In such cases the immediate damage done may be slight; but the effects of prolonged action and the summation of numerous attacks at numerous points are often enormotis, certain of these leafdiseases costing millions sterling annually to some planting and agricultural communities.

When muscle that has remained inactive for some time is excited by a series of single and equal stimuli succeeding at intervals too prolonged to cause summation the succeeding contractions exhibit progressive increase up to a certain degree.

On the other hand, Huxley's summation of the primitive characters of all the mammals led him to an amphibian stem type, a prophecy which has proved faulty because based on erroneous analysis and comparison.

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Y ...a n v, the summation being for all permutations of the n numbers, is called the determinant of the n 2 quantities.

Proceeding on this suggestion, and misled by the mathematical expression which he had given to Weber's law, Fechner held that a conscious sensation, like its stimulus, consists of units, or elements, by summation and increments of which conscious sensations and their differences are produced; so that consciousness, according to this unnecessary assumption, emerges from an integration of unconscious shocks or tremors.

But there is no doubt that it is very difficult to detect the summation tone by the ear, and many workers have doubted the possibility, notwithstanding the evidence of such an observer as Helmholtz.

The practical bearings of a science, it will be granted, are simply, as it were, the summation of its facts, with the legitimate conclusions from them, the natural application of the data ascertained, and have not necessarily any direct relationship to its pursuit.

There is not much difficulty in detecting the difference tone by a resonator if it is held, say, close to the reeds of a harmonium, and Helmholtz succeeded in detecting the summation tone by the aid of a resonator.

Relation of Binomial Coefficients to Summation of Series.

Thus the heat of formation of anhydrous zinc sulphate, ZnSO 4j which cannot be determined directly, may be arrived at by summation (in Hess's units) as follows: Heats of formation are still determined for the most part in a precisely similar manner.