Publication Approved by the Director of the Bureau of Standards of the U. S. Department of Commerce.

L. T. Troland, Report of the Committee on Colorimetry for 1920–21, J.O.S.A. and R.S.I., 6, 547–553; 1922.

Spectrophotometry; Report of O. S. A. Progress Committee for 1922–3, J.O.S.A. and R.S.I., 10, 230; 1925.

I. G. Priest, The Computation of Colorimetric Purity, J.O.S.A. and R.S.I., 9, 503–520; 1924. D. B. Judd, The Computation of Colorimetric Purity, J.O.S.A. and R.S.I., 13, 133–152; 1926.

D. B. Judd, Extension of the Standard Visibility Function to Intervals of 1 Millimicron by Third-difference Osculatory Interpolation, B. S. Jour. Research, 6, 465–471; 1931; J.O.S.A., 21, 267–275; 1931.

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George King, On the Construction of Mortality Tables from Census Returns and Records of Deaths, J. Inst. Actuaries, 42, 238–246; 1908. James Buchanan, Osculatory Interpolation by Central Differences; with an Application to Life Table Construction, J. Inst. Actuaries, 42, 369–394; 1908; see also an appendix by G. J. Lidstone, Alternative Demonstration of the Formula for Osculatory Interpolation, pp. 394–397. George King, On a New Method of Constructing and of Graduating Mortality and Other Tables, J. Inst. Actuaries, 43, 109–184; 1909.

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The check was carried out by taking the differences in the ascending order rather than in the descending order as indicated in the formula. See Tables 2 and 4. It might naturally be supposed that about twice the time to calculate nine values would be required to calculate and check them by an independent method, but this is not quite the case. The time actually required is considerably less than twice because the products found for checking the values in one interval may be used to calculate values in the four subsequent intervals.

See footnote 3, p. 531. The values referred to here are included in Table 5 along with the values obtained from them by interpolation.

The values for ρ_{0} from 451 to 459 and from 461 to 469 mµ result from substituting in the formula ƒ(-20) equal to 4 and 1, respectively; that is, we have taken ρ_{0} for 430 and 440 mµ equal to ρ_{0} for 470 and 460 mµ, respectively, instead of zero as shown in Table 5. This choice was made in order to bring the interpolated function to zero at 450 mµ with a zero slope; then, for λ less than 450 mµ, ρ_{0} is arbitrarily set at zero instead of at the values which would be obtained by mechanical application of the formula. Similarly for β_{0} between 590 and 610 mµ, we choose β_{0} in the formula as 1 and 2 for 620 and 630, respectively, although β_{0} is given in Table 5 as zero for wave lengths greater than 610 mµ.