and Maximum of Magnetism of Nickel and Cobalt, 329 



greatest relative error is seen to be in the first line, where «£) is 

 small : this does not indicate any departure from the curve, but 

 is only due to the too small deflections of the galvanometer; and 

 the error indicates that of only a small fraction of a division at 

 the galvanometer. 



In the calculation of /n and k a method was used which may 

 be of use to others in like circumstances, who have to calculate 

 a large number of values of one variable from a function which 

 cannot be solved with reference to that variable, but can be 

 solved with reference to the other. Thus we have 



/* = /3sin^ £ j, (1) 



which can be solved with reference to 53 but not to /j, ; for we 

 have . , u \ 



53 = Dsin- 1 (Jj-^--7r (2) 



Suppose we have values of 53, and wish to find the correspond- 

 ing values of /£. We first calculate a few values of 53 from (2) 

 so that we can plot the curve connecting 33 and /ul. We then 

 from the plot select a value of /jl which we shall call jrf, as near 

 the proper value as possible, and calculate the corresponding 

 value of 53, which we shall call 53'. Our problem then is, know- 

 ing 58' and fju', to find the value of /j, corresponding to 53 when 

 this is nearly equal to 33'. Let 33' receive a small increment 

 A53', so that 53 = 58' + A33'; then we have, from Taylor's theorem, 

 since /a = <£(53'4- A53') and /// = <£(58'), 



f,=f,'+ g (A») + j^gj (A58') 2 + &c. 



Remembering that the constants in (1) refer to degrees of arc 

 and not to the absolute value of the arc, we have 



53—53' 

 /*=**' + .. - + &c, 



V /3 2 



which is in the most convenient form for calculation by means 

 of Barlow's Tables of squares, &c, and is very easy to apply, 

 being far easier than the method of successive approximation. 



On comparing the magnetic curve Table II. with the normal 

 curve Table I., we see that the magnetic curve of nickel bears 

 the same relation to the normal curve as we have already found 

 for iron; that is, the magnetic curve falls below the normal 

 curve for all points before the vertex, but afterwards the two 

 coincide. 



Hence wc see that at ordinary temperatures the magnetic pro- 



