[ad. mod.L. summātio, ōnem, n. of action f. med.L. summāre to SUM. Cf. F. sommation.]
1. Math. The process of finding the sum of a series. Also in fig. context.
1760. Phil. Trans., LI. 553. Any branch of it [sc. the analytic art] that relates to the summation of series.
1842. Penny Cycl., XXIII. 267/1. The summation of a finite number of terms of a series.
1860. Sylvester, Math. Papers (1908), II. 228. The (Σ)r meaning merely the sign of summation r times repeated.
1874. Stubbs, Const. Hist., I. i. 4. The constitutional history of France is thus the summation of the series of feudal development in a logical sequence.
1885. Watson & Burbury, Math. Th. Electr. & Magn., I. 167. If the system consist only of conductors on which the charges are e1, e2, &c., we have E = 1/2ΣVe, Σ denoting summation for all the conductors.
2. The adding up of numbers; casting up an account; an addition sum.
1816. Scott, Antiq., xxii. It amounts … to eleven hundred and thirteen pounds, seven shillings, five pennies, and three-fourths of a penny sterling—But look over the summation yourself.
1854. H. Miller, Sch. & Schm., xxiii. (1858), 512. I never acquired the facility, in running up columns of summations, of the early-taught accountant.
1883. Nonconf. & Indep., 28 Dec., 1168/3. A summation made up by me to the end of last year.
3. The addition of mensurable quantities (distance, time, etc.).
1860. Tyndall, Glac., I. xi. 81. The summation of distances twenty paces each must finally place us at the top.
1914. Petrie, in Anc. Egypt, 32. I confess to venturing the suggestion that this was a date from some earlier starting point, giving a summation of years.
b. The accumulation of a number of stimuli applied to a muscle.
1877. M. Foster, Physiol., III. v. (1878), 471. The central mechanism … being thrown into activity through a summation of the afferent impulses reaching it.
1883. Nature, XXVII. 8 March, 438. This relation of the contractile tissue to stimuli is usually expressed by saying that the tissue has the power of summation.
1889. Lancet, 3 Aug., 203/1. A summation of the stimuli appears to go on in the cells.
4. The computation of the aggregate value of conditions, qualities, etc.; summing-up.
1836. Lytton, Athens (1837), I. 455. Valour seems to have been for his [Miltiades’] profound intellect but the summation of chances.
1856. Dove, Logic Chr. Faith, V. i. 262. Our conception of duty is either ‘Yea,’ or ‘Nay’ without … summations of advantages.
1908. Daily Chron., 26 Feb., 3/3. Such is Mr. Wyndham’s summation of Scott.
5. The aggregate or sum-total; the resultant or product.
1840. Carlyle, Heroes, i. (1872), 20. They are not one coherent System of Thought; but properly the summation of several successive systems.
1879. J. Jacobs, in 19th Cent., Sept., 500. He is the summation of Hebraism and Hellenism, the two great factors of civilised life.
1885. Manch. Exam., 13 July, 6/1. Mr. Harrison … regards God as the summation of Humanity.
6. attrib.: summation tone, Acoustics [G. summationston (Helmholtz)] = summational tone (see TONE sb. 2).
1867. Tyndall, Sound, vii. 285. Resultant tones are of two kinds…. The former are called difference tones, the latter summation tones.
1875. Encycl. Brit., I. 118/2. [Helmholtz] was led … to surmise the formation of summation-tones by the interference of two loud primaries.
1901. E. B. Titchener, Exper. Psychol., I. II. 90. If we are not satisfied with this ‘summation’ theory, we may have recourse to a subsidiary hypothesis. We may suppose that the gaps in sensation are filled out by association.
