^g PROFESSOR FORBES'S EXPERIMENTS ON 



a, b, and c, indicating the position of the point by reference to the three co-ordi- 

 nates, whilst x, y, and z denote the coefficients of variation of intensity accord- 

 ing to each of these, and which are to be discovered. The above expression being 

 the equation to a plane, denotes that the isodynamic lines are not considered as 

 curved, but as straight, which though not absolutely accurate, may be admitted 

 in a countiy of small extent. 



28. Eq. (1) gives the intensity I in terms of a, h, and c, the co-ordinates of the 

 place, a being reckoned in minutes of latitude, h in minutes of longitude, c in hun- 

 dreds of feet of elevation. It is convenient to assume some station as a point of 

 reference, and write for a, b, and c, the differences of the co-ordinates merely, and 

 for I the difference of intensities. Let a', h', d, and I' represent these quantities 

 for the fundamental station, and then for any other the expression will be 



(a — a')x + (b — h')7j + {c — cf)z= I — I' 



and by a combination of all the equations of similai' form which the observations 

 furnish, we are to deduce the most probable values of x, y, and ;:;, the coefficients 

 of variation in each direction. If, farther, we wish to have the most probable 

 absolute value of the horizontal intensity at the fundamental station before men- 

 tioned, it must cleai'ly be dedviced from the whole mass of the observations, and 

 not from the observation made there alone. Let us suppose, then, that the inten- 

 sity at the fundamental station requires a small correction, 1 1', we shall write 

 r -f H' instead of I' in the preceding expression, considering S I' as another un- 

 Icnown quantity, which wiU give us a series of equations (for the different points 

 of observation) of the form 



(a — a') X + {b — b') 1/ + {c ~ c') z = I_I'_ JI' (2) 



or using the letters with subscript numerals instead of a — a', &c. and putting 

 all the unknowns on the left hand, we shall have a series of equations of condi- 

 tion of the form 



a^x + b^y + c.z + W =J, ^ 



a x + b,y + c^z + n'=I^ r*^ ' 



Sec. 



from which the most probable values of x, y, z, and cfl' are to be deduced by the 

 method of least squares. 



29. The obsei-vations contained in Table VII. include two groups of observa- 

 tions, to which we mean to apply the method in question. One of these includes 

 the alpine observations made in August, September, and October 1832 ; the other, 

 a short series in the Pyr^n^es, made almost entirely with reference to the effect 

 of height in 1835. The remaming observations must be considered for the pre- 

 sent as isolated. They are important, however, as fixing the relative horizontal 

 intensities at Pai-is, Edinburgh, Bmssels, Heidelberg, and some points of less note. 

 The admirable coincidence of the Edinbiu-gh observations made in different years 

 gives great confidence in the accuracy of the determination of .8402 for the hori- 



