132 Journal of the Mitchell Society. [Dec. 



six points 1, 2, 3, 4, 5, 6; the remaining- lines are be, ca, ab; 

 gh) kf,fg, These are Pascalian lines 



be of the hexagon 162435, 



ca " 



u 



152634, 



ab " 



It 



142536, 



gh " 



It 



152436, 



hf " 



it 



142635, 



fg " 



(< 



162534, • 



which appears thus, viz. 







line be contains points bef, beg, bch. 







¥ ■ ¥ h g - c g-> hh • ch 







35 . 26, 16 . 34, 24 . 15; 



that is, be is the Pascalian 



line 



of the hexagon 162435; and 



the like for the rest of the six lines. 



The final conclusion has already been stated above in § 1. 

 The drawing- explains everything; a few words of explana- 

 tion and interpretation, however, are perhaps not amiss. By 

 means of four separate scales and the emploj^ment of a num- 

 ber of principles of Graphics, I first laid down the tetrahe- 

 dron ABCD and the fifteen lines in space, af, ag, ah) bf, bg, 

 bh, cf, eg, ch', and 1, 2, 3, 4, 5, 6. In the drawing, the pro- 

 jection of the line of is written {af), and so in other cases. The 

 projection of the line bf, for example, was found by joining 

 the meets of the lines 5 and bf with the plane of projection, 

 and similarly for other cases. Only three of the Pascalian 

 lines, viz. be, ca, ab were drawn, to avoid giving the figure a 

 too complex appearance. The projection of line ab, for exam- 

 ple, was obtained in the following manner: lines ag, bg lying 

 in planes a and b respectively intersect in a point P, say, on 

 the line ab; the projections of the points P and P x are the 

 meets of the projections of the pairs of lines ag, bg; ah, bh 

 respectively. The projection of line ab then is the join of the 

 projections of the points P and P x . 



The Steiner point S (shown in the figure), the common 

 meet of the three Pascalian lines be, ca, ab, is one of the two 



