Om the Analysis of the Spectrum by Absorption. 461 



32. We may also say that if of a quadrilateral (ABED'), 

 of 'which one side (AB) is given in length and in position, the 

 two diagonals (AE, BD') be equal to each other in length, and 

 intersect (in D) on the surface of a given sphere (with centre C), 

 of which a chord (AD') is a side of the quadrilateral adjacent 

 to the given side (AB), then the other side (BE), adjacent to the 

 same given side, is a chord of a given ellipsoid. Tlie foi'm, 

 position, and magnitude of an ellipsoid (with three unequal 

 axes), may thus be made to depend on the form, position, and 

 magnitude of a generating tria?igle ABC. Two sides of this 

 triangle, namely BC and CA, are perpendicular to the trvo 

 planes of circidar section ; and the third side AB is perpendi- 

 cular to one of the tzvo planes of circidar projection of the ellip- 

 soid, because it is the axis of revolution of one of the two cir- 

 cumscribed circular cylinders. This triple reference to circles 

 is perhaps the cause of the extreme facility with which it will 

 be found that many fundamental properties of the ellipsoid 

 may be deduced from this mode of generation. As an ex- 

 ample of such deduction, it may be mentioned that the known 

 proportionality of the difference of the squares of the recipro- 

 cals of the semiaxes of a diametral section to the product of 

 the sines of the inclinations of its plane to the two planes of 

 circular section, presents itself under the form of a propor- 

 tionality of the same difference of squares to the rectangle 

 under the projections of the two sides BC and CA of the ge- 

 nerating triangle on the plane of the elliptic section. 

 [To be continued.] 



LXX. Observations on the Analysis of the Spectrmn by 

 Absorption. By Sir David Brewster, K.H., D.C.L., 

 F.R.S., and V.P.ll.S. Ed.* 

 1 N a paper On the Production of Light and Heat by Dr. 

 ■■- Draper, published in the last Number of this Journal, the 

 ingenious author has made some observations on my Analysis 

 of the Solar Spectrum, which it is necessary that I should 

 notice. While he admits that I have " shown \.\\a.i red, yellow, 

 bbie, and consequently white light exist in every part of the 

 spectrum," he ascribes this result to the non-coincidence, or 

 tlie overlapping of the colours of the several spectra formed 

 on a screen by the rays falling near the edge, and those falling 

 near the back of a prism with a refracting face of considerable 

 magnitude. " In such a spectnun," he says, " there must 

 undoubtedly be a general conunixture of the rays ; but may 

 we not fairly in(juire whether, if an elementary prism were 

 * Communicated by the Author. 



