2. That all the images of these objects, formed by an odd number of reflexions, move round =O= in the same direction as the mirrors, and with an angular velocity double that of the mirrors. 3. That when the angle =A O B= is an _even_ aliquot part of a circle, the number of moving sectors is equal to the number of stationary sectors, a moving sector being placed between two stationary sectors, and _vice versa_. 4. That when the angle =A O B= is an _odd_ aliquot part of a circle, the two last sectors adjacent to each other are either both in motion or both stationary, the number of moving sectors being greater by one when the number of sectors is 3, 7, 11, 15, etc., and the number of stationary sectors being greater by one when the number of sectors is 5, 9, 13, 17, etc. And, 5. That as the moving sectors correspond with those in which the images are inverted, and the stationary ones with those in which the images are direct, the number of each may be found from the table given in page 24. When one of the mirrors, =A O=, is stationary, while the other, =B O=, is moved round, and so as to enlarge the angle =A O B=, the object =X=, and the image of it seen in the stationary mirror =A O=, remain at rest, but all the other images are in motion receding from the object =X=, and its stationary image; and when =B O= moves towards =A O=, so as to diminish the angle =A O B=, the same effect takes place, only the motion of the images is towards the object =X=, on one side, and towards its stationary image on the other. These images will obviously move in pairs; for, since the fixed object and its stationary image are at an invariable distance, the existence of a symmetrical arrangement, which we have formerly proved, requires that similar pairs be arranged at equal distances round =O=, and each of the images of these pairs must be stationary with regard to the other. Now, as the fixed object is placed in the sector =A O B=, and its stationary image in the sector =A O _b_=, it will be found that in the semicircle =M _b e_=, containing the fixed mirror, the 1st reflected image and direct object, } 2d 3d reflected image } 4th 5th } are stationary with 6th 7th } respect to each other. 8th 9th } while in the same semicircle =M _b e_=, the 1st reflected image and 2d reflected image } 3d 4th } 5th 6th } are movable with 7th 8th } respect to each other. 9th 10th } On the other hand, in the semicircle =M _a e_=, containing the movable mirror, the phenomena are reversed, the images which were formerly stationary with respect to each other being now movable, and _vice versa_.