244 PROCEEDINGS OP THE AMERICAN ACADEMY. 



Besides the shortening of the wave length due to the increased 

 self-induction of the iron, there is shown a decided increase in the 

 damping, as has already been observed by Trowbridge and Bjerknes. 

 In Fiirure 4 of the Plate the curves for iron fall below the corre- 

 spondiug ones for copper, but owing to the change in the activity of 

 the primary spark no exact measurement was made. It was only ob- 

 served that the bolometer throws with the copper circuit were always 

 greater than those with the iron circuit of same dimensions when the 

 spark was constant as far as the eye and ear could judge. 



A value for the damping factor €~27. can be calculated for the iron 

 and the copper. Lord Rayleigh's formula for the resistance under 

 very rapid oscillations is; 



R = ^/^plfxR. 



For iron wire circuit (diameter 0.1186 cm.), 



I = 1258 ; fji = A30; R= 1.67 X 109 . p = Ux lO^; 



whence 



72' = 403 X 109; Z' = 34 X 10^ 



The damping factor becomes e"*' ^ ^" '. 



The time required for the amplitude to fall to one half of its max- 

 imum value is found from the equation | = e"^'^^" ': 



t = .000000115 sec. 



On the basis of 115,000,000 alternations per second, the number of 

 complete oscillations in this time is 6.5. A similar calculation for the 

 corresponding copper circuit gives nearly sixty times as many. 



It has been suggested that the greater damping of the iron might 

 give an apparent change of wave length. If the iron circuit is chosen 

 too short, and the maximum point is sought by adding to the length of 

 the wire, the increase of length would increase the damping and tend 

 to diminish the bolometer throws while the approach to the point of 

 resonance would tend to increase the effect on the bolometer ; the two 

 in fact would work against each other. If, on the other hand, the 

 circuit be chosen too long, and resonance is sought by shortening the 

 wire, the two would work together. 



If the damping plays an important part we might expect different 

 results under these conditions. Iron wire (diam. 0.08847 cm.) was used, 

 and the circuit shortened until the sides were 15 cm. long and the first 



