The division of the interval \((0,1)\) into \(k\) subintervals by \(k-1\) independent and identically distributed uniform variables is called a spacing. Let \(r(k)\) and \(R(k)\), respectively, be the smallest and the largest subinterval in such a spacing. The authors derive a number of formulas for the moments of \(r(k), R(k), R(k)-r(k)\) and \(r(k)/R(k)\). Additional results are established when the division of \((0,1)\) is made by a Poisson process.