90 



Ocean Magnetic Observations, 1905-16 



If the value of the starboard angle is represented by a', when/ and c are both zero, then 



(39) 



tan a' = p 



which detennines the direction of the resultant of the forces of permanent magnetism 

 that produce semicircular deviation. If the value of this resultant be p', we have 



p' = v'FhPq^ (40) 



Similarly, if the starboard angle is represented by a" , when P and Q are both zero, then 



(41) 



cZ c 



which determines, under the conditions stated, the direction of the resultant of the forces 

 of induced magnetism that produce semicircular deviation. Representing by p" the 



value of this resultant 



p" = V{cZy+ifZY (42) 



The angles a' and a", and the resultant p', are theoretically constant for the same vessel 

 in all parts of the world, but the values of the resultant p" and the starboard angle a 

 depend upon the vertical intensity, Z, of the Earth's magnetic field. 



The angle a' is completely determined by the values and the signs of P and Q. 

 The angle a", however, is not so completely determined from equation (41), since a 

 positive value of c may result from soft iron foi-ward of and below the instrument or from 

 soft iron abaft the instrument and above it. Moreover, a positive value of / may result 

 from the presence of soft iron to starboard of the instrument and below it or from the 

 presence of soft iron to port and above the instrument. 



Table 35. — Values of the Angles a' and a" and of the Resultant of the Components of Permanent Magnetism for the Galilee. 



On the Galilee certain assumptions are admissible which remove the ambiguity of 

 the algebraic signs of c and/. The rigging was changed from iron to hemp. The magnets 

 of the instruments were about 16 feet above the deck. Hence, the iron on the Galilee 

 was practically all below the instruments, so that positive values of c and / indicate com- 

 ponents of induced magnetism respectively forward of and to starboard of the instrument, 

 and negative values indicate components abaft and to port. With these assumptions, 

 the values of a', a", and p' in Table 35 have been calculated. The varying values for 

 different cruises, or even for parts of the same cniise, are explained by changes in the 

 magnetism of the ship and by observational error. It is evident that if the parameters 

 P, Q, c, and / are but little larger than the possible errors of their determinations, then 



Of 

 the ratios —, and - must be very uncertain. Actual changes were made in the Galilee 

 P c 



between emises for the purpose of reducing the deviations. Other changes in the mag- 

 netism of the ship may occur from the continued buffeting of the sea while headed con- 

 tinuously in one direction. 



'From August 24 to December 13, 1905. 



