In 1963 Fellegi proposed a new method of sampling without replacement with probability proportional to size, which allowed for rotation of the sample (within certain limits) simultaneously with the exact calculation of joint probabilities of selection of sets of units. Fellegi was able to show that for samples of size two units his equations always yielded a solution, provided that the largest of the population units did not exceed one third of the size of the whole population. He also indicated that the method would probably work provided the largest unit was less than one half the size of the whole population, and that a proof of this would be desirable. This note supplies geometrical proofs of the existence and uniqueness of the solution to Fellegi's equations given this condition.