18 PROFESSOR FORBES'S EXPERIMENTS ON 



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

 nates, whUst 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 country of small extent. 



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

 place, a being reckoned in minutes of latitude, b 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\ b', cf, and F represent these quantities 

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



(a — a')x-\-{b — b')7j + {c — c')zz^l— I' 



and by a combination of all the equations of similar form which the observations 

 furnish, we are to deduce the most probable values of x, y, and z, 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 clearly be deduced 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 reqvdres a smaU coiTection, I T, we shaU write 

 r 4- S r instead of Y in the preceding expression, considering I V as another un- 

 known quantity, which will give us a series of equations (for the different points 

 of observation) of the fonn 



{a — a') X + {b — b') ij + {c — c') z = I _ I' _ H' (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 



«1 ^ + ^ y + C, 2 + M' = I^ . 



&c. 



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

 method of least squares. 



29. The observations 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 Pyrenees, made almost entu-ely with reference to the effect 

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

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

 intensities at Paris, Edinburgh, Brussels, Heidelberg, and some points of less note. 

 The admirable coincidence of the Edinburgh observations made in different years 

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



