140 Mr. W. L. Upson : Observations 



nearly the truth than the original curves. From this we 

 conclude that, provided the electrodes are o£ solid materials, 

 all arcs o£ constant length are satisfied by the equation 



It is difficult to obtain long enough arcs to prove the 

 validity of a like assumption with regard to arcs of constant 

 current but variable length, which shall cover the whole 

 range of arcs in air and hydrogen. But no case has been 

 found where the arc of constant current is not represented 

 by the equation 



Y A = a + bl. 



Equations of the general form for variable length and 



current given by Mrs. Ayrton, 



c + dl 

 Y = a + bl + -^_ 



have been derived in a number of cases, as follows. 



For carbon-carbon in air, both solid, positive above, 

 0'475 in. diam. ; negative O'l in. diam. 



where I is given in millimetres. 



For copper-carbon in air, electrodes as described, 



V=14-6 + 2^ + 3 -^. 

 For iron-carbon in air, 



For iron-iron in air, the positive cooled, 



18-5 + 3-97/ 



V=18-5 + 3-97/ + 



A 



For copper-copper in air, the positive cooled, 



V = 17-4 + 3-6H 18 - 3+ A 10 -H 



For copper-copper in air, the negative cooled, 



V = 22-2 + l-5^ 31 - ] : 5 - 2 l 



