CONTENTS. xxx i 



PART II. TERRESTRIAL MAGNETISM. 



SECT. PAGE 



I. Useful formula connecting Legendre's coefficients . . . 243 

 Computation of the values of G for a spherical surface . . 265 



II. Computation of the values of G' for the spheroidal surface of 



the Earth 297 



III. On the definite integral of the product of two Legendre's 



coefficients .......... 343 



IV. On the product of any two Laplace's coefficients of the form 



(d m P d p P \ 

 dfji, m '" d^i? / 



On the product of two Laplace's coefficients of the form 



QnXP^, ivhere Q = ( 1 - p?f D m P n 396 



V. The theory of Terrestrial Magnetism, giving the expressions 

 of the magnetic forces on the Earth's surface, the Earth 

 being regarded as a sphere . . . . . .401 



On the relation of the functions Q and H' to one another 



and to the magnetic forces . . . . . . .411 



On the relation of the above definite integrals to the magnetic 



forces ........... 420 



On the relation of these definite integrals to the determination 



of the magnetic constants ....... 436 



VI. The theory of Terrestrial Magnetism, giving the expressions for 

 the magnetic forces on the Earth's surface, taking into 

 account the spheroidal figure of the Earth . . . . 446 



Form of the final equations for the determination of the 



magnetic constants . . . . . . . .459 



