### 3. Three wire readings

Rather than set the four points accurately at an interval of d, it is easier to set them at the approximate interval and then measure the distances as the readings are made. This is done using the instrument's stadia crosshairs. An level has two additional horizontal crosshairs spaced equally above and below the main horizontal crosshair, Figure G-5.

Figure G-5 Stadia Crosshairs |

The instrument's manual will specify the multiplier (or stadia multiplier), k, for the instrument (it's also generally labeled in the case). In most cases the multiplier is 100 (to 3 sig fig).

The stadia interval, i, is the difference between the top and bottom stadia hair rod readings. Multiplying the rod interval by the instrument's multiplier gives the horizontal distance from the instrument to the rod:

Equation G-4 | ||

d: horizontal distance k: stadia multiplier i: stadia interval |

Figure G-6 Horizontal Distance from Stadia Crosshairs |

Besides allowing us to determine the distance to a point, reading all three horizontal crosshairs provides a check on the rod reading: since they are equally spaced, the center hair reading should be the average of all three. The average may not be exactly the same as the center reading because all three readings are subject to random errors.

Example

The following shows a backsight on a point. The instrument used has a multiplier of 100.

top: 4.31 middle: 4.16 bottom: 4.02 |
||

Figure G-7 Readig Stadia Crosshairs |

Average: (4.31+4.16+4.02) / 3 = 4.163' checks middle hair reading

The BS reading is 4.163' - note that we're carrying an additional decimal place since it is the average of three readings (also correct for sig fig).

i = 4.31-4.02 = 0.29'

The distance to the rod is 100(0.29') = 29'

When three-wire leveling the rod must be held vertical using a bubble. Waving the rod does not work, Figure G-8, since the lowest reading on the top and bottom stadia hairs do not occur when the rod is vertical.

Figure G-8 Waving the Rod Introduces Errors |

In the collimation process the distances from point 1 to A and B and from point 2 to A and B are mesaured by stadia.The measurements are used to compute an overall average d used to obtain the collimation error.

Figure G-9 Base Line Point Spacing |

Eqn (G-5) |