106 Proceedings of Boy al Society of Edinburgh. [jan. 31 , 
of various sizes for test-tubes. By placing the test-tubes in 
inverted positions (as in fig.), the heated air rises in the tubes, and 
a current of air in each tube is formed, and thus destroys all 
organisms and their spores, for they are detached by these currents 
(of heated air rising), and exposed on all sides to the full heat of 
the oven. 
Monday, *7th February 1887. 
The Hon. Lord M‘LABEN, Vice-President, in the Chair. 
1. On Cases of Instability in Open Structures. By E. 
Sang, LL.D. 
{Abstract.) 
In the course of some remarks on the design proposed for the 
Forth Bridge, the author of this paper had enunciated the remark- 
able theorem, that any symmetric structure built on a rectangular 
base, and depending on linear resistance alone, is necessarily unstable. 
The proof of it, given in the eleventh volume of the Transactions of 
the Royal Scottish Society of Arts , is derived from considerations 
affecting the special case ; but this theorem is only one of an ex- 
tensive class, and therefore the subject of instability among linear 
structures in general is here taken up. 
In the case of regular or semi-regular arrangements, having the 
corners of an upper supported from the corners of an under polygon, 
it is shown that when the figures are of odd numbers the structures 
are stable, while those with even numbers are unstable ; unless in- 
deed the polygons be placed conformably, in which case the stability 
extends to both classes. 
The paper ends with the following admonition : — These cases 
of instability in open structures have been elicited by means of the 
simplest considerations in geometry and statics they lie indeed 
on the very surface of mechanical inquiry. They do not occur as 
isolated examples, but are arranged in extensive groups ; and, being 
found in those classes of structures which may be called shapely, 
they stand out as warning beacons to those engaged in engineering 
pursuits. 
