170 REPORT—1862. 
irregularities of the earth’s surface, with the effects of convection, in such a 
way as would render the separation of these effects extremely difficult, yet 
the careful study of this pulse in connexion with other phenomena may he 
reasonably expected to add to our power of forming correct conclusions 
regarding the coming changes of the weather. 
Report of a Committee, consisting of the Rev. Dr. Luoyn, General Sa- 
ping, Mr. A. Suirx, Mr. G. Jonnstone Stoney, Mr. G. B. Arry, 
Professor Donxin, Professor Wm. Tuomson, Mr. Cayizy, and the 
Rey. Professor Pricr, appointed to inquire into the adequacy of 
existing data for carrying into effect the suggestion of Gauss, to 
apply his General Theory of Terrestrial Magnetism to the Magnetic 
Variations. 
Iw order to explain the views of the Committee upon the question submitted 
to them, it is necessary to refer briefly to the leading points of Gauss’s 
theory. 
If du denote the quantity of free magnetism in any element of the earth’s 
mass, and p the distance of that element from the point (2, y, 2), and if we 
make 
aes -\%4 
pP 
the partial differential coefficients of V with respect to the three coordinates, 
x, y, z, respectively, are equal to the components of the earth’s magnetic 
force in the direction of the axes of coordinates. V is a function of «, y, and 
z, or of their equivalents wu, A, and r,—r being the distance of the point from 
the centre of the earth, and u and ) the angles corresponding to the north 
polar distance, and the longitude, on the sphere whose radius=r. This 
quantity may be expanded in a series proceeding according to the inverse 
powers of 7, whose coefficients, P,, P,, P,, &e., are functions of w and X» 
alone; and it is readily seen that, at the surface of the earth, the three com- 
ponents of the magnetic force are 
x=-(7 Fi 4+Fs4 be. ), 
dus dws du 
EA a A og & 
rr Crm eee ena 
Z=2P,+3P,+4P,+ &e., 
and are therefore given when P,, P., P,, &c. are known. 
The form of these functions is deduced from the well-known partial dif- 
ferential equation 
nm (n+1)P,+ 
Y=— 
ad? hie yal al ed 
du ne sin? u dd* : 
n being the number indicating the order of the function. It is found that 
the first, P,, contains three unknown coefficients ; the second, P.,, five; the 
third, P,, seven, &c. Hence, if the approximation be extended so as to in- 
clude terms of the fourth order, there will be 24 coefficients to be determined. 
Each given value of X, Y, or Z, on the earth’s surface, furnishes an equation 
=> > 
Pn + cot u 
du 
