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so that the first experiments gave results which were somewhat too high; and the second, results that were somewhat too low. It is allowable, under this hypothesis, to put the two sets of figures together so that the contrasting errors may compensate each other. In this way there was finally obtained out of the 85 double tests the following table.

Number of intermediate syllabes skipped in the formation of the derived series	Time for learning the original series	Time for learning the derived series	Saving of work in learning the derived series	Probable error of saving of work[* 1]	Saving of work in % of original learning time
	(The numbers of the four middle columns denote seconds)
0	(1266)	(844)	(422)		(33.3)
1	1275	1138	137	±16	10.8
2	1260	1171	89	±18	7.0
3	1260	1186	73	±13	5.8
7	1268	1227	42	± 7	3.3
permutation of syllables	1261	1255	6	±13	0.5
The probable errors are calculated from the separate values for savings of work, while the latter, which were actually obtained by subtraction, are considered as the results of direct observation. (see p. 67, note.)

Section 39. Discussion of Results

In the foregoing table an especial interest, it seems to me, is connected with the last, and also with the next to the last, row of numbers. When there was complete identity of all the syllables and the initial and end terms were left in their places, the average saving of time for 17 tests dealing with the learning of the derived series was so slight that it was hardly to be determined. It fell within half of its probable error. The syllables were, therefore, in themselves, outside of their connection, so familiar to me that they did not become noticeably more familiar after being repeated 32 times. On the contrary when a related series was repeated the same number of times, each syllable became so firmly bound to the syllable which followed 8 places beyond that 24 hours later the influence of this connection could be determined in no doubtful fashion. It attains a value 6 times the probable error. Its existence, therefore, must be considered to be fully proved although naturally we cannot be so sure that its size is exactly what it was found