118 
LIEUT.-COLONEL SABINE ON TERRESTRIAL MAGNETISM. 
indeed be detected ; but when the intercomparison is extended from two to several 
needles, the improbability of all being affected at the same time and to an equal 
amount becomes considerable. It is still however possible, because the intercom- 
parison can show nothing beyond the relative condition of the needles. 
In the present case the incompleteness in this respect of the evidence furnished 
by the intercomparison, is supplied by Nos. 7- and 9. having been vibrated at Wool- 
wich in August 1839 and in October 1842: the change in their times of vibration 
at those dates, compared with the loss of magnetism deduced for each by the inter- 
comparison with the other needles, shows whether any and what unaccounted loss 
has taken place in the interval in those two needles, and consequently in all those 
compared with them. 
In what has been said above, it has been assumed that a change taking place is 
always occasioned by a loss of magnetism in one or other of the needles ; it gene- 
rally is so ; but should the case occur, that one of the needles should gain instead of 
lose by any accidental disturbance of its magnetism, the intercomparison with others 
would equally point it out and mark its character. 
An alteration in the ratio of the squares of the times of vibration may be occasioned 
at a particular station by an observation error of unusual magnitude, or by some un- 
known accidental cause of a temporary nature affecting at the one station only the time 
of vibration of the needle which is compared ; an alteration to nearly the same 
amount will, in such case, equally pervade its comparisons with all the needles ; but 
this case is readily distinguished from that of a permanent loss or gain of magnetism, 
requiring a correction to be sought out and applied, — by the ratio reverting to its 
original amount at the succeeding stations. 
The process which has been followed in assigning the corrections for the losses 
thus discovered to have taken place may be best shown by an example. On the simple 
inspection of the observations, it was evident that Nos. 5. and 7- had each sustained 
a loss of magnetism between the Seychelles Islands and Mojambo Bay in the Island 
of Madagascar. The logarithms of the squares of the times of vibration of No. 5. at 
the three stations preceding the period of the loss, and at the three stations following 
the same, being severally subtracted from the corresponding logarithms of the squares 
of the times of vibration of Nos. 9. 11. 12. and 13. at the same stations, the differences 
are arranged in the subjoined Table. The differences for each needle are seen to be 
nearly a constant quantity (a) at Penang, Point de Galle, and Seychelles ; to have 
undergone a change between Seychelles and Madagascar; and to have become again 
a nearly constant, though a different, quantity ( b ) at Madagascar, the Cape of Good 
Hope, and Ascension. The amount of the change between Seychelles and Mada- 
gascar {h — a) is shown by No. 9. to be 9'9856 ; by No. 11, 9'9859 ; by No. 12, 
9’9856; and by No. 13, 9'9859. The mean, 9 - 9857, must be added to the logarithm 
of the square of the time of vibration of No. 5. at Madagascar and all the succeeding 
stations, to make them strictly comparable with the observations of that needle at 
