1148 A TEXTBOOK OF THEORETICAL BOTANY 



expected to be more common than it actually is, if the parts are equidistant 

 on the axis. The valvate condition demands not only equidistant origins 

 of the primordia but an exactly equal rate of growth among them and either 

 or both of these conditions may be lacking in many flowers. Unequal 

 spacing of the primordia is less common than unequal growth, but the 

 majority of flowers are affected in some degree by these two factors, result- 

 ing in the overlapping of parts, which are then said to be imbricate. 

 Sepals are less affected than are petals, so that the calyx may often be 

 valvate while the corolla is imbricate, a condition beautifully illustrated by 

 the flowers of Fuchsia (Fig. 1123). The corolla itself, in Ailaiithus, shows 

 both conditions, the petals being valvate below and imbricate above. 



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Fig. 1 123. — Fuchsia, hybrid. Flower showing valvate 

 sepals and imbricate petals. 



Where there is a definite sequence in the appearance of primordia 

 on the axis, the successive rudiments are separated from one another, in 

 the great majority of cases, by an angle of about 140, which has been 

 interpreted, on geometrical grounds, as being an approximation to what 

 is called the limiting divergence of i37°3o'28". If the growth of such 

 rudiments were perfectly uniform, a uniform order of overlapping would 

 naturally result. This is a common arrangement and is known as the 

 quincuncial order (Fig. 1124). 



The typical quincuncial order of imbrication is that of a f spiral phyl- 

 lotaxy. Parts i and 2 overlap at both edges, being the outermost of the 

 spiral. Part 3 in the sequence overlaps with its backward edge and is over- 

 lapped by 1 at its forward edge, while parts 4 and 5 are overlapped at both 

 edges, being the innermost parts of the spiral succession. Another frequent 



