CALCULATION OF A BLOCK OF STRIPS, ETC. 
II 
in which we have : 
S ls = fW,-*,)*+ (Yt-Ytf 
Assuming as origin of the coordinates the mean point M of the segment A X A 2 , 
and putting : 
x — X — A M ; y = Y — y M ; s = 
we find : 
P = 
q = — ; r = o 
s 
s 
which allows formula 2) to become, in a form easier for calculation : 
D =- p y — q x 
The sign of D results positive in the half-plane which is to the left of anyone 
looking from A 1 to A 2 , and negative in the half-plane to the right. To avoid con 
fusion, it may be advisable to take as point A x , in each stretch, the point of minor 
abscissa. 
b) Equalizing the elevations from the various origins i j... in the points 
Tv- common to several stretches, and equalizing them to the ground elevations 
in the known points A 1 , we obtain the following generated system : 
(T** points) 
(.A 1 points) 
(symbols of para. 5). In this system the unknown quantities are the n rotations 
X 1 ; each point T generates as many independent observation equations as are 
the stretches it connects, less one ; each point A generates as many independent 
observation equations as are the stretches in which it appears. For the block men 
tioned in para. 6, supposing that the common points connect only two transver- 
sally adjacent stretches, and that the known points belong to one stretch only, 
we would get a system of 60 equations with 10 unknowns, much simpler that the 
system of 180 equations with 70 unknowns of the rigorous procedure. 
System 4) may be solved by the method of least squares, using any procedure, 
being considered like a system of observation equations ; in view of the limited 
number of unknowns, calculations may be carried out using a small electronic 
computer also for blocks of very large size. We give below (para. 14,b), as a practical 
example, the calculation of the same block of 15 stretches of para. 8, programmed 
for a 1620 I.B.M. computer.