Mr. R. Phillips on the Magnetism of Steam. 283 



affection ( — I) 2 may always be obtained by prefixing the sign 

 — to that of radicality. 



Waiving this discussion however for the present, let us 

 admit that, in the equation X = 0, x may have given to it the 

 value x = 5( — l) 2 . Then X = is obviously satisfied. But 

 the ordinary double algebra is not relieved from its difficulty. 

 For neither 5( + l) 2 nor 5( — l) 2 will satisfy either Y=0 or 

 Z = 0. If, in the above instances, the difficulty is to be evaded, 

 it is only by greatly refining our solution, and, as it has oc- 

 curred to me, by usingexpressions of theform m{ + 1) 2 + n{ — l) 2 , 

 and by following certain rules respecting our reductions, and 

 the signs to be affixed to the radicals, To those who would 

 attempt such a complex and artificial system of solution rather 

 than admit the existence of an impossible equation I may 

 hereafter address some observations. They will however 

 probably find, as I have done, that their attempts are unsatis- 

 factory, and the results not philosophically admissible. But 

 I shall here content myself with remarking, that, by any 

 system of rules, however artificial, the difficulty is only thrown 

 further back. Thus, the equation 



is utterly intractable. 



Should the restricted view which I have taken of the sym- 

 bol */ be deemed ultimately inadmissible, it would not be 

 difficult to frame a new impossible equation, other than that 

 which I have employed in my Theory of Tessarines, and 

 which should give us a new imaginary, determined, like the 

 unreal quantities of double algebra, by means of an equation, 

 and so constituting a natural extension of that algebra. In 

 refraining the fundamental equation of the Tessarine Theory, 

 or in adopting one which should give rise to a different theory, 

 geometric interpretation should always be borne in mind, and 

 the uniaxal geometry thence arising would be as direct an 

 application of algebra as that which occurs in interpreting and 

 applying the ordinary double algebra. 



2 Pump Court, Temple, 

 August 30, 1850. 



XXXII. On the Magnetism of Steam. 



By Reuben Phillips, Esq. 



[Continued from vol. xxxvi. p. 511.] 



HHHE galvanoscope used in the following experiments 



1JO. X is a modification of that formerly described (2.). 



Instead of two astatic needles, I have employed one sus- 



