( 836 ) 



right we deduce, representing for shortness' sake a ^ « ", — «*, u\ etc. 

 by 1,3 etc; ^.,^\ — ^^'^\ etc. by /„ etc.: 



+ K.t,4-.t,.tJ(X,,+X34) 

 l:,=^'T3--f,+.-r,jrJ(x„+/n)-f(--rr'T3— -Ti''T4)(X3i-fX,4)4- 



X,,=:-(rr,^4-rr,')X„ + (.Tj' + rr/)x,,4-(.T,.T,-f.T3n;J(x„+Xs4)+ 



X,,— .(rr,.-r,— .-r,rr,)(x„ + Xi4)-(^'^3'+-'^i')X.i + (-T.''+^4*)Xo4 + 



-f(.T,?r3+.T,?rJ(Xi,+XM) 



$,^r=(-r,jr,+.-r,rrJ(x,3 + Xi4) + (-Tr'^3"-'^i-'f4)(X3i + X.4)— 



-(.-r,''4-.T,^)X,, + (.'T3^+.T,^)X34, 



from wliich ensues: 



^.3 + êM=(--^i' + -'T4'---T.'--''3')(X.3 + Xx4) + 2(.T,^,+rr,:rJ(x,i-fx,4)4- 



-f2(.T3rrj— .t,.t;)(Xi2+X.4) 



^^,-f|^,=2(rr,.'r,--rr3rrJ(y,3 + x,J + K^ + rr/-rr3^-rr,^)(X3i + X.4) + 



-l-2(.T,.T3+.TrjrT,)(Xi,4-X34) 



§^, + 23,=2(rr3rr,-frT,rrJ(x,3 + Xi4) + 2(-T',.-r3-rr,^,)(X3a-|-X.4)+ 



+ (rr3^ + .T,^-^,'-.T,')(x,,+X34) 



^25 5i4 — Aaa Xl4 



$31 !?24 Xsi A14 



$1S ^34 Xl2 X«4* 



So also if we call /,3 etc. the coeflicients of position of a plane 

 hef or e the equiangular double rotation to the right and \i^^ etc. the 

 coefficients of position after it: 



+ 2Kjr,— rr,.T,)(.Uj,+f/3j 



^3i4-A24=-(-'Tl-Tï--'^3''^4)(M23^Ml4)T(-'f2'+-T4' — -^3'-''^l')(f^8i+f*i»4)-t- 



-f(rr3'+.T,'-.-r,^-.V)(/i,,+fl3,) 



^33 '14 Mas Ml4 



■'•31 ^"24 f*?l M24 



/jj ^84 Ml» Ms4* 



