Motions of mediately agitated Membranes. 339 



which the sand remains, varies as in No. 2 ; and becomes, as the 

 tone of the organ-pipe gets still higher, as in No. 3, 4, 5, 6, 

 where the boundary lines merely consist of four parallel lines. 

 In this manner the boundary lines which at first intersected 

 each other at right angles, are changed into parallel lines. 

 This transmutation may also be effected as represented at fig. 

 2, 3, 4, 5, 6, 7. 



In the same manner four parallel nodes may pass into two 

 parallels which have towards the former a perpendicular po- 

 sition, as shown at fig. 8 ; or four parallel nodes may change 

 into four others intersected by two more perpendicularly, as 

 shown in fig. 9. Other remarkable changes of the position 

 and number of these boundary lines with increasing velocity 

 of the agitating concussions, are seen in fig. 10, 11, 12, 13. 



From these experiments it may be seen that there is a possi- 

 bility of several transitions of one and the same sand-figure to 

 another; as for instance, fig. 10. and fig. 11. The question is, 

 what is it that produces any particular transition? Savart 

 mentions a criterion by which, from the first alteration of the 

 figure, it may be foretold what transition will ensue. He says: 



First. On proceeding from a figure of nodes intersecting each 

 other at right angles, the character of the following changes 

 depends on the magnitude of the vertical angle on the points of 

 intersection separate from one another. This is very apparent 

 in the comparison of fig. 10. with fig. 11. which both form 

 transitions of four parallels, from two other lines normally 

 crossed, into six parallel lines. 



Secondly. If, on the contrary, we have at first only parallel 

 nodes, we may say that the character of the following changes 

 depends on the difference of the curves which these lines may 

 receive, which is distinctly seen from the. same figures (10. and 

 11.), if one begins backwards (from No. 5, 4.); for in fig. 10. 

 the nodes curve inward, whilst in fig. 11. they curve outward. 

 The transitions are particularly remarkable when the lines 

 form two curves outward, and one inward, or vice versa; or 

 when they form three curves outward, and two inward, &c. 

 of which fig. 12. and fig. 13. furnish remarkable instances. 



Circular and triangular membranes produce analogous phe- 

 nomena. On a circular membrane, three diametrical lines 

 may in this manner be produced, and these may be gradually 

 again changed into one diameter and one circular line (fig. 14.). 

 Moreover, on a circular membrane five diametrical lines may 

 be produced and gradually changed into five parallels, as 

 shown in fig. 15; and these five parallels may again be trans- 

 formed into one diametral and two circular lines. 



Very narrow long rectangular strips show similar phamo- 

 2X2 mena. 



