Obsetvations upon Boutigny's recefit Experiment, 137 



but the advantage of (6.)j resulting from the relations between 

 ifjy k) is well known. 



It may be further remarked, that although 



(w, 0, 0, 0) = R„ ,^2.3K 0, 0, 0)=Qo 

 (0, x, 0, o) = R_,o_3, 2(^7,0, 0, 0) = iQo' 

 (0, 0, J/, 0) = R_, 3 „ _,(^,0, 0, 0)=iQo" 

 (0, 0, 0, 2) = R_3 .,, ,_,(2;,0,0,0)=/5:Qo"'^ 



(8.) 



(where the meanings of the expressions Qq, Qo', Qo"j Qq'" ^^^ 

 obvious), and consequently by (7.) 



Q=Qo+^Qo'-f-iQo"+^Qo" • • • • (9-) 



(an expression of the same form as (6.)) ; yet this would not be 

 sufficient for the present purpose, for all the terms on the 

 right-hand side of this equation are themselves quaternions, 

 while the object of the transformation is to exhibit a quater- 

 nion under the form of a series of terms, which admit of being 

 combined by laws in some degree analogous to those of ordi- 

 nary algebra. That expressions of the form (9.) admit of 

 such combinations is certainly true ; but this can be proved 

 only by means of some such formula as (6.). 



As I do not propose to enter at present upon the general 

 idea of this calculus, I will only add, that the form of the ex- 

 pression (3.) seems worthy of attention, from the similarity of 

 the combinations of Rq, Rj, Rg, R3 in it, and those of w, «•, 

 1/i 2,... in the squares and products of quaternions. 



XIX. Observations upon M. Boutigny's recent Experiment. 

 By Professor Plucker of Bonn*, 



IT may perhaps be a matter of interest to you to obtain a 

 confirmation of Boutigny's recent experiment. With his 

 usual kindness, he exhibited to me last Easter his former ex- 

 periments; and whilst admiring his rare perseverance in fol- 

 lowing up a fertile idea, I then acquired an impression that it 

 referred to a law of nature which was by no means com- 

 pletely revealed, and in which opinion I was further strength- 

 ened by the report of his last experiment. In consequence 

 of an oral communication of this experiment, M. Fessel wrote 

 to me from Cologne, stating that on the following day he had 

 dipped his finger into lead heated to its highest point, by 

 • From Poggendorff's Annalen, Dec. 7> 1849. 



