Page:Popular Science Monthly Volume 63.djvu/544

on an average by nearly 6 per cent. (5.98 per cent.) from the averages based upon 500 sentences from each author, with extreme variations as high as 28.8 per cent. It seems quite plain, therefore, that several thousand sentences from each author would have to be examined to get anything like a constant simple sentence percentage.

Now Mr. Gerwig's tables^[1] for predication averages and simple sentence percentages for prose works comprise averages of about 60,000 sentences taken from seventy-one different authors, exclusive of the complete averages for Macaulay's 'History.' These tables I utilized for a preliminary test^[2] by employing the following device. I grouped together all the works whose predication averages fell between 1.50 and 2.00 per sentence. This group yielded an average of 1.83 predications per sentence and 53 simple sentences per hundred. Next I averaged the works which contained between 2.00 and 2.25 predications per sentence, and the average for this group was found to be 2.15 verbs per sentence and 38 simple sentences per hundred. Proceeding similarly by grouping the works whose predication averages fall between 2.25 and 2.50, between 2.50 and 2.75, and so on, we obtain the following table:

Index.	Predications per Sentence Between.	Averages		$P{\sqrt {S}}$
		P	S
1	1.50 and 2.00	1.86	53.0	13.54
2	2.00"2.25	214	39.1	13.38
3	2.25"2.50	2.34	32.9	13.41
4	2.50"2.75	2.62	25.9	13.33
5	2.75"3.00	2.88	23.2	13.87
6	3.00"3.25	3.10	19.2	13.59
7	3.25"3.50	3.39	15.9	13.52
8	3.50"4.00	3.70	13.4	13.55
9	4.00"4.50	4.84	8.3	13.94
10	4.50"5.00	4.84	8.3	13.94
11	5.00"5.50	5.38	6.7	13.92

The numbers P, the predication averages, and S, the simple sentence percentages, aside from the general reciprocal relation which we should expect, manifest a more specific uniformity. The square-root of 53, the first number under S, multiplied by 1.86, the corresponding number under P, is 13. $+$, but so also is the square-root of 39.1, the second number under S, multiplied by 2.14, the corresponding number for P. Similarly for the third, fourth, fifth pairs of corresponding numbers. That is, we find

$1.86{\sqrt {5}}3.0=13.+$

$2.14{\sqrt {3}}9.1=13.+$

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1. 'University (of Nebraska) Studies,' Vol. 2, No. 1.
2. For a detailed discussion of this experiment, together with other matter of a more technical nature, see 'University Studies,' University of Nebraska, Vol. 111., No. 3.