32 LIEUT.-COLONEL SABINE ON TERRESTRIAL MAGNETISM". 



M. Erman's determination differs 40*0, and Captain FitzRoy's 91*0 from Captain 

 Belcher's ; the former thirteen times, and the latter thirty times, the probable error 

 of a determination with a single needle of steady magnetism, where the spot of ohser- 

 vation is the same. 



We have considered Captain Belcher's seven needles as giving equal and inde- 

 pendent results for the ratio of the horizontal intensity at Otaheite and Panama ; but 

 the result with No. 8. is not strictly an independent one, inasmuch as at San Bias 

 that needle received a small correction assigned from its comparison with the others; 

 and the claim of the result of No. 5. to be considered as of equal value with that of 

 each of the remaining needles is impaired by the probability of that needle having 

 sustained a slight loss of magnetism at or before Martins Island (page 16.). If, 

 therefore, we were to exclude the results of Nos. 5. and 8, and to derive the hori- 

 zontal intensity at Otaheite from the five needles, which we may consider as of strictly 

 independent and equal authority, we should have as their mean 966*8, with a pro- 

 bable error of r2, and the probable error of a determination with a single needle 

 2*6. It is true that the number of partial results from which this amount of the 

 probable error is derived is small ; but the probability of its being an approximately 

 , just representation of the errors of instrument and observation in this method, with 

 needles of steady magnetism, is strengthened, if we examine in the same manner the 

 results with the same five needles at the four stations preceding Otaheite; by so 

 doing we obtain the probable error of a single needle from each as follows : — 



Bow Island . . . 2'2 



Martins Island . . 16 



San Bias .... 15 



Mazatlan .... 22 



The integers in these quantities represent hundredth parts of the space comprised 

 between two adjacent lines of horizontal intensity in M. Gauss's theoretical map 

 of that element. 



Uncertainties in respect to the magnetism of needles need no longer prove a source 

 of vexatious anxiety and embarrassment even to travelling observers ; with the simple 

 apparatus described by M. Weber* the magnetic state of a needle maybe examined 

 at pleasure, and its magnetism may be altogether eliminated in the result. 



With this advantage, however, — and it will be scarcely less valued by the confi- 

 dence it creates whilst the observations are in progress, than by the independency it 

 confers on their results, — and with a probable error of observation of extremely small 

 amount, the magnetic traveller has still two serious sources of error to contend with : 

 1st, the values of the magnetic elements which he determines may not be mean va- 

 lues, by reason of the periodical or irregular fluctuations of the magnetic direction or 



* Resultate fur 1837, and Scientific Memoirs, vol. ii. Art. IV. 



I 



