532 PROFESSOR W. E. AYRTON, MR. T. MATHER AND MR. F. E. SMITH: 



the observations were of such a nature that a decision to disregard the result was 

 arrived at before its computation. Such occasions were very rare. 



Table XII. gives the results obtained when only one set of coils (left or right) was 

 made use of, so that there were no secondary forces to be eliminated. They are 

 inserted to show the order of the agreement attainable in this way, and are not 

 considered to be so reliable as the values deduced from the (D + S) and (D S) tests. 



When both sets of coils are operative, the balancing mass for 1 ampere is 7 '49964 

 grammes this has been denoted by m in Table XIII. 



PROBABLE ERRORS. 



The mean error of a single observation in Table XIIL, viz., 6 parts in 1,000,000, is 

 surprisingly small, for this comprises the error of the balance reading, the inaccuracy 

 of the estimation of the secular change of the secondary standard resistance coil, the 

 variation in E.M.F. of the standard cell (including polarisation during the observations), 

 uncertainty in temperature readings, and the error introduced by the non-main- 

 tenance of an absolutely steady current. The probable observational error of the 

 mean value of CxR at 17 C. is less than 1 in 1,000,000. 



The probable error of the ratio of the diametral dimensions of the coils, viz., 5 in 

 1,000,000, and the uncertainty in the axial dimensions of 15 in 1,000,000 (intro- 

 ducing a possible uncertainty in the value of the mutual induction of about 5 in 

 1,000,000 and in the measurement of current of about 1 part in 100,000) have not 

 been under-estimated. Evidence in favour of a small error is afforded by the satis- 

 factory agreement of the calculated and observed differences of the forces due to the 

 left and right systems when a current of 1 ampere circulates through them ; in 

 addition there is the estimate of the difference in radii of neighbouring coils from 

 observations of the force (p. 516). These measurements lead one to suppose that the 

 errors have been closely approximated to. The electrical method of setting the coils 

 in position has been shown to be subject to an error not greater than 1 in 5,000,OoO 

 of the mutual induction ; the magnetic susceptibility of the parts of the balance and 

 its support is negligibly small, and the effect of the current in the leads to and from 

 the suspended systems is too small to be measurable. The magnitudes of the errors 

 arising from the finite thickness of the wire used, and the assumption that one of the 

 coils is a current sheet instead of a helix, are discussed in Appendix B, and shown to 

 be practically negligible. 



The possibility of error due to the oscillation of the suspended systems has not yet 

 been considered. For a small axial displacement of the suspended coils the force is 

 (1 11 x 10~ 8 c? 2 ) times the maximum,* where d is the axial displacement in mils from 

 the plane of minimum mutual induction. One division of the pointer scale is equal 

 to 3 '75 mils (= 95/j.) ; the length of the pointer is 14' 6 inches (37 centims.) and half 



* See p. 502. 



