Dr. A. Paalzow on the Heat of the Electric Spark. 4*27 



the axis of revolution and which pass through the fixed points ; 

 or we may suppose that this restriction is not imposed. We 

 have hitherto considered the problem without the restriction ; 

 it is easy to see that the investigation will require only a slight 

 modification if the solid should stretch beyond the space bounded 

 by the two fixed planes just mentioned. 



If, however, the restriction be imposed, the solution already 

 obtained holds so long as the given surface is not greater than 

 that of a sphere described on the given length of axis as a dia- 

 meter ; when the given surface is greater than this, the solu- 

 tion is, I believe, that which was proposed in the ' History of 

 the Calculus of Variations/ page 410, and adopted in the Phi- 

 losophical Magazine for August 1861 and September 1862. 



In conclusion I will state briefly the grounds on which I con- 

 sider that the results published in the Philosophical Maga- 

 zine for March 1866 are unsatisfactory. In the first place, the 

 solutions there obtained do not satisfy the fundamental condition 

 A = 0; and in the second place, they are liable to the objection 

 which I have drawn from the admitted result respecting a sphere. 



Cambridge, May 9, 1866. 



LXIII. On the Heat of the Electric Spark. 

 By Dr. A. Paalzow*. 



TO test an electrical exploding-apparatus, the fuse of which 

 is to be ignited by one spark, we must possess some know- 

 ledge of the heat of the electric spark itself. Investigations have 

 already been made on this subject; the earlier results will be 

 found collected in Kiess's workf, whilst later researches on the 

 question have been communicated by PoggendorffJ and Reit- 

 linger§. Their experiments have shown that when a series of 

 sparks from the electrical machine or the induction-coil is dis- 

 charged between wood and wood, or wood and metal, a consi- 

 derable rise of temperature is the result. The production of 

 heat, however, by the single sparks of a battery of Ley den jars 

 could not be proved. Neither a mercurial thermometer nor a 

 thermopile with galvanometer, when in the immediate neigh- 

 bourhood of the discharge, was in the slightest degree affected. 

 When, however, the platinum wire of Riess's air-thermometer 



* Translated from the Monatsbericht of the Academy of Sciences of 

 Berlin, November 1865, p. 563. 



f Lehre von der Reibunyselektricitdt, §§ 550 and /00. 



X Berliner Monatsbericlite (1861) pp. 349-377 ; Pogg. Ann. vol. xciv. 

 pp. 310 and 632-637 ; vol. cxxi. p. 307. 



§ Zeitschrift fur Math, und Phys. vol. viii. pp. 146 -149. 



