26 Sir W. Rowan Hamilton on Quaternions. 



The two metallic caps of a high insulated glass cylinder 

 were connected by a freshly split leaf of mica in the interior 

 of the cylinder: either cap discharged an electrometer on 

 touching the other with the hand. When however the air 

 was rarefied in the cylinder to two lines barometrical pressure, 

 the electrometer was not discharged, for then the leaf of mica 

 insulated completely. The insulation lasted for twenty-two 

 hours, when on admitting a small quantity of air insulation 

 was again destroyed, and the mica conducted as well as 

 before. 



Exposed to the air, mica retains this property but a short 

 time. In a few hours parts of the fresh surface become dim 

 when breathed on; in a day or two the whole surface, and 

 the mica then insulates to a considerable extent. 



The property of not becoming dim when breathed on is 

 common to the scaly varieties of gypsum, and probably to 

 other minerals. Calcareous spar possesses the property in a 

 very slight degree, and loses it in a few minutes. 



VI. On Quaternions ,- or on a New System of Imaginaries in 

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

 V.P.R.I.A., F.R.A.S., Correspondifig Member of the Insti- 

 tute of France, Member of several other Scientific Societies in 

 these and in Foreign Countries, Andrews' Professor of Astro- 

 nomy in the University of Dublin , and Royal Astronomer of 

 Ireland. 



[Continued from vol. xxvi. p. 224.] 



18. 'TPHE separation of the real and imaginary parts of a 

 A quaternion is an operation of such frequent occur- 

 rence, and may be regarded as being so fundamental in this 

 theory, that it is convenient to introduce symbols which shall 

 denote concisely the two separate results of this operation. 

 The algebraically real part may receive, according to the 

 question in which it occurs, all values contained on the one 

 scale of progression of number from negative to positive infi- 

 nity ; we shall call it therefore the scalar part, or simply the 

 scalar of the quaternion, and shall form its symbol by prefix- 

 ing, to the symbol of the quaternion, the characteristic Seal., 

 or simply S., where no confusion seems likely to arise from 

 using this last abbreviation. On the other hand, the alge- 

 braically imaginary part, being geometrically constructed by 

 a straight line, or radius vector, which has, in general, for 

 each determined quaternion, a determined length and deter- 

 mined direction in space, may be called the vector part, or 



