Publication Approved by the Director of the Bureau of Standards of the U. S. Department of Commerce.
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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 ρ0 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 ρ0 for 430 and 440 mµ equal to ρ0 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, ρ0 is arbitrarily set at zero instead of at the values which would be obtained by mechanical application of the formula. Similarly for β0 between 590 and 610 mµ, we choose β0 in the formula as 1 and 2 for 620 and 630, respectively, although β0 is given in Table 5 as zero for wave lengths greater than 610 mµ.