entrance pupil the axis of the pencil or principal ray, it can be said: the rays of the pencil intersect, not in one point, but in two focal lines, which can be assumed to be at right angles to the principal ray; of these, one lies in the plane containing the principal ray and the axis of the system, i.e. in the first principal section or meridional section, and the other at right angles to it, i.e. in the second principal section or sagittal section. We receive, therefore, in no single intercepting plane behind the system, as, for example, a focusing screen, an image of the object point; on the other hand, in each of two planes lines O' and O" are separately formed (in neighboring planes ellipses are formed), and in a plane between O' and O" a circle of least confusion. The interval O'O", termed the astigmatic difference, increases, in general, with the angle W made by the principal ray OP with the axis of the system, i.e. with the field of view. Two astigmatic image surfaces correspond to one object plane; and these are in contact at the axis point; on the one lie the focal lines of the first kind, on the other those of the second. Systems in which the two astigmatic surfaces coincide are termed anastigmatic or stigmatic. Sir Isaac Newton was probably the discoverer of astigmation; the position of the astigmatic image lines was determined by Thomas Young; and the theory was developed by Allvar Gullstrand. A bibliography by P. Culmann is given in Moritz von Rohr's Die Bilderzeugung in optischen Instrumenten. Aberration of lateral object points with broad pencils — coma By opening the stop wider, similar deviations arise for lateral points as have been already discussed for axial points; but in this case they are much more complicated. The course of the rays in the meridional section is no longer symmetrical to the principal ray of the pencil; and on an intercepting plane there appears, instead of a luminous point, a patch of light, not symmetrical about a point, and often exhibiting a resemblance to a comet having its tail directed towards or away from the axis. From this appearance it takes its name. The unsymmetrical form of the meridional pencil—formerly the only one considered—is coma in the narrower sense only; other errors of coma have been treated by Arthur König