An important notion is that of conjugate partitions.
When the conjugate axis of the hyperbola increases without limit, the loops of the nodoid are crowded on one another, and each becomes more nearly a ring of circular section, without, however, ever reaching this form.
The linear invariant a s is such that, when equated to zero, it determines the lines ax as harmonically conjugate to the lines xx; or, in other words, it is the condition that may denote lines at right angles.
Proposition 14 shows how to draw an ellipse through five given points, and Prop. 15 gives a simple construction for the axes of an ellipse when a pair of conjugate diameters are given.
Ramsden's dioptric micrometer consists of a divided lens placed in the conjugate focus of the innermost lens of the erecting eye-tube of a terrestrial telescope.
It is notorious among engineers that retaining walls designed in accordance with the well-known theory of conjugate pressures in earth are unnecessarily strong, and this arises mainly from the assumption that the earth is merely a loose granular mass without any such adhesion.
In elliptic harmonic motion the velocity of P is parallel and proportional to the semi-diameter CD which is conjugate to the radius CP; the hodograph is therefore an ellipse similar to the actual orbit.
Although in the forms without aecidia the two generations are not sharply marked off from one another, we may look up the generation with single nuclei in the cells as the gametophyte and that with conjugate nuclei as the sporophyte.
Thus a partition of 6 is 42; writing this in the form z 11' and summing the columns instead of the lines, we obtain the conjugate partition 2211; evidently, starting from 2211, the conjugate partition is 42.
From one cell to another or C, A further stage in which whether two daughter nuclei from sm l the first aecidiobecome conjugate in one cell, spore (a) and the intercalary is not yet clear.