We consider the problem of the distribution of a specified number of measurments on a given interval, ensuring the least variance of the estimate of one of the parameters linearly related with the function being measured. Assuming a normal distribution law for the measurement errors, we derive equations describing necessary extremum conditions for the corresponding variance. Using these equations we analyze the case of optimal disposition of the measurements at the ends of an interval. We investigate in more detail the case of parabolic regression, for which we establish the nature and the number of optimal points. One of the peculiarities of the problem of optimal spacing of observations is connected with the fact that it arose as a result of applying the methods of mathematical statistics, but its resolution requires us to bring in other branches of mathematics. Thus, for examole, in [1] a bound on the maximum numer of optimal (with respect to the variance of the estimate of some parameter) observation instants was established by methods of mathematical analysis, in [2] it was shown with the aid of linear programing theory that the number of optimal points with different vector-gradients of the function being measured with respect to the parameters being estimated does not exceed the total number of parameters being determined. This proposition is proved under an essential condition on the admissibility of any noninteger values of the weighting coefficients (i.e. on the continuality of their values) with the single requirement that the sum of these coefficients equal the total number of measurements. The first investigation of this question was apparently carried out in [3] wherein the stated problem was considered for two parameters under the assumption that an arbitrarily large number of measurements can be made at a point. Papers [4, 5], using the results of [2], examined the problem of the simultaneous choice of an optimal strategy and of the composition of the measurements under certain assumptions on the nature of the correlation between them. The assertions and algorithms presented in these papers are valid, strictly speaking, under the condition that the weighting coefficient values are continual, i. e. at a sufficiently large composition of measurements. The general problem of observation was investigated in [6] from the viewpoint of Pontriagin's maximum principle as it applies to systems of linear differential equations; the measurement process is interpreted as a control process with specified constraints. Below, under the assumptions in [1], we look at certain questions connected with the problem of an optimal disposition of the measurements without the condition on the continuality of the values of the weighting coefficients. Here, however, we do not pose the problem of constructing a computation algorithm, therefore, the derived equations for the necessary conditions are not supplemented by conditions of sufficiency. These equations are used for obtaining certain results analytically; in particular, they allow a sufficiently detailed investigation of the parabolic regression case. The existence of the so-called ballast instants of measurements, i.e. those not leading to a lessening of the a priori variance of some parameter, is proved for this case. We show that in the given case these instants alternate with the optimal instants of measurements.