OF ARTS AND SCIENCES. 241 



of values are satisfied by the equations (27) r= 6.70 -[- .09 I for 

 the silent arc, and (28) r = 3.02 + .97 I for the whistling arc. The 

 corresponding values of the inverse electromotive force are the same 

 as before, viz. 46.9 and 21.1, respectively, showing that the changes 

 observed in the difference of potential between the carbons were due 

 to variations in the conductive resistance, and not to variations in 

 the inverse electromotive force of the arc. These resistance varia- 

 tions, while amply large to affect the readings of the voltmeter, were 

 too small to produce any sensible change in the strength of the main 

 current. It also appears by a comparison of the equations just given 

 for the shielded arc with equations (2) and (7) that the coefficient of I 

 is decidedly less with the shielded arc, showing that the conductive 

 resistance of the arc is diminished by the increased temperature, as 

 would be anticipated. The increased inverse electromotive force is 

 much greater than we had expected to find it, and at first might lead 

 one to surmise why, with the ordinary arc, the inverse electromotive 

 force does not rise with increased strength of current. This is prob- 

 ably to be explained by the fact that the chief effect of an increase in 

 current is to heat a larger area of the carbons to the same temperature, 

 rather than to raise them to a considerably higher temperature. 



Observing the position of the point of intersection of the lines repre- 

 senting the silent and whistling arcs, we find that the passage from low 

 to hiwh inverse electromotive force occurs with a length of arc of 

 3g^5 = .123 in. for the line represented by equation (26), and of 

 -*j2 9 = .131 in. for that of equation (28), which values are greater than 

 those occurring with the normal arc and the same strength of current. 

 The corresponding equivalent resistances are 7.34 ohms and 7.07 ohms. 



We next tried the reverse experiment of cooling the upper positive 

 carbon. This was done by surrounding the lower end of the carbon 

 with a brass tube through which a current of cold water flowed. The 

 negative electrode was left in its usual condition. The arc under 

 these conditions was extremely unstable; the slightest breath would 

 extinguish it, and even with a current of 10 amperes it could not be 

 elongated to a greater length than -^^ in. It was quite blue, whistled, 

 and gave but very little light. The extreme length of arc used was 

 ^^ in. with the weaker, and ^^ in. with the stronger current. Plotted 

 curves gave the following equations, satisfying the observations with 

 tolerable exactness. 



Current. Number. Equation. 



7 29 r = 1.67 + 1.11 1 



8 30 r = 0.70 -j- 1.82 / 



VOL. XXII. (N. S. XIV.) 16 



