Royal Society. IAS 



The author finds that the principal results of the superposition of 

 two similar modes of vibration are the following : — first, the points 

 where the quiescent lines of each figure intersect each other remain 

 quiescent points in the resultant figure j secondly, the quiescent lines 

 of one figure are obliterated, when superposed, by the vibratory parts 

 of the other j thirdly, new quiescent parts, which may be called points 

 of compensation, are formed whenever the vibrations in opposite di- 

 rections neutralize each other ; and, lastly, at other points, the mo- 

 tion is as the sum of the concurring, or the differences of the opposing 

 vibrations at these points. After considering various modes of binary 

 superposition, the author examines the cases of four co-existing su- 

 perpositions. 



When the vibrations of the superposed modes are unequal in inten- 

 sity, there is formed a figure intermediate between the perfect re- 

 sultant and one of its compounds. These figures the author denomi- 

 nates imperfect resultants. 



In each' series of transitions there are certain points which are in- 

 variable during all the changes : these are quiescent points, formed 

 by the nodal lines of one figure intersecting those of the other, and 

 the centres of vibration, where the maxima of positive or negative 

 vibration agree in each component mode of vibration. The points of 

 compensation are changeable. Transitional figures appear when the 

 sides of the plate are nearly, but not exactly, equal. 



The author next considers the figures obtained on square plates of 

 wood and other substances, having different degrees of elasticity in 

 different directions. He concludes this part of his paper by an account 

 of some optical means of representing the figures noticed by Chladni. 



March 21. — The reading of a paper, entitled, " Experimental Re- 

 searches in Electro-magnetism," by the Rev. William Ritchie, LL.D. 

 F.R.S. was commenced. 



March 28. — The reading of Dr. Ritchie's paper was resumed and 

 concluded. 



This communication consists of three parts. In the first part the 

 author shows that the common deflecting galvanometer, in which the 

 deflecting forces are assumed to be as the tangents of deflection, is 

 founded on false principles, and consequently leads to erroneous re- 

 sults. The wire forming the coil is of considerable thickness, and 

 therefore there is no fixed zero from which the deflections can be 

 reckoned. The length of the coil, also, being generally short, occa- 

 sions another serious error, as the theoretical investigation is founded 

 on the supposition of an indefinite length. In proof of the inaccuracy 

 of the indications of the common deflecting galvanometer, the author 

 took two elementary batteries, the plates of one being one inch square, 

 and those of the other two inches. The tangents of the deflections of 

 the needle (proper precautions having been taken for the equally free 

 passage of all the electricity evolved in either case,) were very nearly 

 as 1 to 2, though it is obvious that the real quantities of voltaic 

 electricity were as 1 to 4. The author's torsion galvanometer gave 

 the degrees of torsion nearly as 1 to 4. Other experiments led to 

 similar conclusions. 



Third Series. Vol. 3. No. 14. Au«. 1833. U 



