691 



From some investigations effected by interchanging the symbols 

 X and D in the solution of the general linear equation in finite dif- 

 ferences of the first order, it would seem that definite summations 

 may be used to represent the solutions of certain forms of equations. 

 Thus a partial solution of 



is c2(r2)»£-^ from = — cx to ^ = 0. 



7. In attempting the solution of some equations by means of suc- 

 cessive operations, not consisting exclusively of D combined with 

 constants, but involving also functions of x, the only result which 

 appeared to the author worthy of notice is the solution of 



D2w + 6DM-f c%-7z(/i+ 1)^^=X ; 



from a particular case of which, the general solution of Laplace's 

 equation, 



may be found in the simple form 



with a similar function using — ^^ — 1 for ^ — 1. 



7. Researches on the Function of the Intercostal xMuscles and 

 on the Respiratory Movements, with some remarks on Muscular 

 Power, in Man." By John Hutchinson, M.R.C.S. Communicated 

 by Sir Benjamin Brodie, Bart., F.R.S., Sec. 



The object of this paper is to demonstrate by models and dis- 

 sections the action of the intercostal muscles. 



After premising an account of the views of several eminent phy- 

 siologists, and in particular those promulgated by Haller, the author 

 shows that they resolve themselves into the general opinion that the 

 scalene or other muscles of the neck fix the first rib, in order to 

 enable the two sets of intercostal muscles to act either separately or 

 conjointly, as inspiratory or expiratory muscles. He then proceeds 

 to state the proofs that the intercostal muscles possess an action 

 which is independent of any other muscle, and also independent of 

 each, other, so that any of the twelve ribs may be elevated or de- 

 pressed by them either separately or conjointly. He demonstrates 

 the nature of this action by means of models, producing oblique 

 tensions between levers representing the ribs, and allowing of rota- 

 tion on their centres of motion ; and he shows that such tension in 

 the direction of the external intercostal muscles, elevates both the 

 levers until the tension ceases, or the position of the bars by proxi- 



