( 394 ) 



as base circle we can ol)tain a circle with fiiiile radius in t. For 

 the generatrices of this cone the second point J\, coincides with the 

 second point at infinity; so the projection consists of the infinite segment 

 0,DP\ 'Mk\ the isolated second point at infinity of this line. 



For lines / outside this cone this isolated point vanishes, and on 

 account of this the second vanishing point; for its determination remain 

 however B, and the first vanishing point (),. Now however, the 

 per[)endicular OS still increasing, / can become parallel to p^, and 

 hence parallel to e or to t; it is then at right angles to the bisectrix 

 of the acute angle between ^>i and OO^, as well as ro that of the 

 right angle between e and (\\\^, which bisectrices are respecti\'ely 

 divergent. All lines showing this [)roperty form a second asymptotic 

 cone of revolution, for which however t is now the asymptotic plane; 

 they have a picture point at infinity, but are no less determined by 

 this point and the first vanishing [)oint (),. 



If / also lies outside this second cone, it becomes divergent with 

 respect to t, so it loses its picture [)oint B; but now its second point 

 at infinity lies again inside the cone x, which makes it projectible, so 

 that in this case / has two \'anislüng points but no jiicture point ; 

 however, the two vanishing points are sufficient for its determination 

 (see W. 3). The originals at infinity corresponding to it are both 

 under the picture plane; in connection with the preceding it would 

 be preferable, in order to avoid confusion, to say that / has in this 

 case two "first points at infinity" and therefore also two "first 

 vanishing points". 



The lines containing the second point at infinity J\^ of 00^ 

 behave in like manner; we again find two asymptotic cones of 

 revolution, one with the asymptotic plane t, a second with the 

 asymptotic plane t*, and we terminate with lines with two "second 

 vanishing points" and without picture point. 



Belft, September 1905. 



Physiology. — "A method for determinim/ the o.wiotic pressure 

 of very small qi(antities of liquid." By Prof. H. J. Hamburger. 



It not unfrequently happens that one wishes to know^ the osmotic 

 pressure of normal or pathological somatic tluids of which no more 

 than 7, or 7^ cc. are available. 1 recently had such a case when an 

 oculist asked me what should be the concentration of liquids used 

 for the treatment of the eye. It seemed to me to be rational — and 

 the investigations of Massart ') justified this opinion — to prescribe 



A) Massart, Archives de Biologie 9 1889, p. 335. 



