No abstract

The symbol An, for example, means A3 X A2, the A, values being those of eq. 4.) This equation is solved for the ß values by inverting the matrix A and multiplying A by A-1. One manipulative detail which may be troublesome is that the matrix elements cover a wide range of values-in the work reported here, 10-31 to 10~9-and the weights may have to be multiplied by some constant to keep the numbers within the capacity of the computer used. This constant can be factored out later.The least-squares procedure gives not only a set of ß values but also their standard deviations if the weights are on an absolute basis, i.e., if the terms in eq. 9 are all known and the proper estimates of and V are used. If this is done, the standard deviations of the ß values are equal to the square roots of the corresponding diagonal elements of the inverse matrix [i.e., ß2The last information available is the "goodness of fit,'' x, described in the text. This is calculated by evaluating F (eq. 6) at each point («, [L]) using the calculated ß values. These quantities are called the residuals; they would be zero if there were no errors in ñ, [L], or the ß values. The residual at each point is multiplied by the weight calculated for that point;where N is the number of observations (number of points) minus the number of parameters determined (3 in this case: ß , ß2, and ß ). The interpretation of X is described in the text.Contribution from the Chemistry Research Sect ion, Rocketdyne,

Exact proton magnetic resonance eigenspectra of the spin Hamiltonian are calculated for a system containing one group of six identical protons and one group of two identical protons. The method of calculation considers each group of identical protons as a composite ``particle'' with fixed total spin, and does not require determination of the explicit form of the zero-order eigenfunctions. The calculated spectra are compared with experimental high-resolution spectra of propane at both 40 Mc and 60 Mc. Thevalues of p, the ratio of the spin coupling constant to the chemical shift, are found to be 0.415 and 0.277, respectively, at the two frequencies. The frequency-independent spin coupling constant is 7.26 cps.

Selected phase and electrical properties of chlorine pentafluoride (CIFs) have been experimentally determined over useful liquidus temperature ranges. The liquid density

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