June 20, 1959
p-CYANOPHENYLPHOSPHONIC ACID
This finding suggests an examination of the differences in sp. Accordingly the relative magnitudes of s, ( i e . , sp/p) were compared for the meta and para groups of each series. The number of series for which the relative value of sp/p for the meta series was appreciably larger, appreciably smaller and approximately equal to the value for the paru series were counted, and the results of these counts are presented in Table 11. It is apparent that there is no significantly better overa11 precision in either series.
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is borne out statistically. This conclusion does not, however, detract greatly from the usefulness of the Hammett equation. Table I shows that, in the majority of the cases (75 to 85%, depending on the criterion chosen), no significant difference exists between pp and p m and between the intercepts. The differences that are encountered are generally quite small. Considering the approximate and empirical nature of the Hammett equation, this new limitation pointed out by Hine docs not appear serious.
Calculations.-The calculations were performed on a n IBM 650 MDDPM by a modification of a program now in use in this Laboratory.5 The changes in the program consisted COZfPARISON O F TIIE PRECISION O F THE HAMMETT EQUATION of successively reading the d a t a , comparing series identificaAPPLIED SEPARATELY T O m- AND p-SUBSTITUTED COM- tion, letting the computer determine whether the substituent POUNDS (ENTRIES ARE NUMBERS OF SERIES) was a fused ring system or a heteroatom (identification number between 800 and 999, 3800 and 3999, 6800 and -sp/p(meta)-. sp/p(Para) , Y"tll. - Ypora 6999), in which case t h e piece of d a t a was by-passed, a n d then whether t h e identification number was even (meta) or Applicaodd (para). Data (u and log k ) , and their squares and ble u >1 -1 < l 2 0 1 3 -0 1' -0 -0.1 0 Do ik .rnd I 1) I rcedm in T i 1 1 5 TOTTRVAI 1 3 , 7 6 5 8 1451) ( 5 ) C hI, I
