576 REPORT— 1897 



When the Length of the Arc is kept Constant and the Current is varied. 



1. The P.D. is in all cases bigber -witli the solid than with the cored carbon. 



2. With a solid carbon the P.D. continually diminishes as the current increases ; 

 ■with a cored carbon the P.D. either diminishes much less than with a solid carbon, 

 or remains constant for all currents above a given value, or actually increases with 

 .the current after falling to a minimum. 



Current is kept Constant and the Length of the Arc is Varied. 



1. The P.D. is always higher with solid carbons than with a cored positive car- 

 ton, but the difference between the two diminishes as the arc increases in length. 



2. The rate of change of P.D. with change of length is constant witJi solid 

 carbons, but diminishes as the length of the arc increases with a cored positive 

 carbon. 



3. This rate of change becomes smaller and more nearly constant for all lengths 

 of arc as the value of the constant current increases. 



4. The P.D. corresponding with length of arc diminishes as the current in- 

 creases with solid carbons, but increases with the current with a cored positive 

 ■carbon. 



These differences can all be accounted for on the hypothesis that icith a given 

 solid negative carbon and a positive of a given diameter the P.D. required to send a 

 yiven current through a fixed length of arc depends principally, if not entirely, on 

 the nature of the surface of the crater, being greater or less according as the carbon 

 of lohich this surface is composed is harder or softer. 



By the term ' area of the crater' is meant the area of the mouth of the crater, or, 

 etill more accurately, the plane area of that region of the end of the positive carbon 

 which is sharply cut off from the rest by its peculiar brilliance and whiteness. The 

 Jirea of the soft carbon in the surface of the crater is taken to be the projection on 

 the mouth of the crater of that area of the crater that is composed of soft carbon, 

 and the proportion of soft carbon in the surface of the crater is measured by the 

 ratio of the area of the soft carbon to the total area of the crater. This ratio for 

 each current and length of arc will be called its ' soft crater ratio.' 



The ratio of the area of the hard carbon in the surface of the crater to the area 

 of the crater will be called the 'hard crater ratio.' 



Arcs of Constant Length. 



The area of the crater is known to increase as the current increases. With a 

 •constant length of arc, therefore, when the current is very small the whole of the 

 crater will be in the core ; as the current increases some hard carbon will be em- 

 braced by the crater, and the P.D. will therefore, by the hypothesis, be higher than 

 if the whole crater were of soft carbon. The larger the current the greater will 

 Ibe the area of the crater, and consequently the greater will be the amount of hard 

 carbon in its surface ; there will be a tendency of the P.D. to rise on account of 

 this increasing amount of hard carbon in the crater, which will struggle with its 

 tendency to fall on account of the increase of the current. According as the one 

 or other of these tendencies gets the upper hand, or as they exactly counterbalance 

 one another, will the P.D. increase, diminish, or remain stationary as the cm-rent 

 increases. 



Constant Currents. 



It has not hitherto been known how the area of the crater varied with the 

 length of the arc. Hence a very good way of testing the accuracy of my hypo- 

 thesis suggested itself. The hypothesis was used in conjunction with the curves 

 ■connecting P.D. with length of arc for constant currents, to determine what should 

 "be the form of the curves connecting the area of the crater with the length of the 

 arc when the current was constant. If these curves were the same as those obtained 

 from actual measurements of the crater, the presumption would be that the 



