34 differ only little in the partial longitudinal chamber 7 34 the temperature drops further however and specifically from right to left so that in the left hand region hot pressure liquid in the partial longitudinal chamber 7 39 confronts the heavily cooled down pressure liquid in the partial longitudinal chamber 7 34 and thus an equlization is obtained which leads to the condition that the temperatures at the left and right ends of the hollow roll 1 differ only by a small amount in the embodiment of fig1 to 3 the lengthwise subdivision 11 is provided in a longitudinal chamber 7 which is located on the side of the rolling gap and therefore contributes substantially to the formation of the line pressure the opposite longitudinal chamber which occupies the rest of the circumference is not empty but contains the leakage oil which passes at the longitudinal seals 5 and is continuously drained therefrom in some cases a certain amount of pressure is intentionally maintained in this longitudinal chamber disposed opposite the longitudinal chamber 7 so that the effective pressure is obtained from the pressure difference when the opposite chamber contains fluid under pressure the longitudinal subdivision 11 does not have to be provided on the side of the rolling gap in the case of the roll 10 39 shown in fig4 the transverse end seals 6 39 extend over the entire circumference and by means of additional semiannular transverse seals 6 34 there are formed on the.