In a similar way it follows from the right-hand triangle: 
1 
T = 1, (x we Yi+1) — (Hi— Hi41) 
The angle between the air bases then is, if we put yi = yi 1 — y by ap- 
proximation: 
1 
n—S—T = yo 5 (ns — 21 Hits) 
Appendix III. 
The symbolic calculus of weight- and correlation numbers has been invented 
by Prof. Tienstra ®). The principle is that the square of a weight symbol Q, or the 
product of two weight symbols Q. and Q, stand for the weight number or the 
correlation number of the quantities concerned: 
Q = Qo, and Q.Qy= Qu 
It can easily be proved that the commutative and distributive properties of 
multiplication of algebraic quantities are valid also for these symbols. 
Example: 
If x = az + bt 
and y-m.ez vct. dt 
we obtain by applying the law of propagation of errors: 
Q. — aQ. 4- bQt 
Q, = <Q: dO 
whence: 
d Q;? E (aQ, + bQ:)” = eo? de 2 abQ;Q. + BO 
an 
QQ, = (aQz + bQr) (cQ + dQ:) = 
= acQ + (ad + bc) Q:Qı + bdQ 
or in non-symbolic form: 
Qu = as +2 abQa + b?Qu 
Qu = acQz: + (ad + bc) Qet + bdQu 
The weight- and correlation numbers given in table 2 have been derived in 
this way. We will limit ourselves to giving some examples, leaving the derivation 
of the other weight- and correlation numbers to the reader. 
Computation of the weight number of fi. 
From (20) it follows by symbolic squaring: 
Q' B, -ie d q) (Q qa + Qui+1) — 9 (Q qi + Qui) d 
e mut 
or taking into account that all quantities concerned are non-correlated except 
$i-1 and pi and accordingly y/ and gii: 
8) J. M. Tienstra: Het rekenen met gewichtsgetallen. Tijdschrift voor Kadaster en Landmeet- 
kunde, 1934, p. 37. 
W. K. Bachmann: Calcul symbolique des coefficients de poids. Schweizerische Zeitschrift 
fir Vermessung und Kulturtechnik, 1945, p. 131. 
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