1863.] 481 



III. Supplement to a Paper " On the Differential Equations of 

 Dynamics." By Professor GEORGE BOOLE, F.R.S. Re- 

 ceived February 9, 1863. 



(Abstract.) 



It is sbown in the general paper that if an integral of any one 

 equation of the peculiar system of (partial differential) equations 

 there discussed be found, then if a certain numerical result of sub- 

 sequent and always possible operations prove odd, an integral of the 

 entire system can be found by the solution of a single differential 

 equation of the first order. It is shown in the paper now sent that, 

 when the above numerical result is even*, we can reduce the original 

 system of partial differential equations into a new system, fewer in 

 number by unity at least, and of the same general character, so as 

 to admit of a repetition of the same procedure. Thus the common 

 integral sought will finally be given either by the solution of a single 

 differential equation of the first order, or by finding one integral of 

 the single partial differential equation, which, in the most unfavour- 

 able case conceivable, will remain at last. 



March 19, 1863. 



Major-General SABINE, President, in the Chair. 

 The following communications were read : 



I. "On Peculiar Appearances exhibited by Blood-corpuscles 

 under the influence of Solutions of Magenta and Tannin/' 

 By WILLIAM ROBERTS, M.D., Physician to the Manchester 

 Royal Infirmary. Communicated by Dr. SHARPEY, Sec. 

 R.S. Received February 18, 1863. 



The object of the following paper is to give an account of certain 

 observations which seem to indicate that the cell- wall of the verte- 

 brate blood-disk does not possess the simplicity of structure usually 

 attributed to it. 



It is well known that the blood-corpuscles, when floating in their 

 cwn serum, or after having been treated with acetic acid or water, 

 * Also when odd, but then not required. 



