136 PROCEEDINGS OF THE AMERICAN ACADEMY. 



(A\ + A^,)/2 + NJ, + Nih = Po 

 Nxh + (A^ + A^3 + A^4)/3 + (A^i + A^4)/5 = Po (10) 



Nih + (A^ + A^4)/3 + (A^ + iV4 + A^5) h = Po 



If then A denote the determinant of the coefficients, 



A = A^A^oA^s + A' iA'3A^4 + A^A^3xV5 + A^iA^sA^s + A'iA^4A^5 



+ A^aA^sA^s + A^2A^3A^4 + A^2A^4A^5, 



and the vahies of h, h and h just after the gap is opened, are 



(A^3A'4 + A^3A^5 + AuA^5)Po/A, NoN,Po/A, and N.NsPo/^. (H) 



The total amount of electricity carried by the currents I2, I3, and I5 

 are 0, 0, and 12; and to find 12 we may integrate the second equation 

 of the system (2) with respect to the time from to go and use the 

 initial values of I2, h, I-o just found. This procedure leads to the 

 equation : 



12 



and this is evidently the same result that would have been obtained 

 for the whole discharge through the galvanometer, if the branches (2) 

 and (3), with their condensers, were removed from the secondary cir- 

 cuit. It is easy to compute the sudden loss of energy when the gap 

 is opened. 



Results. 



For the purposes of the investigation here described, we used about 

 twenty-five different brands of iron obtained from several flift'erent 

 sources. Of these, five gave values of I larger than 1700 for compara- 

 tively low excitations of about 2800 gausses. 



About ten of our specimens were described by the dealers as " Bes- 

 semer" and showed similar micrographs. jNIost of these were in 

 no way remarkable. For excitations of about 2700 they gave values 

 of I of about 1675 in the average and might be expected to give 1685 

 for fields of strength 5000. One specimen (No. 10) was quite different 

 from the others. For H = 2730 the corresponding value of /was 1727. 

 This result is basetl upon several difi^erent determinations made upon 

 different days, and during the interval the rod was once annealed. 

 A long series of annealings however reduced the permeability so that 



