1877.] o4:7 [Frazer. 



He concludes by calling attention to the following epochs. 



Differences. 



Deduced maximum declination in 1679 ±10 ^ 



}- 63 years, 

 years ) "' 



Known first point of inflexion 1741 ± 10 years i 57 years. 



Known minimum declination 1798 ± 2 years i 53 years. 

 Supposed second point of inflexion 1850. 



"From which it appears that the periods are diminishing or the velocity 

 of the secular variation is increasing, which latter is sustained by a compari- 

 son of V i„i — — 4'.6 with V 1850 = + 6'.8 or + 5'.9," &c. 



In Coast Survey Report for 1858 p. 193 to 197 Mr. Schott resumes the dis- 

 cussion of the subject. He announces the discovery at Hatboro, Pa. of a 

 longer period of 234 years and a shorter one of 88 years, the range of the 

 secondary motion being about j'- of that of the primary or about 0O.35- 

 The length of the shorter period as well as its epoch and range is difterent 

 in diflerent localities, but the fact of the existence of two such periods was 

 afterwards confirmed by discussions of the periods at Burlington Vt. and 

 Providence, R. I. 



For the representation of the Hatboro observations the form was emploj^ed: 



D = d + r cos. (an -|- c) -j- v^ cos. (a, n -\-c{) when n =; number of years 



I after 'I 

 — before i ^"^ assumed epoch ; in this case the year 1830. 



In the numerical application, the last term being neglected, the form 

 adopted for the conditional equations was : 

 0= — D + d, -fx + COS. a n r cos. c — sin. a n r. sin. c. 



The first assumption for d^ was = 5.3 and a = 11^= 1-44 as pointed out 

 in discussion of 1855. 



In a second and third assumption (a) was varied. Afterwards that 

 value was assumed which made the sum of the squares of existing differ- 

 ences a minimum. The probable ^^ was dz 8'. 6 as against zb 11'. in the 

 former discussion. 



The condition of the minimum declination is expressed by the formula 

 = 5.05 sin. (1.54n -f 46^.8)— 0.90 sin (40.1 n— 130) from which 

 n = — 33.7 years. Hence the minimum occured in 1796.3. 



The effect of the last term is to place the minimum 3.3 years earlier. 

 The former discussion (in 1855) placed the minimum at 1806.1 ± 19.3 

 years and the mean for all stations then discussed gave 1797.6 + 1.8 years. 



By a first and second differentiation of the above formula v ^= -|-45.3 or 

 the maximum annual change will occur in 1875.3. 



From the observations since 1750, separately discussed in 1855 T =^ 

 1799.5. 



Fi'om the next following discussion of the magnetic declination at Wash- 

 ington, it is concluded that the maximum declination at the close of the 

 last century was -j- 0^^.42' or the line of 7io variation at its highest. 



