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(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).

00xxvi.) "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.

00As in algebra we say that an equation of the mth order has in roots, viz.

00we 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,.

00We 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."

00We 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.

00Although 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.

00

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