LIEUT. CLERK’S REPORT: ELEMENTS OF REDUCTION. 
353 
sin — A+Bg+Cg+Dg— E 2 
sin S 27 =A-B 5 +C 3 -D 6 -E 2 
sin & n =A+B g — C 3 — D 6 — E 2 
sin£ 21 =A— B 5 — C 3 +D 6 — E 2 
sin^ 6 =A+B 6 +C 2 +D 4 — E 4 
sin S 26 =A-B 6 +C 2 -D 4 -E 4 
sin 5 10 = A-{-B 6 — C 2 — D 4 — E 4 
sin c> 22 =A— B 6 — C 2 +D 4 — E 4 
sin =A+B 7 +C 1 +D 2 — Eg 
sino 23 =A-B 7 +C 1 — D 2 — Eg 
sin = A+B 7 — C 4 — D 2 — Eg 
sin ^ 23 =A— B 7 — C 1 +D 2 — Eg 
sin =A+B— E 
sin£ 24 =A— B — E. 
“ £ If the deviations are under 7° or 8°, the angles of deviation may be used in the for- 
mulae instead of the sines of the angles without producing a sensible error in the result. 
It may be observed that <p' cost)' and ©'sin & would be themselves properly ex- 
pressed in a series containing sines and cosines of and 2 and this would in- 
troduce into the expression for sin B terms of the form 
F sin 3^'+G cos 3^'+H sin 4^'+K cos 4 
“ ‘The omission of these terms from the formula we have used does not affect the 
values we have found for A, B, C, D, E; and the values of the additional coefficients 
may be determined from the following expressions, in which we make use of the ob- 
servations on the sixteen principal points only: — 
F=-1155 (log =1-06252) {s 2 -%-K 4 -%}, 
+•0884 (log =2-94639) {^ 4 —.y 28 +A' 12 —5 20 }, 
-•0478 (log =2-67975){*g- % +.? 1 o — s 22 }, 
( s 8 ~ '%) (31.) 
1 * 
G=-^-(.?o %) 
+ •0478 (log =2'67975 ){s 2 +.s 30 — s 14 -s 18 }, 
— •0884 (log =2-94639) {s 4 +%— -? 12 — .%>}, 
— *1155 (log =T06252){$ 6 +tf 26 — j 10 — s 22 }. .... (32.) 
H=^{^2— ^30-%+%— - s 6+%+ 5 io~'y 22 } (33.) 
K = jg{^ 0 + % + ^8‘i‘' S 24 — 5 4 — ,y 28 -,S 12“' y 2o}- • • 
• ( 34 .) 
