258 Professor Forbes's Experiments on 



§ 4. On the Direction of the Isodynamic Lines {for horizontal 

 Intensity) in the Central Alps, and in the Pyrenees ; and on 

 the Iiifluence of Height. 



25. The next question comes to be how to deduce the ge- 

 neral results contained in the preceding tables. Where it is 

 merely required to deduce the position of isodynamic lines 

 (which may be considered as sensibly straight for a district of 

 moderate extent), projection of the results upon paper would 

 afford quite a sufficient approximation, where the stations are 

 sufficiently multiplied. Thus the variations in latitude and 

 longitude would be determined, and lines of intensity 1*00, 

 1-01, 1*02, &c. might be drawn with great accuracy upon a 

 geographical map. 



26. But the same process will not suffice, if we have a third 

 variable, such as height, and require to extract its influence. 

 The problem, then, is not to draw lines, but planes of equal 

 intensity. For its solution I resolved to use the method of 

 least squares*, which is peculiarly applicable to a question of 

 the kind just stated, and may be made to give, as will imme- 

 diately be seen, the most probable value of the four following 

 quantities, viz. the variation of intensity for 1' of latitude; its 

 variation for l f of longitude; its variation for J00 feet of ele- 

 vation; its most probable absolute value at the origin of the 

 coordinates, or the station to which the others are referred. 



27. I assumed that the intensity of any point whose coor- 

 dinates of latitude, longitude, and height, might be denoted 

 with sufficient accuracy by an expression of the form 



ax + by + c z = 1 (1.) 



a, b 9 and c indicating the position of the point by reference to 

 the three coordinates, whilst x, y, and s denote the coefficients 

 of variation of intensity according to each of these, and which 

 are to be discovered. The above expression being the equa- 

 tion to a plane, denotes that the isodynamic lines are not con- 

 sidered as curved, but as straight, which though not absolutely 

 accurate, may be admitted in a country of small extent. 

 •28. Eq. (1) gives the intensity I in terms of a, b, and c, the 



• It would be absurd to claim any merit for the application of a method 

 so universally known. But lest I should be supposed to have borrowed 

 without acknowledgement the method of reduction employed by Professor 

 Lloyd and Captain Sabine in their excellent Magnetic Survey of Ireland 

 (Fifth Report of the British Association), I desire to state, that I had some 

 years ago proposed to myself the present method of reduction as the only 

 one adapted finally to solve (within the present limits of error) the question 

 of the influence of height, which so greatly complicates the problem. 



