Since (ab) = a l b 2 -a 2 b l, that this may be the case each form must be linear; and if the forms be different (ab) is an invariant (simultaneous) of the two forms, its real expression being aob l -a l b 0.
For w = i the form is A i ai+Bib i, which we may write aob l -albo = ao(I) b -(I)abo; the remaining perpetuants, enumerated by z I - 2' have been set forth above.
This can be done by placing at B an equal negative point-charge -q in the place which would be occupied by the optical image of A if PO were a mirror, that is, let -q be placed at B, so that the distance BO is equal to the distance AO, whilst AOB is at right angles to PO.
But, if the pasteboard be interposed so as to intercept the vibrating segments AOB, DOC, the note becomes much more distinct.
The reason of this is, that the segments of the plate AOD, BOC always vibrate in the same direction, but oppo sitely to the segments AOB, DOC. Hence, when the pasteboard is in its place, there are two waves of same phase starting from the two former segments, and reaching the ear after equal distances of transmission through the air, are again in the same phase, and produce on the ear a conjunct impression.