I harp (multiplied quant.
And similar records might be multiplied almost to any extent.
Hence_li y ` A 1n where A li and A li, are minors of the complete determinant (a11a22...ann)ï¿½ an1 ant ï¿½ï¿½ï¿½an,n-1 or, in words, y i is the quotient of the determinant obtained by erasing the i th column by that obtained by erasing the n th column, multiplied by (-r)i+n.
The i t " power of that appertaining to a x and b x multiplied by the j t " power of that appertaining to a x and c x multiplied by &c. If any two of the linear forms, say p x, qx, be supposed identical, any symbolic expression involving the factor (pq) is zero.
These images take the place of the coloured fragments of glass, and they are symmetrically multiplied by the mirrors.
Meanwhile his academic honours from home and foreign universities multiplied, and he became a fellow of the Royal Society in 1894.
Among the ruder or savage tribes they possess but one form; but the ingenuity of man has devised many inventions to increase his comforts; he has varied and multiplied the characters and kinds of domestic animals for the same purpose, and hence the various breeds of horses, cattle and dogs.
Thus all that was shocking in the barbarism of Africa was multiplied and intensified by this foreign stimulation.
The expenses were met by collections made in the Calvinistic Methodist Societies, and as the funds increased masters were multiplied, until in 1786 Charles had seven masters to whom he paid £io per annum; in 1787, twelve; in 1789, fifteen; in 1794, twenty.
Shirazi (f9o5); but the literature in new translations and imitations has recently multiplied exceedingly.
- The value of a determinant is unchanged if we add to the elements of any row or column the corresponding elements of the other rows or other columns respectively each multiplied by an arbitrary magnitude, such magnitude remaining constant in respect of the elements in a particular row or a particular column.
The discriminant of the product of two forms is equal to the product of their discriminants multiplied by the square of their resultant.
And take therein the coefficient of the function (mi t tm7t t m 31 t ...), we obtain the same result as if we formed the separation function in regard to the specification (mï¿½ It t'tm2 32tm"`l3t...), multiplied by Alt!!
If u, a quantic in x, y, z, ..., be expressed in terms of new variables X, Y, Z ...; and if, n,, ..., be quantities contragredient to x, y, z, ...; there are found to exist functions of, n, ?, ..., and of the coefficients in u, which need, at most, be multiplied by powers of the modulus to be made equal to the same functions of E, H, Z, ...
Even before the Reformation, however, signs of decay had already begun to appear, and these multiplied in the 16th and 17th centuries.
With the aid of the Jesuits, whose privileges he multiplied, he conducted a vigorous propaganda.
The population of Victoria was doubled in the first twelvemonth of the gold fever, and the value of imports and exports was multiplied tenfold between 1851 and 1853.
After his death in 1054 the process of disintegration went on apace and the family feuds multiplied at an alarming rate.
Every symbolic product, involving several sets of cogredient variables, can be exhibited as a sum of terms, each of which is a polar multiplied by a product of powers of the determinant factors (xy), (xz), (yz),...
1 And The Actual Forms For The First Three Weights Are 1 Aobzo, (Ao B 1 A 1 B O) Bo, (A O B 2 A 1 2 0 Bo, Ao(B2, 3 A1B2 A2B1 A O (B L B 2 3B O B 3) A I (B 2 1 2B 0 B 2); Amongst These Forms Are Included All The Asyzygetic Forms Of Degrees 1, 1, Multiplied By Bo, And Also All The Perpetuants Of The Second Binary Form Multiplied By Ao; Hence We Have To Subtract From The 2 Generating Function 1Z And 1 Z Z2, And Obtain The Generating Function Of Perpetuants Of Degrees I, 2.
The sum of the corresponding numbers multiplied by 332600 gives Log.
When P is the neutral point, H is equal and opposite to R; therefore M = Hd 3, or the moment is numerically equal to the cube of the distance from the neutral point to a pole, multiplied by the M.
When the magnetizing current is twice reversed, so as to complete a cycle, the sum of the two deflections, multiplied by a factor depending upon the sectional area of the specimen and upon the constants of the apparatus, gives the hysteresis for a complete cycle in ergs per cubic centimetre.
Thus the magnetization which the sample of Swedish iron received in a field of 1490 was not increased (beyond the limits of experimental error) when the intensity of the field was multiplied more than thirteen-fold, though the induction was nearly doubled.
At the temperature of liquid air (-185°) the application of a field of 21,800 multiplied the resistance of the bismuth no less than 150 times.
In opposition to this Nominalistic view, which implied the reversal of his whole position, William may have meant to say that, instead of the universal being multiplied, it is rather the individuals which are reduced to unity in the universal.
Matthias laboured strenuously to develop and protect the towns, multiplied municipal charters, and materially improved the means of communication, especially in 1 We know actually of fifteen, but there may have been many more.
It means that i lb is to be multiplied by 7, the result by 3, and the new result by 5.
If it is intended that the first number is to be multiplied by the second, a special sign such as X should be used.
The number by which an algebraical expression is to be multiplied is called its coefficient.
- (i.) An expression such as a.2.a.a.b.c.3.a.a.c, denoting that a series of multiplications is to be performed, is called a monomial; the numbers (arithmetical or algebraical) which are multiplied together being its factors.
(I) The heat, H, absorbed in isothermal expansion (latent heat of expansion) from p to p" is equal to the diminution of pressure (p' - p”) multiplied by the absolute temperature and by the expansion per degree (v" - v')/(o' - o") at constant pressure.
(2) The heat, H, absorbed in isothermal expansion from v to v" is equal to the increase of volume (v" - v') multiplied by the absolute temperature, and by the increase of pressure per degree (p' - p")/(o' - o"), at constant volume.
Throughout the whole of this period, embracing about a hundred years, there still continued to work, altogether apart from the men who were making the success of popular art, a large number of able painters of the Kano, Tosa and Chinese schools, who multiplied pictures that had every merit except that of originality.
Yahweh's judgments are multiplied against the land, and the issue can be nothing else than its total desolation.
With him the unit is termed "digitus"; when multiplied by ten it becomes the "articulus"; while the combination of the articulus and the digitus is the "numeras compositus."
Infirmities multiplied upon him, until his death at Washington on the 22nd of October 1900.
Four series of "Researches on Heat," in the course of which he described the polarization of heat by tourmaline, by transmission through a bundle of thin mica plates inclined to the transmitted ray, and by reflection from the multiplied surfaces of a pile of mica plates placed at the polarizing angle, and also its circular polarization by two internal reflections in rhombs of rock-salt.
While Berlin and Budapest have made the most rapid progress of all European cities, having multiplied their population by nine in the period 1800-90, Vienna - even including the extensive annexations of 1892 - only increased sevenfold.
The moment of inertia of the body about the axis, denoted by But if is the moment of inertia of the body about a mean diameter, and w the angular velocity about it generated by an impluse couple M, and M' is the couple required to set the surrounding medium in motion, supposed of effective radius of gyration k', If the shot is spinning about its axis with angular velocity p, and is precessing steadily at a rate about a line parallel to the resultant momentum F at an angle 0, the velocity of the vector of angular momentum, as in the case of a top, is C i pµ sin 0- C2µ 2 sin 0 cos 0; (4) and equating this to the impressed couple (multiplied by g), that is, to gN = (c 1 -c 2)c2u 2 tan 0, (5) and dividing out sin 0, which equated to zero would imply perfect centring, we obtain C21 2 cos 0- (c 2 -c 1)c2u 2 sec 0 =o.
High, obviously act as efficient mercury-traps; but the already considerable height of the pump is thus multiplied by two.
Multiplied by the total rubbing or friction surface of the air-ways in square feet and by the coefficient of friction.