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A theory previously developed by the author to describe the horizontal spreading of liquids in paper has been applied to the case of a liquid rising by capillary action in a vertical strip of filter paper. The phenomenon is complicated by a surface roughness effect which had to be taken into account. The theory leads to simple expressions for the rate of rise and the distribution of liquid which are in agreement with experiment. When gravity can be neglected, the height of rise is proportional to the square root of the time. When gravity is important, the height of rise is a more complex function of time than the simple square root dependence. In addition, the liquid approaches a limiting height.

This article is an attempt to throw more light on the problem of choosing plotting positions for the frequencies related to ordered sample values. The problem is particularly pertinent where special-scale graph paper is used such that a straight line indicates conformance of data to type of distribution assumed to apply. Such graph paper is often briefly referred to as “probability paper.” The types of distributions here considered are the normal and the extreme-value distribution of Type I, with the accent on the extreme-value case. Various methods of determining plotting positions have been put forward and there is confusion of thought in judging what plotting convention is optimum. An optimum criterion proposed by Chernoff and Lieberman has received wide attention. Blom in a recent book develops further criteria [2]. To clarify the problem the author has analyzed the purposes to be served in plotting data on probability paper. With a specific concept of the purpose to be served in mind, it bec...

The nature of electrical conduction in paper is discussed, particularly with regard to the formation of potential discontinuities. Experiments are described which indicate the formation of soft x‐rays in paper insulated cables under voltage. Methods of measurement of potential distribution in paper insulation are given, together with preliminary results, which show large electrode drops under certain conditions. The relation of these experiments to those of Reboul and Bodin is pointed out.

In this paper it is shown that the statistical theory of the distribution of extreme values is pertinent to the study of the way in which the breakdown strengths of paper capacitors depend on capacitor size. The theory presented in this paper permits a quantitative explanation of this phenomenon and results are given which should be useful to design engineers.

Experiments of the above title are done by middle rotations of the homogenizer, which rotates a little more than 26 r.p.m. and mixes moths twice per rotation by the action of agitation vane inserted at 45 degree to the base of a drum. As the number of an unit group, 600 and 200 moths are adopted in accordance with the ordinary custom of egg producers. Results are as follows.1. After rotation of the homogenizer for only five seconds, the distribution of almost all groups of diseased moths becomes already binomial or normal.2. As the rotation time of the homogenizer becomes longer and longer, the distribution of diseased moths tends more and more to fit the normal formula than the binomial, and in some cases, it takes PEARSON'S II-type distribution curve or in other cases, even if rare, more than halves of the number of experiments centre to the position of population mean value p, though their mode deviate slightly to right or left side of the position p'.3. The effect of homogenizing action of this machine seems to be not seriously influenced by the percentage of diseased moths.4. Interaction-test, comparing p & p' and q & q' or by SNEDECOR'S R×2 method using population variance, pq, shows in all cases the uniformity of variance, after rotated samples for five seconds or more.5. Inspections using confidence interval p±3√pq/nκ and p±2√pq/nκ show equivalence in all former cases and in latter cases, when the time of rotation becomes fifteen seconds or longer. POISSON distribution inspection using x2-test also proves to be equivalent in all cases of experiments.6. Abstraction of the required number of moths to be inspected can be easily done from any part of their unit group by picking out at a sampling and the number of sampling units, fifty, may not necessarily be needed, if the homgenizer is previously used.7. If the high rotatory speed is used, the required time of rotation can be reduced to half, however in order to exclude fine scales of moths, infected with spores of pebrine, by the electric fan, the rotation time for thirty seconds may be desirable.

In response to a recent paper by Jakeman and Pike, it is pointed out that the classical and quantum-mechanical treatments of the fluctuations of the integrated light intensity are equivalent. The choice of the observable is dictated not by theoretical conditions, but by reference to what is usually measured.

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A primary purpose in plotting a set of ordered observations on probability paper is to simplify the inspection of their distribution. With this limited objective a plotting rule for the ith of n ordered observations from a double exponential distribution is obtained as i = (i - 0.44)/(n + 0.12), where n is the number of observations, i is the order of the observation from the smallest, and i is the estimate of the cumulative frequency of the ith term.

IN this paper Haldane points out (p. 142) a difference between his results for the mean and variance of x2 in a 2 x n-fold contingency table when the expectation p is fixed and the results obtained by me in my paper (Annals of Eugenics, Vol. VII, part III, p. 211). The difference is that I have (n 1) throughout where Haldane has n. Haldane writes, "my own results would appear to be slightly more accurate than Cochran's", which might, I think, give the impression that both Haldane's results and mine are only approximations. In fact, both results are mathematically exact, the difference between them being one of definition of x2. My paper is almost entirely concerned with the distribution of x2 when the expectation p is not known. In the results which I gave for the distribution of x2 when p is known, I retained the term S (x -x-)2 in the numerator of x2 instead of S (x np)2, to facilitate comparison between this and my other results. Thus my x2 has (n 1) degrees of freedom, whereas Haldane's x2 has n degrees of freedom. Unfortunately I did not emphasize this point in the passage concerned, and as it may have appeared misleading to others besides Haldane, I welcome this opportunity of drawing attention to it. Haldane's x2 is, of course, the one which is normally appropriate in testing the departure from independence when the expectation is known.

THERE have been placed in my hands, by Mrs. Bashford Dean, for distribution among students of fishes, certain reprints of Dr. Dean's studies on the archaic fishes, found among his effects after his untimely death.