102 



For the solution of mechanical problems, two methods in general 

 present themselves : the one furnished by the variation of parameters, 

 or constants, which complete the integral obtained by the first ap- 

 proximation, — the other furnished by;the integration of the differen- 

 tial equations by means of indeterminate coefficients, or some equi- 

 valent method. Each of these methods is applicable to the theory of 

 the perturbations of the heavenly bodies, and they lead to expressions 

 which are of course substantially identical, but which do not appear 

 in the same shape except after certain transformations. 



The object of the author in the present paper is to effect transforma- 

 tions, by which their identity is established, making use of the de- 

 velopments given in his former papers, published in the Philosophical 

 Transactions. The identity of the results obtained by either methods 

 affords a confirmation of the exactness of those expressions. 



Sir Charles Bell's paper "On the Organs of the Human Voice" 

 was then read in continuation. 



February 16, 1832. 



HIS ROYAL HIGHNESS THE DUKE OF SUSSEX, K.G., 

 President, in the Chair. 



The reading of Sir Charles Bell's paper " On the Organs of the 

 Human Voice " was resumed and concluded. 



The author complains that the actions of the organs of the voice 

 have been negligently treated by physiologists, and that many of 

 the offices of the structures subservient to that function have been 

 overlooked ; and expects that the study of them will lay a founda- 

 tion for prosecuting the intricate anatomy of the nerves of the 

 neck, which he proposes to himself as an ulterior object. The 

 subjects to which he particularly directs his attention in the present 

 paper, are the Muscularity of the Trachea, the Position of the 

 Thyroid Gland, and the Action of the Pharynx, which he alleges to 

 have been entirely omitted in previous systematic accounts of 

 articulate language. 



The trachea is strengthened by imperfect circles of cartilage, 

 the ends of which are united at the back part of the tube by a 

 transverse layer of muscular fibres,— a structure which is very dis- 

 tinctly seen in the horse. This transverse muscle is an antagonist 

 to the elasticity of the cartilages, and the effect of its action during 

 expiration is, by contracting the diameter of the tube, to favour the 

 propulsion of the mucous secretion, which may have been accumu- 

 lated in the passage, and to contribute effectually to expel it by the 

 effort of coughing. The same action leads also to the expulsion 

 of foreign bodies which may have accidentally got into the trachea. 

 In birds, where the inner surface of the passage is without moist- 

 ure, no such provision was required ; and accordingly we find the 

 cartilages of the trachea are complete circles, not admitting of con- 

 traction. 



