'RADIAL SHOOTS. MECHANICAL HYPOTHESIS OF LEAF-POSITION 75 



one can easily convince oneself by means of a cardboard model that, in con- 

 sequence of longitudinal pressure, the angle of the span-roof must increase, and 

 that the foot-points must be pushed away from one another. The apex of the 

 span will then not only sink but will also suffer a lateral displacement in a direction 

 towards the longer rafter. A limit to this displacement is reached in our example 

 when the organ 37 comes into contact with organ 29, and the angle between the 

 third and fifth rows has increased to 120 (see Fig. 34). When this occurs the 

 organs of the third and fifth rows touch not only one another but also those on 

 the eighth row (that is to say 27, 19, n ....). If the pressure continues the 

 contact with the third row ceases, and the fifth and eighth form a new span in which 

 the features which have been described are repeated. As however the longer 

 rafter will now lie upon the opposite side, the lateral displacement must also take 

 place in the opposite direction. If the apical angle again reaches 120 the thirteenth 



FIG. 34. 



FIG. 33. Scheme of the arrangement of cylindric 

 organs. After Sch \vendener. 



FIG. 34. Position of organs derived by longitudinal pres- 

 sure from that shown in Fig. 33. After Schwendener. 



FIG. 33. 



row will come into contact, and if the pressure continues contact with the organs 

 of the fifth row ceases, the eighth and thirteenth row will then form a span, and 

 so on the process will go so long as the longitudinal pressure lasts, and the 

 twenty-first, the thirty-fourth, and the fifty-fifth rows will successively come into 

 contact. In consequence of this alternating combination of the series the single 

 organs move slowly to and fro, oscillating as it were about a middle position. 

 These oscillations however decrease in amount step by step, because the base of 

 the span sinks lower with each change of the contact-line to an always smaller 

 fraction of the original amount. Schwendener has calculated accurately the course 

 of these oscillations. If we start from the | position the oscillations always 

 approach more and more the known limiting value of 137 30' 28"; the 



