Notices respecting New Books. 219 



triangle ABC is a semidiameter of the ellipsoid, drawn in the 

 direction of the axis of one of the two circumscribed cylinders 

 of revolution ; a property which was mentioned in the 32nd 

 article, and which may be seen to hold good, not only froni 

 the recent analysis conducted by the Cartesian method, but 

 also and more simply from the geometrical consideration that 

 the constant rectangle under the two straight lines BD and 

 AE, in the construction, exceeds the double area of the triangle 

 ABE) and therefore exceeds the rectangle under the fixed 

 line ABand the perpendicular let fall thereon from the varia- 

 ble point E of the ellipsoid, except at the limit where the 

 angle ADB is right; which last condition determines a cir- 

 cular locus for D, and an elliptic locus for E, namely that 

 ellipse of contact along which a cylinder of revolution round 

 AB envelopes the ellipsoid, and which here presents itself as a 

 section of the cylinder by a plane. The radius of this cylinder 

 is equal to the line BG, if G be the point of intersection, di- 

 stinct from A, of the side AB of the generating triangle with 

 the surface of the diacentric sphere; which line BG is also 

 easily shown, on similar geometrical principles, as a conse- 

 quence of the same construction, to be equal to the common 

 radius of the two circular sections, or to the mean semiaxis 

 of the ellipsoid, which is perpendicular to the greatest and the 

 least. Hence also the side AB of the generating triangle is, 

 in length, a fourth proportional to the three semiaxes, that 

 is to the mean, the least, and the greatest, or to the mean, the 

 greatest, and the least, of the three principal and rectangular 

 semidiameters of the ellipsoid. 



[To be continued.] 



XXXVII. Notices respecting New Books. 



Notice of a Memoir on Meteors of various sorts. By T.I. M. Forster, 

 F.R.A.S., &;c. Bruges, 1846. 



EXPERIENCED in observing and in treating of these phseno- 

 mena, Dr. Forster refers his readers to his former communica- 

 tions of them, and to the numerous articles in the Royal Society's 

 Transactions, as well as in the Gentleman's and Philosophical Ma- 

 gazines. 



He carefully examines the theory of phosphorescent jets of gas 

 rising unperceived while traversing the low and damp strata of the 

 atmosphere, but becoming ignited as soon as they reach a sufficiently 

 dry stratum. The ignition is then supposed to run down the column 

 of gas, and reveal the several bends it had been subjected to by 

 Various currents of wind. The occasional explosions may be ex- 

 plained by supposing the running fire to reach a spot overabounding 

 itl hydrogen, instances not unfrequent after heavy rains. 



