204 Dr. Schunck on Colouring Matters. 



larly by any one common surface (notwithstanding the analogy 

 of their arrangement, or distribution in space, in many respects, 

 to that of the normals to a surface). In fact, the two systems 

 of developable surfaces, (d') and (d"), are not generally rect- 

 angular to each other, in the arrangement here considered, 

 though they are so for any system of normals. 



XIV. Through any given point of space, A2m+i» which is at 

 once exterior to the inscribed ellipsoid (e'), and to both sheets 

 of the exscribed hyperboloid (e"), it is in general possible to 

 draw two, and 07ily two, distinct and real straight lines, p'p'2m 

 and p"p"2mj of which each shall touch at once a curve (c') on 

 (e'), and a curve (c") on (e"), and of which each shall coincide 

 isoith one of the positions of the closing chord, pP2,„ ; in such a 

 manner as to be the last side of a rectilinear polygon of 2m + 1 

 sides, p'p'jP'a . . p'2m5 or p"p"^p"2. . p"2,n) inscribed in the given 

 ellipsoid (e), under the condition that its sides shall pass, re- 

 spectively and successively, through the 2m + 1 given points, 

 AjAg . . A2mA2TO+i. But if the last of these points were given on 

 either of the two enx)eloped surfaces, (fJ), (e"), the problem of 

 such inscription would in general admit of only one distinct 

 solution, obtained by drawing through the given point the 

 tangent to the particular curve (c') or (c"), on which that 

 point was situated. And if the last given point A2m+i were 

 situated within the inscribed ellipsoid (e'), or within either 

 sheet of the exscribed hyperboloid (e"), the problem of the 

 inscription of the polygon of 2m + 1 sides would then become 

 geometrically impossible: though it might still be said to admit, 

 in that case, o^ two imaginary modes of solution. 

 [To be continued.] 



XXVIII. On Colouring Matters. By Edward Schunck*. 



IN the report which I had the honour of presenting last year to 

 the British Association on Colouring Matters, I gave the results 

 of my investigation of the colouring matters of madder. This in- 

 vestigation I have continued and brought to a conclusion. The sub- 

 ject has however proved so extensive, the number of questions 

 arising in regard to this valuable and extensively-used tinctorial sub- 

 stance being very great, tliat I have been unable to examme any other 

 colouring matters very minutely. 



I stated in my last report, that when finely-ground madder roots 

 are treated with hot water, a brown liquid is obtained having a 

 sweetish bitter taste, in which acids produce a dark brown precipi- 

 tate. This precipitate I stated to consist of six substances, viz. two 

 colouring matters, two fats, pectic acid and a bitter substance. To 

 these I now add a seventh : it is a dark brown substance which re- 

 • From the Report of British Association for 1848. 



