Sine Galvanometer 389 



In this test currents twenty times as great as those normally traversing the coils 

 of the instrument were used. As a precaution against permanent magnetization, the 

 instrument was demagnetized by reversals from a greater current, and with the axis of 

 the coil in two azimuths with respect to the tripod differing by 90. None of the currents 

 used heated the conductors appreciably. 



From these tests it appears certain that any modification of the instrument's con- 

 stant produced by its magnetic impurities is of no consequence. 



18. In order to form an estimate of the precision with which the constant G of the 

 coils can be determined, we may differentiate (5) logarithmically and assume that the 

 Helmholtz relation holds exactly. We thus obtain 



AG^AN_ 0A Ad_ QQ Ax (g) 



G N d x 



It is readily seen that AN/N, the error in the number of turns, is quite negligible. 

 Each coil consists, in effect, of exactly 10 turns except for the fact that the centers of the 

 terminal holes do not lie exactly in an axial plane, that the diameter of the wire, viz, 

 0.576 mm., is slightly less than that of the pyralin bushings at the terminals, viz, 0.61 

 mm., and that the terminal loops do not lie exactly in the horizontal plane. 



In order to make the first error as small as possible, the terminal holes were located 

 and bored, with a diameter considerably larger than that of the wire, on a Brown and 

 Sharpe universal milling machine, and the bushings were accurately machined. Never- 

 theless, there are slight displacements diminishing the number of turns of each coil, 

 the mean relative displacement for the ends of coils 1 and 4 being about 0.21 mm.; that 

 for coils 2 and 3, about 0.25 mm. If we add to these the maximum possible displace- 

 ment due to the difference of diameters of wire and bushings, viz, 0.03 mm., we obtain 

 0.24 mm. and 0.28 mm., with a mean of 0.26 mm. about 1 part in 36,000 of the total 

 length of a single spiral. This would be the fractional diminution of the constant if this 

 length of wire were simply cut off from the ten complete turns of each spiral. 



A simple calculation shows that a terminal loop, if oriented into the most favorable 

 equatorial position for producing horizontal intensity at the center of the coil system, 

 would produce only 1/3,000 the intensity due to one of the spirals. As the loops are 

 very nearly alike and are traversed by the current in such a way that their magnetic 

 effects at the center of the system cancel one another hi pairs, and as they lie very closely 

 in the central horizontal plane so that their intensities at the center are very closely 

 vertical, their effect is seen to be very minute indeed. 



From these terminal loops connections are made symmetrically to the inner and 

 outer conductors of small cylindrical coaxial cables. This is magnetically equivalent 

 to bringing the terminals accurately together at a short distance from the points at which 

 their peripheral displacement was 1/36,000 of the length of the spiral. The error due 

 to this displacement is thus reduced far below this fraction; and the total error in the 

 number of turns must be considered entirely negligible. 



If we assume that the errors in the mean axial distances and the diameters are not 

 greater than 4n, as estimated in sections 15 and 16, equation (8) gives 



0.4^+0.6^=0.4^ + 0.6^ 

 d x 300 150 



or about 1 part in 47,000, as the maximum possible error due to imperfect knowledge 

 of the linear distances. This error, also, is thus entirely negligible when it is considered 

 that the instrument was designed to measure the horizontal intensity only to 1 part 

 in 10,000. Indeed, 1 part in 5,000 is considered sufficient by the magneticians. 



