The method of correlates is used in case of more complexity. In that case, it involves usage all information available and conditions mentioned so that it provides result regarding problem raised.

The most probable value obtained from unknowns of normal equation helps in determination of direct observations from equal and unequal weights, indirect readings from equal and unequal weights, observations accompanied by condition equation.

The laws of weight are established based on method of least squares in which it describes true value among list of possible errors. It consists of sum of squares with a minimum residual error.

The probable error of measurements can be given as,
Probable error of measurement = \(\sqrt{E1^2+E2^2+E3^2+E4^2} \). On substitution, we get
= \(\sqrt{5.64^2+2.98^2+0.98^2+2.54^2} \)
= 6.93.

The normal equation for x can be found out by multiplying equations with constant of x i.e.,
5*(5x+2y+3z-6 = 0) = 25x+10y+15z-30 = 0 and similarly,
2*(2x+4y+6z-10 = 0) = 4x+8y+12z-20 = 0. On adding we get normal equation for x i.e.,
29x+18y+27z-50 = 0.

The term must always be positive because it eliminates possible error which will occur during process of recording values. It can also be believed that presence of square can make it positive.

By applying principle of least squares value of N can be determined by,
?r?² = ?r² + n*(N-(?V/n))². On substitution, we get
24.98 = 13.76 + 8*(N-(3.32/8))²
N = 1.6.

It is a primary rule in every surveying method employed. It helps in equal distribution of error which can actually increase rate of output and accuracy of output.

The value of most probable value can be obtained by using formula,
M = (V1 + V2 + V3 +V4) / n. On substitution, we get
M = (2.76 + 4.32 + 9.87 + 8.83) / 4
M = 6.45.

The value of E for a single wave length with dual weights can be given as
E = ?*(1/w1 + 1/w2). On substitution, we get
E = 21*(1/6 + 1/2)
E = 14.