(7) If B m denote the brightness of the **mth** lateral image, and Bo that the central image, we have amp 'cosx' dx= a d (1) (-) m7r B.: Bo= a+d am?r sin' a4 d (1).

Xxvi.) "the numerical orders of the image," are consequently only odd powers; the condition for the formation of an image of the **mth** order is that in the series for and the coefficients of the powers of the 3rd, 5th.

As in algebra we say that an equation of the **mth** order has in roots, viz.

We state this generally without in the first instance, or it may be without ever, distinguishing whether these are real or imaginary; so in geometry we say that a curve of the **mth** order is met by an arbitrary line in m points, or rather we thus, through algebra, obtain the proper geometrical definition of a curve of the **mth** order, as a curve which is met by an arbitrary line in m points (that is, of course, in m, and not more than m,.

We find in it explicitly the two correlative definitions: " a plane curve is said to be of the p ith degree (order) when it has with a line m real or ideal intersections," and " a plane curve is said to be of the **mth** class when from any point of its plane there can be drawn to it m real or ideal tangents."

We can only use the general equation (*fix, y, z) m = o, say for shortness u= o, of a curve of the **mth** order, which equation, so long as the coefficients remain arbitrary, represents a curve without nodes or cusps.

Although Royalists formed but a petty fraction of the majority, they raised the alarm that **Mth** i t w as seeking to restore monarchy and undo the work of the /8th g y of the Revolution.