360 
COLONEL SABINE ON PERIODICAL LAWS DISCOVERABLE 
accordingly, the difference, whatever that might be, between the observation at that 
hour and its proper normal. These two columns then exhibited all the larger 
disturbances of both the Horizontal and Vertical components whenever either com- 
ponent was disturbed, with the contemporaneous difference of the other component 
from its mean or normal value in the cases when one only of the two components 
exhibited a large disturbance. The entries in the two columns had each their proper 
signs prefixed, + if the disturbance or difference from the normal were in augmenta- 
tion of the force, and — if in diminution of the force. These two columns then 
AY AX 
expressed the values of for the Vertical Force, and for the Horizontal Force, 
AY 
for every hour at which either equalled or exceeded four scale-divisions, or *00026 
AX 
parts of the Vertical Force, or -y equalled or exceeded fourteen scale-divisions, or 
*0012 parts of the Horizontal Force. A third and fourth column were then filled in, 
the third expressing the values of A^, or the disturbances of the Inclination, and the 
fourth the values ^5 or the disturbances of the Total Force (in parts of <p the Total 
Force at Toronto) corresponding to the entries in the first and second columns, and 
computed by the formulse — 
^ . /AY AX 
A^=sm 6 cos 0 I -y — 
A® AX , . „ ,AY 
-^ = cos ^ -y- -[-sm 0 
From the third and fourth columns all the disturbances of the Inclination (A^) which 
equalled or exceeded l'*0 in amount, and all the disturbances of the Total Force 
equalling or exceeding *0004 in amount were taken, as forming respectively a suffi- 
cient body of the larger disturbances of each element to permit their periodical laws 
to be investigated and shown. These disturbances were then dealt with in regard to 
classification and tabular arrangement, in the same manner as that which has been 
already explained in treating of disturbances of the horizontal and vertical compo- 
nents of the force. 
In deriving the disturbances of the Inclination and Total Force from those of the 
Horizontal and Vertical Forces, all the calculations and arrangements in tables were 
prepared under the superintendence of Mr. Magrath, Chief Clerk, by the Non-com- 
missioned-officers of the Royal Artillery employed in the Woolwich Office, every 
part of the process having had the advantage of two independent computers. 
To complete the view of the periodical laws of the magnetic disturbances at 
Toronto, a revision has been made of the analysis of the larger Disturbances of the 
Declination, the results of which were contained in a former paper presented to the 
Royal Society in 1852. These disturbances have now been computed from normals on 
