4 REPORT 1872. 



been stated in proper form and has been greatly simplified, since theory has 

 shown tliat, and how, all kinds of magnetic secular changes, for any arbitrary 

 time and place, depend on one common cause, viz. on the synchronous changes 

 of the Gaussian constants. Indeed these quantities only can give to the alge- 

 braic expressions of magnetic elements different numerical values at various 

 epochs, because the quantities r, u, and \ are by their nature once and for 

 ever invariable ; and then, as only the first power of every Gaussian constant, 

 and no products of them, occurs in the potential, the following general rule can 

 evidently be laid down : — The amount of change for any element of terrestrial 

 magnetism (as, for instance, for the declination, the inclination, one of the 

 three rectangular components, and so forth) during a given period must be 

 calculated by that same formula which expresses its absolute value, if only 

 instead of each Gaussian constant there is placed the increment which its 

 value has received during the same period. This plain corollary of the magnetic 

 theory has been of twofold use for the reductions we had to make, and will 

 serve in the same way for all future ones. Indeed its inverse application 

 gives, from observed changes of magnetic phenomena, the synchronous 

 changes of the Gaussian constants; and by substituting these latter results in 

 the direct formulfe, the changes of every phenomenon may be computed for 

 places where they have never been observed. The first part of this pro- 

 ceeding is immensely preferable to empirical guessings ; for it makes an almost 

 equal use of the variations in any kind of magnetic phenomena, and therel)y 

 leads to the knowledge of these variations in those kinds for which experience 

 is wanting. The secular changes of intensity may therefore bo ascertained 

 for periods in which we know only changes of inclination and declination, 

 or even for those in which the latter only have been observed, ^tloreover it 

 is only by these means that the consequences of experience on secular changes 

 in certain parts of the earth can very confidently be extended to the re- 

 motest parts. 



Nevertheless, before we could make the application of this memorable 

 method, a decision was wanted concerning two points, according to the result 

 of which our proposed reductions might prove to be either easy or difficult, or 

 even wholly impracticable ; to wit : — 



1. What kind of connexion exists between llic lapse of time and 



the variations which are undergone by magnetic phenomena and 

 consequently by the Gaussian constants ? and 



2. In how many and in Avliich of the Gaussian constants will the varia- 



tions be of most influence, and in which others may they be 

 neglected for practical approximation ? 



As to the first question, it has been proved by the changes of the three 

 magnetic components at Berlin, observed fuUy during the last forty-five 

 years by Erman, and partially at intervals during almost a hundred years 

 by others, and besides by a great number of partial series of observations 

 at other places, that during the last century the variations of magnetic 

 phenomena, and consequently those of the Gaussian constants, have never 

 happened by a leap, but have always progressed according to the law of 

 continuity, and especially so that their amount has been merely proportional 

 to the lapse of time and to its square. If, therefore, the increment of one of 

 these constants from a year denoted by T' to another denoted by T has been 



ascertained, the (;pp-^,Jth* of this quantity will be equal to the annual 



rp . rp: 



increase of the same constant for the 3*ear denoted by — ^f— . More- 



