The centrifuge method is commonly used to determine the capillary pressure of a porous medium, and the original approximating method for data analysis developed by Hassler and Brunner is still being used. Its limitations are, however, not well understood. Application to analyze experiments where one of the assumptions was obviously violated had been given in the literature. While the result appeared to be quite reasonable, it was not clear how close was it to reality. One of the objectives of this paper is to review the assumptions that is required to develop this method, so that the experimental condition in which it is applicable can be established. The other objective is to derive a completely different solution technique to this problem. There is no need to assume that the ratio of the inlet radius to the exit radius of the core to the center of the centrifuge be close to 1. With the freedom from this limitation it is, therefore, possible to construct machines at lower cost and to improve on the data quality by allowing longer cores.