The Correlativity between Triangle Closures in First Order Triangulation Chain

The paper first analyzes the effect of refraction on triangle closure in extensive tri angulation chain.Then in considering the effects of random error,refraction and error of centring correction,the formula for estimating the correlation coefficient ρ_△ between two adjacent triangle closures is derived,and the relation between the ratio K_f of the random m.s.e.to m_f,which is the angle m.s.e.gd:\PDF\.pdfiven by Ferrero criterion,and the estimation of ρ_△,and the formula to estimate the m.s.e.of observation of any certain angle in a chain are further deduced.The latter two formulas are K_f²=A-ρ_△/1/3+A,K_f=m_n/m_f,A=s₀²-4.33D_s/3(s₀²+D_s) and the approximate formula for estimating the variance of any given angle α m_α²=m_f²+B-2B/1+Ds/s₀²COSα,B=m_f²(1-K_f)²,where m_n is the random m.s.e of the observed angle awithout refraction effects,and s₀,D_s the mean value taken over all sides in the chain and the variance to the mean.Applying the above formulas to the Chinese first order triangulation chain,the result is that K_f²≈0.61=0.61,i.e.,the effect of random errors is 61% in m_f²,and that of nonuniform refraction fields is about 39% in the chain.In addition,it may be considered that ρ_△=-0.13 and the tendency for large angles to be less accurate in the chain both are caused by the effect of non-uniform refraction fields.