chap, xx.] SECONDARY SYMMETRY : RULES. 479 



found to hold good with certain exceptions to be hereafter 

 specified. 



I. The long axes of the normal appendage and of the 



two extra appendages are in one plane : of the two 

 extra appendages one is therefore nearer to the axis 

 of the normal appendage and the other is remoter 

 from it. 



II. The nearer of the two extra appendages is in structure 



and position formed as the image of the normal 

 appendage in a plane mirror placed between the 

 normal appendage and the nearer one, at right angles 

 to the plane of the three axes; and the remoter append- 

 age is the image of the nearer in a plane mirror 

 similarly placed between the two extra appendages. 



Transverse sections of the three appendages taken at homo- 

 logous points are thus images of each other in parallel mirrors. 



As the full significance of these principles may not be at once seen 

 it may be well to add a few words of general description. The relation 

 of images between the extra legs is easy to understand. They are a 

 complementary pair, a right and a left. This might indeed be pre- 

 dicted by any one who had considered the matter. 



The other principles, which concern the relations of the extra legs 

 to the normal leg, are more novel. For first it appears not that either 

 of the extra legs indifferently may be adjacent to the normal, but that 

 of the extra pair the adjacent leg is that which is formed as a leg of 

 the other side of the body. If therefore the normal leg bearing the 

 extra legs be a right leg, the nearer of the extra legs is a left and the 

 remoter a right. This principle holds in every case of double extra 

 appendages of which I have any accurate knowledge, where the struc- 

 ture of the parts is such that right limbs can be distinguished from 

 left. 



But perhaps of greatest interest is the fact that the inclination of 

 the surfaces of each extra leg to those of its fellow and to those of the 

 normal are determined with an approach to uniformity in the manner 

 described. 



These principles of arrangement may be made clear by a simple mechanical 

 device (Fig. 153). A horizontal circular disc of wood has an upright rod fixed in its 

 centre. This rod passes through one end of a vertical plate of wood which can be 

 turned freely upon it as an axle, so as to stand upon anj' radius of the horizontal 

 circle. The head of the axle bears a fixed cog-wheel. In the vertical wooden plate 

 are bored two holes into which two rods each bearing a similar cog-wheel are 

 dropped, so that each can rotate freely on its own axis. The three cog-wheels are 

 geared into each other. They must have the same diameter and the same number 

 of teeth. Three wax models of legs are fixed on the head of each wheel as shewn in 

 Fig. 153. In that figure, R represents the apex of the tibia and tarsus of a normal 

 right leg. The anterior surface is dark, and the posterior is white. The anterior 

 and posterior spurs of the tibia are shewn at A and P. SL and SE represent the 

 two supernumerary legs, SL being a left, SR a right. (They are supposed to arise 

 from the leg R at some proximal point towards which they converge.) When the 

 wooden plate is put so that the arrow points to the word "Posterior" on the disc, 

 the models will then take the positions they would have if they arose from the 

 posterior surface, all the ventral surfaces coming into one plane. If the arrow be 



