594 



DR, GOLDSCHMIDT ON THE OBSERVATIONS 



puted by this formula, and their deviations from the observed 

 values, are as foUows : — 



According to this table the mean deviation of a determination 

 of the dechnation deduced from one year is 48""942 ; the mean 

 error to be feared in the determination of the absolute part of 

 the formula is .34""92 ; and the mean error to be feared in the 

 determination of the coefficient of Hs 1 1"'53. 



It is more natural to suppose that the decrease is uniformly 

 accelerating than constant ; therefore the declination may be 

 represented by the formula a + b t -r ct^. Giving t the same 

 signification as before, we obtain by the combination of the six 

 data, using the method of least squares, 



S = 18° 41' 3l"-442 - 3' 09"-5 14^-0' 13"-453 f; 

 and the values of S, computed by this formula, as well as the 

 deviations from the observed values, are as foUows : — 



The sum of the squares of the remaining deviations is 2515'4; 

 hence the mean deviation of a single year's determination, so far 

 as it can be derived from six years' obser\^ations, is 2S"*96. The 

 weights of a, b, c are 1*31 7, 1 '3 76, and 37'34, where the weight of 

 a mean value of the declination, deduced from a whole year, is 

 unity ; with 2 8"" 96 as the mean deviation of such a mean 

 value, we have the mean errors of a, b and c, 25"'23, 24"'68, 

 and 4""74. Our formula gives 18° 52' 38" for the maximum of 

 the declination, and the corresponding t = — 7*043 ; so that 

 on the 14th of September, 1827, the declination had become 

 reti'ograde. It need scarcely be remai'ked, that both these num- 

 bers are uncertain, as the coefficient of ^^, on which the determi- 

 nation of the time of the maximum principally depends, is un- 

 certain to one-third of its whole value. Unfortunately we have 



