372 Royal Society, 



in or about the 43rd parallel of south latitude j and to the south-east 

 of the Island of Madagascar, a situation extremely convenient for 

 ascertaining its exact position, which he considers as an object of 

 great theoretical as well as practical importance. 



The reading of a paper was then commenced, entitled, " An Ex- 

 perimental Inquiry into the Cause of the grave and acute Tones of 

 the Human Voice." By John Bishop, Esq. Communicated by 

 P. M. Roget, M.D., Sec. U.S. 



February 26. — The reading of a paper, entitled, " An Experimental 

 Inquiry into the Cause of the grave and acute Tones of the Human 

 Voice." By John Bishop, Esq. Communicated by P. M. Roget, M.D., 

 Secretary to the Royal Society, was resumed and concluded. 



The author considers all the theories hitherto proposed respecting 

 the functions of the organs of the human voice, as not only unsatis- 

 factory, but as being founded on erroneous views. He shows that 

 the modulation of the tones of the voice is not the result of variations 

 either exclusively in the length or in the tension of the vocal chords, 

 or in the size of the aperture of the glottis, or in the velocity or the 

 temperature imparted to the air in its transit through these passages. 

 He regards the organs of the voice as combining the properties of wind 

 and of stringed musical instruments ; and shows, first, that for the pro- 

 duction of any musical tone it is necessary that the vocal chords should 

 previously be made mutually to approximate ; and, secondly, that the 

 muscular forces acting on the arytenoid cartilages and vocal chords 

 are adequate not only to resist the pressure of the column of air issu- 

 ing from the lungs, but also to render either the whole or certain 

 portions of the vocal chords susceptible of vibration when traversed 

 by the current of respired air. In proportion as these parts of the 

 vocal chords, thus rendered vibratory, increase in length, the number 

 of their vibrations, performed in a given time, diminishes, and the 

 tone of the sound emitted becomes, in consequence, more grave; 

 and, conversely, the tone is more acute as the vibrating portions of 

 the chord are shorter : these phsenomena being precisely analogous 

 to those which take place in stringed musical instruments. 



The author concludes his paper with some observations on the 

 comparative physiology of the voice; and on the extensive range and 

 superior excellence of this faculty in man. 



March 5. — A paper was read, entitled, " A new Method of dis- 

 covering the Equations of Caustics." By G. H. S. Johnson, M.A., 

 Tutor of Queen's Collea^e, Oxford. Communicated by the Rev. 

 Baden Powell, M.A., F.R.S. 



Peculiar difficulty has hitherto attended the determination of the 

 equation of the curve formed by the perpetual intersection of rays, 

 which, diverging from a luminous point, are reflected by a polished 

 surface of a given curvature. Curves of this description have been 

 denominated caustics ; and the method usually employed to discover 

 their polar equations, or the relation between the radius vector of any 

 point of the curve and the tangent at that point, is both long and in- 

 elegant, and is considered by the author as involving considerable 

 inaccuracy of reasoning. He proposes, therefore, to substitute a new 



