Sir W. Rowan Hamilton on Quaternions. 305 



ascertained that a current of steam passing through the tin 

 pipe simultaneously with a current of drops of water produces 

 no electricity of condensation, provided the air is not admitted 

 at the same time. This result is, as far as the electricity of 

 condensation is concerned, similar to those of (89.), in which 

 the necessity of a good supply of air is fully seen. 



I do not here give the details of the above experiments, 

 being willing that they should form part of a paper which I 

 hope shortly to communicate. 



I am, Gentlemen, 



Your very obedient Servant, 

 7 Prospect Place, Ball's Pond Road, Reuben Phillips. 



March 5, 1850. 



XXXVIII. On Qiiaternions ; orona New Systemof Imaginaries 

 in Algebra. By Sir William Rowan Hamilton, LL.D.^ 

 M.R.I. A. i F.R.A.S., Corresponding Member of the Insti- 

 tute of France^ Src., Andrews' Professor of Astronomy in the 

 University of Dublin ^ and Royal Astronomer of Ireland. 



[Continued from vol. xxxv. p. 204.] 



88. ^T^HE writer desires to put on record, in this place, 

 J- the following enunciations of one or two other theo- 

 rems, out of many to which the quaternion analysis has con- 

 ducted him, respecting the inscription of gauche polygons in 

 surfaces of the second order; without yet entering on any 

 fuller account of that analysis itself, than what is given or 

 suggested in some of the preceding articles. See the Num- 

 bers of the Philosophical Magazine for August and September 

 1849. And in the first place he will here transcribe the me- 

 morandum of a communication, hitherto unprinted, which was 

 sent by him, in the month last mentioned, to the Mathematical 

 and Physical Section of the Meeting of the British Association 

 at Birmingham. 



89. Conceive that any rectilinear (but generally gauche) 

 polygon of « sides, bb,B2..b„_i, has been inscribed in any 

 surface of the second order ; and that n fixed points, Aj, Ag, 

 . . a„, not on that surface, have been assumed on its n success- 

 ive sides, namely Aj on bBj, Ag on BiBg, &c. Take then at 

 pleasure any point p upon the same surface, and draw the 

 chords PAjPj, PjAjPg) . .Pra-iA„p„, passing respectively through 

 the n fixed points (a). Again, begin with p„, and draw, 

 through the same n points (a), n other successive chords, 

 P„AiP„+„ p„+iA2P„+2, ..P2„_i A„P2„. Again begin with P2„, 

 and draw in like manner then chords, P2„AiP2„+i, P2n+iA2P2«+2» 

 . . P3n_iA„P3a. Then one or other of the two following 



