36 
THE KEY. STEPHEN J. PERKY ON THE MAGNETIC 
Table III. contains the equations of condition formed from the data in Tables I., II. 
4'825=§+143a+ 53 y 
5-497=§+318a+ Sly 
4 - 807=§ + 235a+ 81 y 
4T62=§ + 134a+ 94 y 
3-490=§ + 93^+156^ 
2*403=&+138a+276y 
l-483=§+196a+376y 
l-523=§ + 183a+369?/ 
0*990=^+130^*+ 383y 
1- 037=H 43a+361?/ 
2- 417=§+ 76a+252?/ 
3- 562 = §- 3a+121y 
5- 688=§ + 2a- Toy 
In these equations § = the dip at the central station diminished by 61° ; and a=r cos u, 
y—r sin u, where u is the angle which the isoclinal lines make with the meridian, and r is 
the increase in the angle of the dip for every change of a geographic mile in the direc- 
tion normal to the isoclinal lines. 
Solving these equations by the method of least squares, we obtain the following equa- 
tions : — 
f 41-884= 13§ + 1690a- + 2480 t/] 
•j 5718-258 =1690§ + 319466a+ 326949?/ 
(4912-379 =2480§ + 326949a+ 757700?/. 
These give 
f 487347-924= -59137§+239731870a 
(19552806 -880 = 3699700§+ 4696 79480a; 
.-. 44585338 = 9147115^, .-. §=4-874. 
Hence the most probable dip at Paris derived from the observations taken at the 
other stations is 65 0, 874 = 65° 52 ,- 44. 
By substitution in the above equations we find the values of a, ?/, u, and r, 
a=0-0032352, y= -0-0108651, u= -73° 25'-10, r=0°-0113. 
The isoclinal lines are therefore in the direction 
N. 73° 25' 10" E. to S. 73° 25' 10" W., 
and the distance between the lines representing the difference of 30' in the dip will be 
44 "25 geographical miles. 
The substitution of these values of a, ?/, and § in our original equations will give us 
the values of the computed dip at each station. 
