribution F and, for i = 1, …, N, R , the rank of |X1 - q1ø| among |X1 - q1ø|, …, |XN - qNø|. It is shown that, under certain regularity conditions on F and on the constants pi and qi, TøN(t) is asymptotically approximately a linear function of ø uniformly in t and in ø for |ø| ≤ C. The special case where the pi and the qi, are independent of i is considered.