1877.] On the Length of the Voltaic Spark. 227 



The properties here considered are those which appertain to the 

 points, if any, through which all the surfaces pass, or, as they may 

 be termed, the principal points of the system, and they consist mainly 

 in the nature of the contact of the hyperjacobian surfaces with the sur- 

 face U, and the multiplicity of the hyperjacobian curve at the points in 

 question. 



The present investigation extends to the cases of two-branch contact 

 of the given surface with a one-fold and with a two-fold pencil, and of 

 three-branch contact with a four-fold pencil. In the latter case notice 

 is also made of some properties appertaining to the points, if any, where 

 all the surfaces touch one another, or, as they may be termed, the 

 secondary points of the system. In particular it is shown that in the 

 case of common, or two-branch, contact and a one-fold pencil the jaco- 

 bian curve has a double point at the principal points ; while in the case 

 of three-branch contact and a four-fold pencil the hyperjacobian curve 

 has a triple point at the same points. 



II. " On the Length of the Spark from a Voltaic Battery in dif- 

 ferent Gases at ordinary Atmospheric Pressures.". By Warren 

 De La Rue, M.A., D.C.L., F.R.S., and Hugo W. Muller, 

 Ph.D., F.E.S. Received May 17, 1877. 



W e venture, in anticipation of a more detailed account, in course of 

 preparation, of our experiments with the chloride-of-silver battery which 

 have engaged our attention for more than three years, to lay before the 

 Society the results of some investigations we were induced to make in 

 consequence of phenomena we have observed in the voltaic discharge in 

 different residual gases contained in vacuum tubes. "We have found, as 

 we anticipated we should do, that the length of the spark at ordinary 

 atmospheric pressures in the following gases is the longest in the order 

 in which they are enumerated — hydrogen, nitrogen, air, oxygen, carbonic 

 acid — it being nearly twice as long in hydrogen as in air. The spark 

 in air between a point (positive) and a plate (negative) with our battery 

 of 8040 cells is about 0*34 in., and in hydrogen 0*60. We may mention 

 that we are making up our battery to 10,440 cells. The length of the 

 spark does not appear to be dependent on the specific gravity of the 

 gas, but may have some relation to its viscosity. 



e2 



