x PREFACE TO PART II. 



them for any point of the Earth's surface in series consisting of quantities 

 to which he gave the name of magnetic constants, with coefficients involving 

 Legendre's coefficients, and which are functions of the colatitude of the 

 point. 



From the very imperfect data which he possessed, Gauss determined 

 the numerical values of the magnetic constants by his equations up to terms 

 of the fourth order i.e. he determined the values of the first twenty-four 

 magnetic constants, i.e. three of the first order, five of the second, seven 

 of the third, and nine of the fourth order. 



No one could be more conscious of the fact than Gauss himself was 

 that his data were so meagre and so insufficient that he could by no means 

 rely on the values derived from them, and I fear that even now, at the 

 end of this nineteenth century, we must say with him that the observed 

 facts are far too scanty and that our stock of observations is still too small 

 to enable us to get out trustworthy values of the magnetic potential and 

 the magnetic elements for a given epoch. For this purpose the observations 

 should be strictly contemporaneous, and so we require more Observatories 

 where continuous records are taken. 



For Gauss's method, which was also the method followed in practice 

 by my brother, it is important for the accuracy and trustworthiness of the 

 resulting values of the magnetic constants that the observations shall be 

 taken from stations distributed as uniformly as possible over the Earth's 

 surface ; whereas we see that in the northern hemisphere the Observatories 

 which exist are very unequally distributed, and that in the southern 

 hemisphere there are only three first-class magnetic Observatories where 

 continuous records are taken, viz. those of Batavia, Mauritius, and Melbourne. 



This work on 'Terrestrial Magnetism' has been arranged under eight 

 Sections. The first two sections treat of and establish simple and convenient 

 relations between successive Legendre's coefficients and their derived differential 

 coefficients regarded as functions of the colatitude = cos' l p.. 



Taking P n to represent Legendre's coefficient and (ft to denote the 

 value of 



certain simple and useful relations are found between successive values of 

 Q for different values of n and m. 



