INSTABILITY IN OPEN STRUCTURES. 



327 



He connected three points in the stationary part of the instrument with three 

 points in the ground by means of six straight rods inclined to each other. In 

 this arrangement, the stability in every direction is derived from the resistance 

 to longitudinal compression, the flexure of the rods having an infinitesimally 

 small influence. It takes essentially the form of 

 the octahedron or sixnib, as in fig. 10 ; a self-rigid 

 structure having six connected points. 



This beautiful Robinson stand keeps the alt- 

 azimuth so firmly in position that, even during a 

 heavy gale, the image of the moon may be seen to 

 move without tremour across the cobwebs of the 

 field-bar. Yet it has not been adopted by engineers 

 and surveyors ; the exigencies of the photographer, 

 however, have determined his recourse to it. 



It is not essential that the supports meet two 

 and two as in this arrangement ; they may be quite 

 detached, connecting six points in the supported Fig. 10. 



structure with six points in the ground ; but in all cases they must be so dis- 

 posed that any dislocation whatever would imply a change in the length of 

 some of them. 



It might have sufficed merely to remark that this condition excludes the 

 parallelism of the supports ; but it is expedient to insist, seeing that, in the 

 deplorable case of the Tay Bridge, the fabric was set upon two rows of upright 

 columns. The opinion is still held that the effective base is equal to the whole 

 breadth of such a structure, whereas the most casual examination may show 

 that, no matter how broad the structure may be, its effective base is only that 

 of a sinele column. 



When the superstructure is not rigid in itself, or indeed whether it be so or 

 not, the entire number of the members above the ground must be thrice that 

 of the supported points. If we attempt to do with fewer the fabric must fall ; 

 if we place more we cause unnecessary internal strains. I hope in a subse- 

 quent paper to treat of redundancy, meantime our attention may be confined 

 to structures having the proper number of parts. 



If the supported points belong to one system they must be mutually con- 

 nected, and, at the least, there must be as many of these connections as there 

 are points, less one, wherefore the number of supports can never exceed twice 

 the number of the points by more than one. 



Out of the endless variety of cases we may select one class for examination, 

 that in which the supported points are connected so as to form a polygon, not 

 necessarily all in one plane. The number of the connections being already n, 



