( i-is ) 



visual represeutatlou -|- ^ representation of a respiratiou-moveraent, 

 performed iu a special way. Self-observation calls this complex the 

 apperceived or the attentively observed visual representation. 



Though psychology cannot be treated now experimentally, yet the 

 theory of physiological parallel processes justifies the opinion that 

 attention and representations of movements originated by special 

 respiration movements, are closely connected. Closer investigations 

 on monkey's brains will be necessary. The other movements expres- 

 sing attention will have to be submitted to a systematical investi- 

 gation in the same way, to throw further light on the problem 

 treated in this paper. 



Physics. — yiSimplc deduction of the characteristic equation for sub- 

 stances with extended and composite molecules''. By Prof. J. D. 

 VAN DER Waals. 



If the quantity of substance inclosed in a certain volume is con- 

 sidered as consisting of material points, which may also be done 

 with extended molecules, composed of atoms, the equation 



cl ^- HIT 

 ^ i/„ m T'2 = V, _-^ y,SiX:v +Yy + Zz) («) 



holds, provided that the quantities occurring in this equation be 

 applied to all material points. 



If groups of these material points are united to separate systems, 

 as is the case with molecules, whicli cannot be considered as one 

 single point, the equation mentioned above, becomes : 



, d^-'2 mrJ^ , , d^ 22 u r,? 

 2 v. m VJ^ + 22 V. .. T- = V. -.^ + V. — ^ - 



- 1/2 :^ (X^. + Yy, + Zz,) - '/2 22 (AV, + Yy, + Zz,.) . • {b) 



in whicli the index z relates to the centres of gravity of the systems, 

 aud the value r indicates the value of a quantit\ relatively to the 

 centre of inertia. 



For the stationary condition of the centres of gravity as well as 

 of the systems themselves, this equation is simplified to: 



2 Va m T',^ + 22 '/a ft V,!^ = -'1,2 (X,r, + Yy. + Zz^) - 



- V2 ^^ (Xr, + Yy,. + Zz,) (.) 



