24 TEXTBOOK OF BOTANY 



numerator of any fraction in the series is equal to the sum of the two 

 preceding numerators. The same relationship holds for the denominators. 



These arrangements of leaves are not invariable. Owing to the influ- 

 ence of light on the growth of stems and leaves that are not equally illu- 

 minated on all sides, the stems become twisted and the arrangements are 

 altered. 



Other stem characters. Certain other stem characters are often used to 

 identify trees and shrubs. Since a htid is present in the axil of each leaf of 

 most deciduous trees and shrubs, bud arrangement is a useful character 

 in the dormant season when there are no leaves on the stems. Buds differ 

 in size and form in different species. Their outer scales may be smooth 

 or hairy. Leaf scars, which are left when the leaves have fallen, also have 

 rather definite shapes and patterns. The outer covering or bark of a twig 

 may be green or gray or brown, and various other descriptive terms are 

 applied to its surface, such as smooth or rough, ridged or wartv. In a 

 few instances the color and form of the pith may be distinctive. 



Keys to plants based on vegetative characters. If we examine a maple 

 tree we notice that its leaves are simple, lobed, palmatelv veined, and 

 oppositely arranged on the stem. No other trees in North America have 

 all four of these characters. The eastern hemlocks have short-petioled, 

 needle-like flattened leaves with white lines on the under surface. When 

 characters such as these are definitelv assorted and grouped so that by 

 careful reading and comparison with the specimen in hand we may deter- 

 mine the name of the plant, we have v/hat is known as a key. 



Many keys have been published for the plants of local, state, and 

 national regions. Local keys are usually more convenient because the 

 number of plants included is smaller. For the beginner those based on 

 such external characters of leaves and stems as are outlined above are 

 most useful; moreover, thev are quite adequate for the identification of 

 most trees and shrubs.^ Keys are often based on the forms and detailed 

 structures of flowers, fruits, and seeds; such kevs are necessary to identify 

 many of the common herbs. Keys based on both vegetative and repro- 

 ductive characters are more difficult to use since they imply considerable 

 knowledge of structures and terminology. 



Species and genus. No one expects anything but an oak tree to develop 

 from an acorn, or anything but a hickory tree from a hickory nut. To go 



^ Every student should find the most convenient keys to the trees, shrubs, and herbs 

 of his region. There are many keys available that cover limited areas. These have been 

 published by agricultural experiment stations, museums, state academies of science, and 

 various other institutions. 



