38 " Prof. Rood on some Experiments connected 



equation becomes 



(a, b, c, djx, yfx+{a\ V, c', cl'Jx, y) 3 z = 0. 



And by means of the equation xiv—yz = of the quadric surface 

 this is reduced to 



(a, b, c, djx, yf + a'x' 2 z + Sb'xyz + Sc'y' 2 z-{-dyw = 0, 



which is the equation of a cubic surface containing the line 

 (#=0, y = 0) twice, and therefore along this line touching the 

 quadric surface xw — yz = 0; and consequently intersecting it 

 besides in a quartic curve. And in like manner for the curves 

 of the fifth and higher orders which lie upon a quadric surface. 

 . The combination of the equations 



shows at once that two curves on the same quadric surface of the 

 species (p, q) and (p' } q') respectively intersect in a number 

 {pq' -\-p'q) of points. Thus if the curves are (1, 0) and (1, 0), or 

 (0, 1) and (0, 1), i. e. generating lines of the same kind, the num- 

 ber of intersections is 1.0 + 0. 1=0; but if the curves are (1, 0) 

 and (0, 1), i. e. generating lines of different kinds, the number 

 of intersections is 1 .1+0.0=1. 



The notion of the employment of hyperboloidal coordinates 

 presented itself several years ago to Prof. Pliicker (see his paper 

 "Die analytische Geometrie derCurven auf den Flachen zweiter 

 Ordnung und Classe," Crelle, vol. xxxiv. pp. 341-359 [1847]) ; 



but the systems made use of, e. g. £ = , 77= — , with 



f 1 V H' x 



z(z + d)+fixy = for the equation of the surface of the second 

 order, is less simple; and the question of the classification of 

 the curves on the surface is not entered on. 



2 Stone Buildings, W.C., 

 May 24, 1861. 



VII. On some Experiments connected with Dove's Theon/ of 

 Lustre. By Prof. 0. N. Rood, of Troy*. 



IN the Farbenlehre, p. 177, Prof. Dove writes, "In every 

 case where a surface appears lustrous, there is always a 

 transparent or translucent reflecting stratum of minor intensity, 

 through which we see another body. It is therefore externally 



* From Silliman's American Journal for May 1861. 



