398 Proceedings of the Royal Society of Victoria. 



Cg, then 



3so = ;'o -^8 +7io = - 3zs = 3^10 



3^4 = J'4 -^'9 +J'u = - 3s,= 32i„ 

 and if u^, u^, ti.^ be 3 e.s. ordinates of the lialf wave of Cj, then 



S'^-O^Jo— ^3 + 2/6— J»'9+Jl2= -5«3= 5?/s= — 5«9= 5«ij 



5«i=Ji— 74 +77— JJ'io +yvi= - 5«4= 5«,= - 5«io = 5«i, 



5«2=J>'2 -^5 + >'8 -7ll +7l4= — 5«5 = 5?/8 = - 5?/ii = 5«i4 



the figure subscribed to each ordinate indicating the abscissa to 

 which it corresponds. 



Now the full wave 



Ci = H, + H3 + H, + H,+ H9 + etc. 



and C3= Hj+Hg + Hjs 



so that if Hi, be neglected, and the sums of the corresponding 

 ordinates of C;, and C5 be subtracted fram those of Ci, the fifteen 

 remainders are ordinates of 



i.e., of Hj, if we neglect H,. 



If Hjj cannot be neglected it can at once be removed from C5 

 before subtracting from Cj, for as it is {q.p.) the 3rd component of 

 Cj, of vi'hich we have 3 e.s. ordinates Uq, u^, u^, its three corres- 

 ponding ordinates are /(,, —i'q, Iq where 3/o=«o — «i + ?/j, 

 hence H5 will de completely given by 

 Cq, tTj, c, where 



Hjj can now be taken from Cj, thus 



are the 5 e.s. ordinates of H3 + H9. 



In order to determine H3 and Hg it will now be necessary to 

 plot the 5 ordinates of H3 + Hp, measure off 6 e.s ordinates from 

 the smooth curve drawn through them, and from these determine 

 their first component, that is 2 e.s. ordinates of Hg. These will 

 completely determine Hg if H.^, etc., be neglected, and by sub- 

 tracting them from the corresponding ordinates of Hg-^Hg 6 e.s, 

 ordinates of Hg are obtained. 



If H7 cannot be neglected it will be necessary (if the orig- 

 inal wave trace is not available) to plot the 15 ordinates of 



