To explain these facts, Theodor Grotthus (1785-1822) in 1806 put forward an hypothesis which supposed that the opposite chemical constituents of an electrolyte interchanged partners all along the line between the electrodes when a current passed.
1 +hlx-+h2x2+h3x3-}-..., which remains true when the symbols a and h are interchanged, as is at once evident by writing -x for x.
13, interchanged in regard to Israel, on above theory)?
The cases so presented are interchanged by transmission to the opposite party.
Thus any pair of adjoining numbers can be interchanged, so that the numbers can be arranged in any order.
Embassies and courtesies were, indeed, interchanged, and on the 31st of March 1244 a treaty was signed at Rome, whereby the emperor undertook to satisfy the pope's claims in return for his own absolution from the ban.
Pairs of deities whose personalities are often blended or interchanged are Hathor and Nut, Sakhmi and Pakhe, Seth and Apophis.
1, in which the light and shade are interchanged, would give therefore the effect of four equal sources of light shining on a wall through a circular hole.
In this reaction the proportions of aldehyde and acetoacetic ester may be interchanged and ay disubstituted pyridines are then obtained.
Bearing in mind that with ordinary trade balances there is always a possi - bility of the scale-pans and chains getting interchanged, these conditions require; (a) That the beam without the scale-pans and chains must be equally balanced and horizontal; (b) that the two scale-pans with their chains must be of equal weight; (c) that the arms of the beam must be exactly equal in length; i.e.
The position of the coils A and B is then interchanged, and a fresh balance in position on the bridge is obtained.
Next, let the position of A and B be interchanged, and the slide-wire reading be x'; then (B +--x') / (A +1 - x') = P/Q.
It further appears that a determinant is a linear function' of the elements of each column thereof, and also a linear function of the elements of each line thereof; moreover, that the determinant retains the same value, only its sign being altered, when any two columns are interchanged, or when any two lines are interchanged; more generally, when the columns are permuted in any manner, or when the lines are permuted in any manner, the determinant retains its original value, with the sign + or - according as the new arrangement (considered as derived from the primitive arrangement) is positive or negative according to the foregoing rule of signs.
By what precedes it appears that there exists a function of the n 2 elements, linear as regards the terms of each column (or say, for shortness, linear as to each column), and such that only the sign is altered when any two columns are interchanged; these properties completely determine the function, except as to a common factor which may multiply all the terms. If, to get rid of this arbitrary common factor, we assume that the product of the elements in the dexter diagonal has the coefficient + 1, we have a complete definition of the determinant, and it is interesting to show how from these properties, assumed for the definition of the determinant, it at once appears that the determinant is a function serving for the solution of a system of linear equations.
Ch (2n +1)I 7 ry /a yl-R3ct (2n +I)3.ch(2n+I)17b /a ' 16 cos(2n+I) 2 7 z /a w1=4,i+ 4, ii = iR ?3a2 an elliptic-function Fourier series; with a similar expression for 1,'2 with x and y, a and b interchanged; and thence 4, = '1 +h.