Sentence Examples

  • 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.
  • 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.