Clearing the Compass. 373 



the sine of the dip ; so that between the magnetic equator and 

 the magnetic pole, the force ought to vary in the proportion of 

 1 to 2, and the vibrations of a given needle, in a given time 

 ought to vary in that of 10 to 14.142. 



7. This variation of the force is greater than has yet been 

 observed : but on board of the Isabella, when the dip increased 

 from 74° 23' to about 86°, the time of vibration decreased in 

 the proportion of 470 to 436, or 1.078 to 1, and consequently 

 the force increased in that of 1.162 to 1, while the calculation 

 requires an increase in the ratio of 1.095 to 1 only; so that 

 considering the unavoidable uncertainties of the experiment, 

 the general result of observations, in different parts of the globe,' 

 agrees as well with the theory as we have any right to expect^ 

 and justifies us in introducing this variation of the force into 

 our calculations, at least as an approximate expression of the 

 facts, to be compared hereafter ivith more extensive experience. 



8. The force acting on the needle of a compass, limited to a 

 horizontal motion, is reduced, according to the principles of the 

 resolution of forces, in the ratio of the radius to the cosine of the 



dip, so that it becomes proportional to ^ ^~^^ , or inversely 



. / 4—3 ss I \ \ 



10 ^ ^ I _j. 3 



1— ss '^ \1— ss / 



9. Such being then the magnitude of the horizontal force, 

 acting in the direction of the magnetic meridian, we may readily 

 determine the effect of its combination with another force acting 

 in any other direction, so as to afford a result expressed by the 

 third side of the triangle of forces ; for the sine of the angle, 

 formed by this new result with the first line, will be to the sine 

 of the angle which it forms with the second, as the second line 

 to the first ; or, in other words, the sine of the angle formed by 

 the actual direction of the needle, with that which would have 

 been its direction if the magnetic force had been undisturbed, 

 will be to the sine of the angle included by its actual direction,' 

 and the direction of the disturbing force, as the magnitude of 

 the disturbing force to that of the natural force ; and supposing 

 the disturbing force of the ship to be constant in different parts 

 of the globe, the sine of the angular correction, required for its 



