It is always an invariant or covariant appertaining to a number of different linear forms, and as before it may vanish if two such linear forms be identical.
The elongation is generally found to reach a maximum under a magnetizing force of 50 to 120 units, and to vanish under a force of 200 to 400, retraction occurring when still higher forces are applied.
Alarmed at this terrible outburst between the two principal and responsible owners of the ship, and feeling half a mind to give up all idea of sailing in a vessel so questionably owned and temporarily commanded, I stepped aside from the door to give egress to Bildad, who, I made no doubt, was all eagerness to vanish from before the awakened wrath of Peleg.
The two forms ax, bx, or of, 0, may be identical; we then have the kth transvectant of a form over itself which may, or may not, vanish identically; and, in the latter case, is a covariant of the single form.
The supporters of the solar theory look upon Memnon as the son of the dawn, who, though he might vanish from sight for a time, could not be destroyed; hence the immortality bestowed upon him by Zeus.
In the Croatian Karst the seven streams of the Lika unite and plunge into a rocky chasm near Gospic, and the few small brooks of this region usually vanish underground in a similar manner.
Attacked in detail, they vanish one after another into as many teasing spectra of uncertainty.
Such a symbolic product, if its does not vanish identically, denotes an invariant or a covariant, according as factors az, bz, cz,...
If, instead of supposing the motion at dS to be that of the primary wave, and to be zero elsewhere, we suppose the force operative over the element dS of the lamina to be that corresponding to the primary wave, and to vanish elsewhere, we obtain a secondary wave following quite a different law.
Aj Hence the system of values also causes to vanish in this case; dx and by symmetry aj and Fz also vanish.