( 787 ) 



to the riglit and likewise of course by a reflection preceded or 

 followed l)v a double rotation eqniaiignlar to the left." 



The |)iane of rolalion of the equiangular (h)uble rotation passing- 

 through tlie axis of rellectiou remains for both parts of the trans- 

 fornialion in an unaltered position; it undergoes by the double rotation 

 a congruent Iransformation and by the reflection a symmetric one. 



The plane of I'olation of the equiangular double rotation situated 

 in the space per|)eiidicular to the axis of reflection i-emains also for 

 Itolli parts of the transformation in an unaltered position; it is not 

 transformed at the reflection and undergoes by the double rotation 

 a congruent transformation. 



Those t\vo |»lanes of rotation are perpendicular to each other, so 

 that geometrically the wellknown property is proved: 



"For synunetric transformation of S^ about a fixed point one pair 

 of jilanes remains at its place; and one phuie of it is transformed 

 congruently, the other symmetrically." 



Physics. — "Oh the equations of Clausius and van der Waals /}//■ 

 the /nean /eiu/th of path and the ntiinher of collision.s." By 

 Dr. Pn. KouNSTAMM. (Comnuinicated by Prof, van der Waals). 



Several of the methods ])roposed for the derivation of tlie equation 

 of state, make use of formulae for the mean length of path. It is 

 therefore not to be expected that we shall arrive at undoubted results 

 as to the former, so long as the results as to the latter quantity are 

 not concordant. Now it is generally known that van der Waals has 

 found for the length of path and the numl)er of collisions in a gas 

 with perfectly hard, perfectly elastic spherical molecules: 



V — h u jr ns^ — 



^-= 7- ^= — r^ (^) 



vT US' r V — 



It does not seem to be so generally known, that Clausius^) and 



in accordance with him Jager ^) and Boltzmann ^), have obtained 



another result, viz : 



b lib 

 ^ 1—2 — 1 



1=-^^ ^ P=1^7— 1^. . . (2) 



mns'' r . 11 ^ V 1 o^ 



~¥ V ~ V 



1) Kinetische Theorie der Gase, p. 60. 



2) Wien. Sitzungsber. 105, p. 97. 

 '^j BoLTZMANN GaslheoHe, p. 104. 



52^ 



