It is usually the case that the secondary caustic is easier to determine than the caustic, and hence, when determined, it affords a ready means for deducing, the primary caustic. It may be shown by geometrical considerations that the secondary caustic is a curve similar to the first positive pedal of the reflecting curve, of twice the linear dimensions, with respect to the luminous point.
I) on the branched or unbranched stem; (b) the growth of the main stem through the female flower; (c) the presence of a prominent single vein in the linear pinnae; (d) the structure of the female flower, which is peculiar in not having the form of a cone, but consists of numerous independent carpels, each of which bears two or more lateral ovules.
The velocity of propagation of a torsional disturbance along a wire of circular section may be found by the transfer of momentum method, remembering that we must now replace linear momentum by angular momentum.
The first error is to assert that history unfolds in a basically linear fashion, that there is a fundamental continuity between the past, present, and future.
This canonical form depends upon j having three unequal linear factors.
Now the kinetics of a medium in which the parts can have finite relative motions will lead to equations which are not linear - as, for example, those of hydrodynamics - and the phenomena will be far more complexly involved.
One of the most important questions in investigating a linear algebra is to decide the necessary relations between a and b in order that this product may be zero.
They are generally of a more or less oval or elliptical form, or they may be globular, as in Mercurialis annua; at other times linear or clavate, curved, flexuose, or sinuose, as in bryony and gourd.
Both as regards structure and habits, the leopard may be reckoned as one of the more typical representatives of the genus Felis, belonging to that section in which the hyoid bone is loosely connected with the skull, owing to imperfect ossification of its anterior arch, and the pupil of the eye when contracted under the influence of light is circular, not linear as in the smaller cats.
But the present tendency is to regard the early association of arithmetic with linear measurement as important; and it seems to follow that we may properly (at any rate at an early stage of the subject) multiply a length by a length, and the product again by another length, the practice being dropped when it becomes necessary to give a strict definition of multiplication.