402 Proceedings of the Royal Society of Victoria. 



8. It will be noticed in the determination of the phase of H^ 

 in Table I., that the eight values of 12° — a differ considerably 

 from each other, indicating the presence in what we there take 

 for H] of a considerable upper harmonic, probably H.. In order 

 to determine H, fourteen e.s. ordinates of the half wave are 

 required. If the wave trace were given these could be measured 

 oif from it, but if, as in tlie case we are considering, only 15 

 original ordinates are given, it is necessary to plot the 15 ordin- 

 ates of Hj + H^ obtained in Table I., and from the smooth curve 

 drawn through them to measure off 14 e.s. ordinates. This has 

 been done and the values obtained are given in row^ 4, Table 

 II., as well as bhe calculation necessary for the determination of 

 Hy and its elimination from Hj + H-. 



What is called the amplitude of Hj in Table I. is really 

 v/2 R.M.S. (Hj + H-), To get amp. H, it is better to remove 

 the effect of Hy by treating it as a correction, thus avoiding 

 error that might be introduced in the plotting. This is easily 

 done, since 



hence hi (corrected) = v Anip.(Hi-(-H-)^- 



= v'' hi^ (uncorrected) — h^''. 



In Table II. the coi'i-ected crossing point of Hj is determined, 

 and it is seen to differ in phase only by 2 minutes from the value 

 obtained in Table I. 



The difference between the four values of 3(24° — yS) when 

 determining the crossing point of Hg in Table I. point to the pre- 

 sence of a ninth harmonic, which exists as a third component in 

 Hg-fHg. Hg can, if desired, be determined by plotting the 5 

 ordinates obtained in Table I., measuring off from the curve six 

 e.s. ordinates and proceeding as before. It will be found that 

 H9=3sin9(W-13°). 



9. In Table III. is given most of the work required for the 

 determination of the first six harmonics of a complete wave that 

 contains harmonics both of odd and even orders. Twenty-four 

 e.s. ordinates of the full wave are taken. This number is speci- 

 ally suitable, as it enables us to determine directly Cj, C.2, C3, C4 



