The estimation of variance by use of successive differences of higher order is discussed in this paper. Heretofore, attention has been focused, in published works, on estimates of variance obtained by employing the sum of squares of deviations from the mean and also by using mean square successive differences of the first order [1], [2], [3], [9]. A concise description of the method employing differences of any order with appropriate formulae for the precision of estimates so obtained and also a practical example on the use of the technique are given in section 11. Fundamental contributions to the estimation of variance from higher order differences, a study of the efficiency of the technique and proper orientation of the subject matter in the field of mathematical statistics are given in sections 2-10 of the paper.