The tools needed include means of length measurement, and a means of showing direction. Length measurement was covered in Chapter 2; this chapter covers direction sighting and measuring (range finding). On small construction, a sighting instrument may not be needed, but on jobs like laying out house blocks, drainage ditches, dams, irrigation channels, or roads, it is almost essential.


To extend a Straight Line between existing points A and B, to a remote point C. Like this:-

1a. Hang a plumb line from the instrument reference, and position the instrument and stand so that the plumb bob hangs vertically above point B, and the. instrument sight line points at A, Like this:-


1b. With the instrument locked in this position, take a backsight to find the direction of C (see bi-directional sights, Chapter 1). Use a range pole or plumb line as marker.

1c. Lay out the required distance B C with a tape measure, in line with the range pole.

1d. Move the range pole to the end of the tape, and check its alignment with the sights. This is the position of C. If the distance AC is not too great, and the ground between A and C is fairly flat, the alignment of A,B and C can be checked by stretching a string line between A and C; the string line should cross over point B.

To Set Out an Offset Line BC, at right angles (square) to a datum line AB. Like this:-

With the Quick Cross:-
2a. Position the instrument so that the staff stands vertically on point B, and one of the sight lines points at A.

2b. Use the alternative sights to look in the required direction - at right angles to AB. Use a range pole and tape as in 1b and c to find C. Like this:-

With an Adjustable Surveyors’ Cross:-
3a. Lock the diagonal brace so that the arms are at right angles.
3b. As for 1a.
3c. As for 2b.
To check whether the offset is square, use Pythagorus’ Rule, like this:-

Multiples of 3,4,& 5 can be used - for example:- Times x2, use 6,8,& 10. Times x 3, 9,12, & 15.

To set out a square or rectangle ABCD, from a datum line AB. There are two ways to do this. The first is to layout an offset BC as in (2) above. Then go around the square or rectangle; set up the instrument next at point C, and layout CD as an offset from BC; then from D, lay out DA as an offset from CD.
This method is used to teach laying out, or check the accuracy of instruments and observers, because there will usually be a gap between the end of DA and the start of AB. But it is not the quickest or the most accurate method.

Start by laying out AD as an offset from AB (this may need a backsight from A to B), then lay out BC as an offset from AB, either with the instrument , or by laying out BC parallel to AD with a tape measure. The four points ABCD are now located.

To check that the sides of a square or rectangle are parallel.
a. Measure the distances AB and CD; if they are equal, AB and CD are parallel.
b. Do the same with BC and AD.
To check that the sides are square, measure the diagonals AC and BD; if they are equal, the sides are square. See ‘String Lines’, Chapter 3.-


To set out a line DE, at an angle as given by a line B C, to a datum line ABD. Like this:-

With an Adjustable Surveyors’ Cross:-

a. As in step 1a.

b. With the first arm aligned to A, turn the second arm (by adjusting the brace) until the sights are aligned with C. Lock the arms in this position.

c. Move the instrument and stand to D, and repeat step 1a.

d. Sight along the second arm in the direction of E. Use a tape and range pole to find E.

The Quick Cross is an easily made layout instrument, for a quick way of setting out straight lines and right angles. It is a square flat plate on a staff, on which two sets of bi-directional sights are mounted at right angles, like this:-


In use, the point of the stake is placed on a ground marker, usually a peg. The instrument is then turned until one set of sights is in line with a target such as a range pole placed at a second ground mark. (see ‘Laying out a right angle’, above). The stake is fitted with a ground spike on a hinge, which can be kicked down to stop the stake turning, and with shelf brackets at the top to support the plate but allowing it to turn so the sights can be set on a target. An indicator to show when the plate is level is also needed.

The Quick Cross has open bidirectional sights (see Chapter 1); they can be either slit or V-notch sights, and the optics of slits or notches allow each pair of sights to be mounted only 200 mm. apart, making the plate about 150 mm. square. It can be bigger, but not smaller.

Aligning the Sights is done with a test like an end for end test, but the instrument is only turned 90º. First, make sure each set of sights is exactly in line with the centre point of the instrument, by stretching a fine thread across the center of the board, with the ends held in the sight slits or notches; the thread should pass over the centre of the pivot. Mark one set of sights as ‘Set 1’, and the second set as ‘Set 2’. Set 1 can have all mounting screws in place; set 2 should only be held with one centre screw, as shown in ‘Open Sights; in ‘Instrument Parts’.

Mount the instrument (with the quick cross, this may need an improvised stand ) facing a blank sheet of paper 3 -5 M. in front of set 1, and a plumb line in front of set 2. Like this:-

1. Turn the Quick Cross until set 2 is in line with the plumb line.
2. Look at the blank paper through set 1, and have an assistant mark the paper where the sight line comes. If you are doing it alone, note where the sight line comes on a target scale.
3. Turn the Cross 90 degrees, line up set 1 with the plumb line, and again mark the paper where the sight line through set 2 comes. There are now two marks on the paper (or note where the second point comes on the target scale).

4. Make a strong mark on the paper exactly half way between the first two marks, or note the reading half way between the target points, and without moving the instrument, gently tap set 2 sights into line with the middle mark.

5. Check that the line between the set 2 sights passes over the centre of the pivot point. (This is important with the adjustable surveyors’ cross, shown later). When you are sure the sights are in line, put in the remaining mounting screws.

An Adjustable Surveyor’s Cross.

The one shown here consists of two straight sighting arms bolted together at their centres to form a cross, and with bi -directional v-notch sights, as shown in Chapter 1, at both ends of each arm. A diagonal brace keeps the arms accurately at right angles to each other.

However, building lots are not always set out at right angles, so .with a jointed brace, it can be set to any angle, and used to project offset lines at that angle. (See ‘To lay out a line at an angle’, above). As the brace is progressively folded, angles A & B become larger than 90º, and angles C & D become less than 90º. Like this:-

The arms can be made of any straight grained timber of about 50 mm. x 25 mm. (2” x 1” ) cross section. They can be any length; a suggested size is about 350 mm.. One arm can be made short enough to fold inside the sights of the other, if the brace is unscrewed.
Another way to make the Cross is to add a cross arm to a builders’ spirit level. A modern level has 360º barrel shaped phials which will work in any horizontal position, both stood on edge or laid flat on the work. The advantage here is that the bubble indicators show when the cross arms are level, which helps laying out accuracy. (See ‘Bubble Level Phials’ in ‘Instrument Parts’).

If the Cross is mounted on a flat plate, with an eye bolt from underneath at the pivot point, a plumb line hanging from the eye will position the cross accurately over a ground peg.
Aligning the Sights. As for the Quick Cross, above. Take care with this instrument, making sure the sights are exactly at right angles, and in line with the centre pivot point; this Cross can be accurately located when mounted on a tripod.

The Dumpy Plummet. The ancient Egyptians used an instrument called a Groma to re-locate field boundaries after a Nile flood. It could lay out straight lines in opposite directions, and right angle offsets (lines running square to an existing line), and consisted of five plumb lines hanging from a horizontal cross. It must have been a nightmare to use, with five plumb lines swinging in the wind, but it had one big advantage -it showed each direction as a vertical plane, and the observer had only to look up or down to sight points on the steepest ground, and at different distances away.


The Dumpy Plummet also gives wide angle vertical views, but with only one central plumb line - the others are replaced by one set of bidirectional sights, and one set of unidirectional sights, on a T frame, which obstructs less of the view than a cross (Two bidirectional sets are not needed - if the unidirectional sights are pointing the wrong way, just swing the instrument round). It has a fine nylon plumb line which is the foresight crosshair, a low inertia water damped bob weight ( See ‘Re-thinking the Plumb Line’ in the Design Notes), and variable height bidirectional sights, and can be made in 3 stages:-

1. With the bidirectional sights, it is useful for setting up towers, masts, light and power line poles, or tall fence posts, both singly and in rows. It will also set out straight lines in opposite directions.
2. With the unidirectional sights added, it can check levels - a trick the Groma never had - and set out right angle offsets to a given line.
3. And with the addition of horizontal sight slits and a vertical scale, it will measure vertical heights.

In contrast to an instrument with only slit or V-notch sights, which projects a single sight line, the Dumpy Plummet projects the sight line as a vertical plane, like this:-


This makes it good for setting out long straight lines for roads, boundaries or fences, in steep or rough country.






The instrument has a short plumb line of fine Nylon fishing line of 2 Kgm. breaking strain, or Nylon sewing thread of about 0.2 mm. diameter, (even cotton if there is nothing else), hung from a screw at the top of a frame made of two vertical posts. The bob weight is an open ended tin or, preferably, aluminium can hanging in water in a larger tin can at the bottom of the frame, to stop it swinging. The line is passed through a fine hole in the centre of the can top, and tied to any small object -e.g. a brass nut or small fishing sinker -which will stop it pulling out.
The water container is an ordinary tin can. Old cans are fairly easy to get and there is nothing quite as suitable. Provided it is painted (preferably with oil paint) to stop rust, and protected with a strong saddle or clamp, it will last a long time. Like this:-


The bob weight is best made from an unpressurised aluminium can used for ‘sport’ or ‘energy’ drinks, to prevent magnetic effects. DO NOT USE A PRESSURE PACK CAN. The can as it comes is too high for the water container, and must be cut to fit. Like this:-





If you can’t get an aluminium can, use a tin can of the same size (used for tinned beans). But be careful it doesn’t become magnetised and act like a compass or stick to the water can.

The instrument looks like this:-


One bidirectional sight -sight 1 - is on one end of a horizontal arm - arm 1 - which is joined to post 1 by a machine screw and wing nut, so the arm can pivot up and down to change the height of sight 1. At the other end of arm 1, the second bidirectional sight - sight 2 - is mounted. on a short arm - arm 2 - attached to arm 1 by a second machine screw and wing nut; this lets arm 2 pivot about arm 1, allowing sight 2 to change height or be swung out of the way when not needed.
The unidirectional backsight - sight 3 - is on a third arm - arm 3 - which is hinged on the back of arm 1, and the unidirectional foresight - sight 4 - is screwed to the front of arm 1, allowing sighting at right angles to the sight line through sights 1 and 2. Sights 1 & 2 each have two vertical slits for sighting the plumb line, and sight 1 has a horizontal slit for reading the vertical scale. Sights 3 and 4 have vertical slits only. For laying out, the instrument must be on a stand or tripod, with its plumb line vertically in line with a second plumb line hung under the stand; the universal mount shown in ‘Accessories’ does this.

Construction and Alignment. Figs. 5-1 to 5-4 shows the various parts and assemblies.

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Stage 1 Construction. The wooden parts should be straight grained dressed hardwood - a single length of 20 x 12 mm. cross section for the posts and the scale mounting strip, and a single length of 25 x 20 mm. for the arms and the sight 1 block. If desired, post 1 and the scale strip can be cut as a single piece from the 25 x 20 mm. size. The bridge, mounting block, shelf, and brace joints can be cut from suitable scrap timber. Drill all holes as in Fig. 5-1, except the level lock hole in post 2, taking care with the positions of the pivot holes, and the plumb line screw hole, marked in red; the accuracy relies on it.
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Lay the mounting block and posts on a flat surface, front face up, so they are all in line, and screw them together. Add the bridge and plumb line screw. Screw on the shelf, stand the water can on it, and mark the posts where the top of the can comes; then bevel the inside edges of the posts to let the back of the can sit flush with the back of the mounting block. Use a gutter down pipe saddle to hold it in place, or make a saddle from a tin can larger in diameter but shorter in length..
Make sights 1 and 2 from light gauge aluminium sheet, an offcut of aluminium angle, or tinplate from a can. Sights 1,2 &3 can best be made from 20 x 20 mm. alominium angle. Counterbore sight 1 block & the right hand end of arm 1, and assemble as shown in Fig. 5-1. Screw sight 1 in position with its horizontal slit in line with the centre of the pivot screw head. Like this:-


Screw sight 2 on to arm 2, and arm 2 on to arm 1; the arm 2 pivot screw may if desired be held tight by a locknut let into the back of arm 2, to keep the screw from turning when the wing nut is tightened, similar to the sight 1 block assembly. Now screw arm 1 to post 1; a locknut let into the back of post 1 will also keep this screw from turning.

. Make the bob can and plumb line as shown above. Set the plumb line screw slit vertical, put the top of the line through the slit. and clamp it with a wing nut and washer, making sure the bob can is swinging free of the bottom of the water can, but with the top of the bob can below the top of the water can, so that the bob is completely covered with water when in use.This is important.
Alignment. (a).Adjust the lock nuts on the plumb line screw to make it 38 mm. from the plumb line to the front face of the bridge.
(b). . Mount the instrument on a stand - the Universal Mount (See ‘Accessories’) is ideal - and adjust its tilt to bring the frame vertical all round, when tested with a separate plumb line. The dumpy plumb line should now be in line with the sights 1 & 2 vertical slits; if not, re-adjust the lock nuts to bring it into line. This is the only alignment needed for stage 1.



Using the Stage 1 Dumpy Plummet

1. To set up a pole, post or tower in the vertical position.

(a). Mount the plummet on a stand (a mounting bracket with levelling screws is desirable but not essential) and position it from the pole a distance roughly equal to the pole height.

(b). Pivot arm 2 up or down so that sight 2 doesn’t obscure the sight line.
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(c). Turn the instrument until a sight line from sight 1 through the plumb line is facing the pole, and swing arm 1 up or down until the both the top and bottom of the pole can be sighted through the plumb line. The pole can now be pulled vertical by aligning it with the plumb line. Like this:-





2. To lay out a straight line AB beginning from point A, in rough country.
(a) Mount the Plummet as in 1(a) and position it vertically above point A, using a separate plumb line hung under the top plate of the stand. This line MUST be exactly in line with the crosshair plumb line. If your stand won’t do this, go to step (g) below.
(b) and (c) As in 1(b) and (c).
(d). Set the instrument in the direction you wish the line to go, either by sighting on a remote reference point or a range pole in the right position.
(e). Move arm 1 up or down until the entire length of AB can be sighted through the plumb line (if you can’t do this, lay out line AB as far as possible, then use procedure no. 3).

(f). As many points in a straight line as you need, can now be laid down by sighting through the plumb line from the backsight. Like this:-


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The line follows the ground shape when viewed from the side, but is straight when viewed from above.

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3. To extend a straight line AB, to point C, using sight 2.
(a) Place the Plummet and stand centred above point B, using a separate plumb line hung under the stand top plate, and with the instrument frame adjusted to plumb as in 1(c) above.

(b) Turn the instrument until a sight line from sight 1 through the plumb line is facing point A - swing arm 1 up or down if necessary, and tighten it firmly in position.
(c). Swing arm 2 up or down until the plumb line, as viewed through sight 2, covers the ground area where C will be, and tighten the arm firmly in place.

(d). Look from sight 2 back to sight 1 , to see if both sights and the plumb line are in line. If not, adjust the frame tilt until all three are in line, and repeat step (b).
(e). Look from sight 2 through the plumb line & sight 1, to locate C.

Because arms 1 & 2 can be turned through large angles, this method can be used to project straight lines in very steep country, like this:-



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4. To set up a row of tall posts.
(a) First locate the positions of the first and last post holes.

(b). Place the Plummet and stand at one end of the row, centred over the post hole position (Use a separate plumb line on the stand).

(c). Set up the instrument as in 1 (b) to (e). Start by setting up the post furthest away from the instrument; the other posts can then be located and set up on the Plummet sight line.
(d). If the row is long, the Plummet may be centred over a post hole in the middle of the row, and sighted in opposite directions with the second backsight, as in (3) above.

Stage 2 Construction . Cut out arm 3, the brace joints, and the spacer, and drill all holes except one in each joint, as in Fig. 5-2. Screw arm 3 to the back of arm 1, with a small (50 - 100 mm.) butt hinge, keeping arm 3 square (vertically) with the back of the posts. Screw the joints to arms 1 & 3 . Make sights 3 &4, cutting the slits with a junior hacksaw, if possible. Sight 3 can be 50 to 80 mm. long; a longer size allows the cross sight line to see tfe ground at a shorter distance from the instrument - useful for short offsets. An optional short slit at the bottom end of sight 3 gives an addifional steep angle view of the plumb line. Screw sight 3 to the side of arm 3 with a 5 mm. machine screw and wing nut; it can then be folded down alonside arm 3.

Hold arm 3 firmly square (horizontally) to arm 2, and the brace joints in a straight line with each other, and drill the remaining hole through both joints, making sure it is exactly half way between the first two holes. Check the folding action of arm 3.
Make and mount sight 4 as in fig. 5-3; the slotted mounting holes allow fine adjustment of the right angle between the centre and cross sight lines. Alignment. (a). Repeat steps (a) and (b) from stage 1 alignment.
(b). Adjust arm 1 up or down until it is square with the side of post 2, then drill the level lock hole in arm 1, using the hole in post 2 as a guide. Then put in the level lock pin to hold arm 1 in place.
(c) Set up an end for end test with a blank sheet of paper (See ‘Aligning bidirectional sights’ in Section 4a), and tap arm 2 up or down until the horizontal slits of sights 1 & 2 are level in both directions. Then drill a hole through arms 1 and 2, and put in a second lock pin.
(d) Look through sights 3 and 4, and turn the plumb line screw slightly to bring the line to the centre of the sight 4 slit. The instrument is now aligned for level.
(e) With a target and plumb line, set up an end for side check (See “Quick Cross Alignment’ in this chapter), and move sight 4 to right or left until the sight lines are square, then tighten its screws.

(f). If the plumb line is now not in line with the sight 4 slot, turn the plumb line screw a little to bring it into line. Do NOT move sight 4 to do this.
The instrument is now adjusted for level , plumb, and square (horizontally). It can set out straight lines in opposite directions, square offsets to a reference line.(See ‘To Set Out an Offset Line’ earlier in this section) and check levels.

Stage 3 Construction. Make the scale mounting strip, the scale mounting bracket (either from aluminium angle or 20 x 12 mm. dressed wood), and the scale, as in Fig. 5-3. A wooden ruler can be used, but is not as easy to see as a plastic one. If you are using a plastic ruler, either paint the scale face of the mounting bracket flat white, or stick a strip of white paper on it, and screw the scale on.

Screw the mounting strip to the side of post 1, then screw the bracket and scale to the strip, making sure the 100 mm. scale mark is exactly in line with the pivot screw. (If you are sure you won’t need to measure downwards from level, you can cut the ruler just above the 220 mm. mark & mount the scale to bring the zero scale mark in line with the pivot screw; this makes the arithmetic easier).

Alignment. Do the stages 1 & 2 alignment, then check that the 100 mm. scale mark is exactly in line with the pivot screw. If not, loosen the scale screws a little, and slide the scale up or down to bring it in line vertically, and adjust the lower scale bracket screw to bring the 100 mm. mark in line horizontally, and the upper scale bracket screw to make the scale parallel with post 1.
You can now measure vertical heights.

5. To measure the vertical height of an object

(a). Place the Plummet and stand at a distance from the object of roughly twice its height.

(b). Turn the instrument until the object can be sighted through sight 1. Adjust the stand to bring the plumb line into line with both sight lines.

(c) Move sight 2 out of the way. Move arm 1 up or down until the bottom of the object, the 100 mm. point on the scale, and sight 1, are in line. Lock arm 1 tight in place.

(d). With a tape measure, find the distance D in Metres, from the bottom of the object to the arm 1 backsight. Note:- This is the straight line distance, not the distance along the ground.

(e). Turn sight 1 up a little, but don’t move arm 1. Look at the top of the object through sight 1, and record the scale reading in line with it (R mm.). Like this:-




(f) Then the object height in Metres is given by :- .

Numerical Example (Best done with a hand calculator ) :-

Let D = 20 Metres. (Note:- It makes the calculation easier if D is a whole number - preferably 20, which when multiplied by 5 equals 100. However, standing the instrument at a distance of about twice the height is more important.)
Let R = 165 mm.
Step 1. Subtract 100 from 165:- 165 - 100 = 65.
Step 2. Multiply D by 5:- 20 x 5 = 100.
Step 3. Multiply 65 x 100 = 6500.
Step 4. Divide 6500 by 1000 = 6.5 Metres (The object height).

D can be measured in feet and inches; the answer is also in feet
and inches.
Bring D to inches, then turn it back to feet at the end, like this:-
Let D = 20 ft. 5 ins. Let R = 165.

Step 1. Subtract 100 from 165:- 165 - 100 = 65.
Step 2. Multiply D by 12 to convert to inches:- 20 x12 +5 = 245.
Step 3. Multiply 245 by 5:- 245 x 5 = 1225.
Step 4. Multiply 65 by 1225:- 65 x 1225 = 79625.
Step 5. Divide 79625 by 1000 = 79.625.
Step 6. Divide by 12 to bring the height to feet and inches:- 79.625 ÷ 12 = 6 ft. 7.625 ins. (Approximately 6 ft. 7 1/2 ins.)

The scale extends a little below the 100 mm. point, so that readings can be taken downwards also. In this case, R is less than 100, and must be subtracted from 100. Example:-

The scale extends a little below the 100 mm. point, so that readings can be taken downwards also. In this case, R is less than 100, and must be subtracted from 100. Example:-

Let D = 25 Metres. Let R = 65.

Step 1. Subtract 65 from 100 :- 100 - 65 = 35.
Step 2. Multiply D by 5 :- 25 x 5 = 125.
Step 3. Multiply 35 x 125 = 4375.
Step 4. Divide 4375 by 1000 = 4.375 Metres, or 4 Metres 375 millimetres (The depth of the object).

6. To Measure the Height of a Hill.

This is useful when the horizontal distance to the object, such as a hill, can’t be measured, and it is too steep to use a dumpy level, staff, & target.
(a). Stand the instrument at position 1, a short distance from the base of the hill, and where it is possible to move the instrument and stand nearer the hill.
(b) Level the instrument, and align the sights with a prominent feature at the top of the hill (or place a target there). Like this:-

(c). Drop a plumb line from the backsight, point C1, and put a peg vertically below it.
(d). Sight the top of the hill and record the scale reading D1 E1. With the Dumpy Plummet, this will be D1 - 100.
(e). Place a staff and target close to the base of the hill, and align the top edge of the target with the level sight line C1 C2 B.
(f). Move the instrument to position 2, sight the lower target,and adjust the instrument height to bring its level sight line on to the top edge of the target.
(g). Sight the top of the hill and record the scale reading D2 E2. With the Dumpy Plummet, this will be D2 - 100.
(h). Drop a plumb line from the backsight, point C2, and measure the distance C1 C2.

Then the vertical height of the hill from the level sight line, A B, is given by:- . With the Dumpy Plummet, K1 = 200.
Numerical Example:- Let C1 C2 = 20 M.
Let D1 = 155.6 mm.. Then D1 E1 = 55.6 mm.
Let D2 = 225.0 mm.. Then D2 E2 = 125.0 mm.

(1) Calculate the top line:- C1 C2 x D1 D2 x D2 E2 = 20 x 125 x 55.6 = 139000.
(2) Subtract D1 E1 from D2 E2 :- 125 - 55.6 = 69.4.
(3) Multiply the answer to (2) by K1 :- 69.4 x 200 = 13880.
(4) Divide the top line by the bottom line :- 139000 ÷ 13880 = 10.014 Metres.


7. To Use as a Sighting Level.

The scale has a red arrow at the 100 mm. mark. Put the lock pins in arms 1 & 2 using sight 1 as the backsight, and check whether the horizontal slits of sights 1 & 2, and the 100 mm. scale mark, are in line. If they are, level sights can be made using sight 1 as the backsight and sight 2, or the scale 100 mm. mark, as the foresight., If not, swing arm 2 out of the way, and just use sight 1 & the 100 mm. mark.

7. To Measure the Gradient of a Channel, Ditch or Roof Gutter.

The scale has a blue arrow on each side of the red arrow. These give the correct drain gradient - approximately 1 in 60 - for roof guttering. A ground drain or irrigation channel often has a smaller gradient (e.g. up to 1 in 1000) .
(a). Set up the instrument and lock arm 1 as in 6 (a).

(b). A sight line from sight 1 through either blue arrow gives the correct gradient up or down for roof guttering.
(c). Hold the staff up to the bottom of the guttering at the instrument site, and mark the position of the sight line on it. Then move staff and target to the other end of the guttering. Like this :-




This brings us to the end of laying out. Chapter 6 extends measuring into Range Finding - measuring distances to targets which are inaccessible.