## Scalar Sentence Examples

- For if 0, A, B be any three points, and m, n any
**scalar**quantities, we have in vectors m.~+n.~=(m+n)O~, (I) - The space within is filled with radiations corresponding to this temperature, and these attain a certain equilibrium which permits the energy of radiation to be spoken of as a whole, as a
**scalar**quantity, without express reference to the propagation or interference of the waves of which it is composed. - Clifford makes use of a quasi-
**scalar**w, commutative with quaternions, and such that if p, q, &c., are quaternions, when p-I-wq= p'+wq', then necessarily p= p', q = q'. - The plane is of vector magnitude ZVq, its equation is ZSpq=Sr, and its expression is the bi-quaternion nVq+wSr; the point is of
**scalar**magnitude 4Sq, and its position vector is [3, where 1Vf3q=Vr (or what is the same, fi = [Vr+q. - This has a reciprocal Q -1= p-r = qq-1 - wp1 rq1, and a conjugate KQ (such that K[QQ'] = KQ'KQ, K[KQ] = Q) given by KQ = Kq-}-rlKp+wKr; the product QQ' of Q and Q' is app'+nqq'+w(pr'+rq'); the quasi-vector RI - K) Q is Combebiac's linear element and may be regarded as a point on a line; the quasi-
**scalar**(in a different sense from the rest of this article) 2(1+K)Q is Combebiac's**scalar**(Sp+Sq)+Combebiac's plane. - Thus, in place of his general tri-quaternion we might deal with products of an odd number of point-plane-
(of form, uq+wr) which are themselves point-plane-**scalars**; and products of an even number which are octonions; the quotient of two point-plane-**scalars**would be an octonion, of two octonions an octonion, of an octonion by a point-plane-**scalars****scalar**or the inverse a point-plane-**scalar**. - Again a unit point p. may be regarded as by multiplication changing (a) from octonion to point-plane-
**scalar**, (b) from point-plane-**scalar**to octonion, (c) from plane-**scalar**to linear element, (d) from linear element to plane-**scalar**. - Although many pseudo-symmetric twins are transformable into the simpler form, yet, in some cases, a true polymorph results, the change being indicated, as before, by alterations in
**scalar**(as well as vector) properties. - If we put qo= Sq' - Vq', then qo is called the conjugate of q', and the
**scalar**q'qo = qoq' is called the norm of q' and written Nq'. - The fundamental character of energy in material systems here comes into view; if there were any other independent
**scalar**entity, besides mass and energy, that pervaded them with relations of equivalence, we should expect the existence of yet another set of qualities analogous to those connected with temperature. - In the third-order complex the centre locus becomes a finite closed quartic surface, with three (one always real) intersecting nodal axes, every plane section of which is a trinodal quartic. The chief defect of the geometrical properties of these bi-quaternions is that the ordinary algebraic
**scalar**finds no place among them, and in consequence Q:1 is meaningless. - While polysymmetry is solely conditioned by the manner in which the mimetic twin is built up from the single crystals, there being no change in the
**scalar**properties, and the vector properties being calculable from the nature of the twinning, in the case of polymorphism entirely different structures present themselves, both**scalar**and vector properties being altered; and, in the present state of our knowledge, it is impossible to foretell the characters of a polymorphous modification. - The mathematical importance of this function called the potential is that it is a
**scalar**quantity, and the potential at any point due to any number of point charges ql, q2, q3, &c., distributed in any manner, is the sum of them separately, or qi/xl+q2/x2+q3/x3+&c. =F (q/x) =V (17), where xi, x2, x 3, &c., are the distances of the respective point charges from the point in question at which the total potential is required. - In the language of vector analysis (q.v.) it is the
**scalar**product of the vector representing the force and the displacement. - In the same way, the work dne by a force acting on a rigid body in any infinitely small displacement of the body is the
**scalar**product of the force into the displacement of any point on the line of action.