# Two - Peg Test for a Level S1

Two - Peg Test for a Level S1 Line of Collimation Horizontal Line A S1 x B L/2 L/2 L x S2

S1 Line of Collimation S2 Horizontal Line A S1 x B L/2 L/2 L The TRUE height difference

hT = S1 - S2 The APPARENT height difference S1 = S1 + x and S2 = S2 + x hA = S1 - S2 x S2 S1 Line of Collimation S2 Horizontal Line A S1

x B L/2 L/2 L The TRUE height difference hT = S1 - S2 The APPARENT height difference S1 = S1 + x and S2 = S2 + x hA = S1 - S2 hA = (S1 + x) - (S2 + x ) x S2

S1 Line of Collimation S2 Horizontal Line A S1 x B L/2 L/2 L The TRUE height difference

hT = S1 - S2 The APPARENT height difference S1 = S1 + x and S2 = S2 + x hA = S1 - S2 hA = S1 - S2 = hT Therefore : hA = hT This is true since the instrument is the same distance from both staff positions and the errors x are equal and cancel out. Now move the instrument outside the odd numbered peg S3 S3 A

B L / 10 S4 S3 S4 S3 A B The APPARENT height difference hA But the TRUE height difference hT L / 10

= S3 - S4 We already know is S4 S4 A The APPARENT height difference hA S3 S3 B L / 10 = S3 - S4 hT = S1 - S2 But the TRUE height difference Therefore if hA = hT then the instrument is OK If NOT then the error is e = (S1 - S2) - (S3 - S4) / L mm / m

Summary : Two - Peg Test Place two pegs about L = 30m (to 40m) apart. Set up level midway between the two pegs. Read staff on each peg, and calculate true height difference. Move level about L / 10 = 3m (or 4m) beyond one of the pegs. Read staff on each peg again, and calculate height difference. Collimation Error e = difference in the differences and is expressed as a number of mm per L m Acceptable errors Uren and Price 1mm per 20m Wimpey 4mm per 50m Test should be carried out regularly say once per week or two. S2 S1

A L/2 B L/2 L S4 A Collimation error, e = (S1 - S2) - (S3 - S4) mm / Lm S3 B L / 10

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