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Special Reports 



abrasion, or otherwise. Examination of pivots under a high-power microscope often 

 shows rust scars or pits of considerable magnitude; extended field experience shows that 

 such oxidation takes place readily, especially in the tropics, despite utmost care. In the 

 cases which have been analyzed, these large deviations in the correction-curves are nearly 

 always such as would be produced by an elevation rather than by a depression on the 

 pivot, that is, the maximum precedes and the minimum follows as the inclination in- 

 creases. As the pivot rolls upon such an elevation with increasing northerly inclination, 

 the needle is at first restrained, giving too small a reading and requiring a positive cor- 

 rection, and then pitches forward over the obstruction, giving too large a reading and 

 requiring a negative correction. Following the usual convention as to sign of southerly 

 inclination the order of maximum and minimum would be reversed in the southern 

 hemisphere (compare Fig. 5). So far no clearly defined case such as would be produced 

 by a simple depression has been revealed; the case of needle No. 1 of circle No. 177, 

 which at first seemed to be of that type, was, as indicated, a combination of other 

 causes not evident from the available data. It is not apparent why curves of the one 

 type should predominate since the microscope shows that pits or scars are often present. 

 It may be that, since the pits are a later development, the behavior of the needle has 

 become so bad by the time they appear as to defy analysis or to cause the rejection of 

 the needle. 



Fio. 7. Showing Time-Change in Correction-Curve for Needle No. 1 of Circle No. 177. 



To determine whether a rust particle adhering to the axle could produce undulations 

 in the correction-curves of the dimensions observed, assume the particle to be of such 

 form that tangents drawn from its apex to the circumference of the pivot do not touch 

 it at any other point. In Figure 8a, representing an enlarged cross-section of a pivot 

 through the point of support, let CM be the direction of the magnetic axis of the needle, 

 which coincides with CI, the direction of the magnetic field of intensity F, the needle 

 being in equilibrium upon the apex of the rust particle; TG and T'G are tangents drawn 

 from the apex to the circumference of the pivot, and 20 is the angle between the radii to 

 the points of tangency. In Figure 86, assume the field to have changed in direction 

 through the small angle /S, which will cause the needle to roll forward, throwing the 

 center of gravity ahead of the point of support so that the needle will rotate through an 

 additional angle t until equilibrium is established with the magnetic axis taking the 

 direction CM according to the condition expressed in the equation 



wgr sin (/3-fe) = Fm sin t (8) 



