ADJUSTMENT BY LEAST SQUARES 163 
be accommodated to the particular degree of accuracy in adjustment 
which is considered worth while. Most practical geophysicists are 
agreed that an elaborate, ultra-precise least-square adjustment of 
their observations is an unwarranted expenditure of time and labour. 
On the other hand, some adjustment is obviously necessary. 
§3. THE NORMAL EQUATIONS 
In the terms used in treatises on the method of least squares* we 
have given a series of ‘‘conditional”’ equations ; 
(AB) = (ab), 
(BC) = (bc), 
(CA) = (ca), 

Fic. 1 
together with a series of “‘rigorous’’ equations 
g 
(AB) + (BC) + (CA) = 0, 
There is one conditional equation for every link in the network, 
and one rigorous equation for every independent polygon in the net- 
work. We shall assume that all the observations and link-increments 
such as (ab) have equal weight. 
For such a system of conditional and rigorous equations, the nor- 
mal equations for a least-square adjustment are obtained as follows. 
For each rigorous equation, provide an unknown multiplier or cor- 
relate m. The unknown increment (PQ), which occurs in one only of 
the conditional equations, namely (PQ) —(pq) =o, occurs also in at 
most two of the rigorous equations. For normally it will be a common 
section of the boundary of two adjacent polygons, e.g., OPQOR, SQPT, 
Figure 1, and at the extreme boundaries of the network one of these 
EF. T. Whittaker, and G. Robinson, The Calculus of Observations, chap. 1x, and 
particularly §129, pp. 252-254 (1924). 
823 
