Note that this is a re-print of the original publication, based on a scanned copy. During the process of converting the original paper copy to this electronic version, the original formatting, page layout and page numbers have been lost. All diagrams and surveys have been scanned from the original and are consequently of poor quality.
Contents
Lundy 1966 by MT Mills
Traverse Closure and Other Errors in Cave Surveying by BM Ellis
Paignton Zoo Caves by WN Tolfree
Review: Journal of the Mendip Nature Research Committee
Journal published by the Shepton Mallet Caving Club
The Mineries, Wells Road, Priddy, Wells, Somerset, BA5 3AU
Editorial
The editor apologises for the very late publication of this journal. Due to difficulties in printing the covers, this issue has arrived four months late. In the future it is hoped that every effort will be made to eliminate this source of delay.
Again no articles about Mendip caves appear in this issue. It appears now that many Mendip cavers do their serious underground work in regions abroad from the Mendips. One article describes the caves of Lundy and, I believe, is the first account of this area to enter any caving club publication. Surveys and descriptions of the Paignton Zoo caves also appear in this issue, and for those who wish to become proficient at high grade cave surveying, an article appears describing the errors in cave surveying, and outlines some methods used to reduce these errors.
Lundy 1966
In June of this year Bill Tolfree and myself spent ten most interesting days on this island in the Bristol Channel, which is 3½ miles long and ½ mile wide, and situated some 11 miles North of Hartland Point, the nearest point on the mainland. The object of our visit was rock-climbing; the island having escaped climbers' notice until 1961 when the first party visited the island, but since that date parties have continued to visit the island and will undoubtedly do so for years to come – increasing in numbers as the island's rock climbing potential is realised and explored.
The island is composed almost entirely of granite (the official guidebook states 93%), and in common with the Cornish sea cliffs the particular problems encountered is the difficulty of finding routes down to the foot of the cliffs. The rock is subject to a growth of hairy lichen, often over one inch thick, which covers the rock above about 150 feet above sea level.
Although the island has much to offer the climber, we were surprised and pleased to find that it also has several features of interest to the speleologist, and which we were able to investigate during our stay (finding several to have intriguing histories), often when it was too wet or hot to climb. Previous to our visit I had learnt that there was at least one cave on the island, and so we had taken a tape and prismatic compass with us intending to make surveys of any caves found; together with 400 feet of ladder to use in a descent of the Devil's Limekiln.
The Earthquake (NGR 131452)
Situated about two-fifths along the length of the island Northwards on the West coast, just beyond the Quarter Wall at a height of about 375-400 feet above sea level. This peculiar geological feature extends for about 100 yards along the cliff top and comprises a great dislocation and fracturing of the rocks and is not merely a landslide of the surface, but faulting with the rocks fractured at right angles to their line of strike. The result is many depressions often 20 feet deep with vertical sides and floors of jammed blocks between which can be seen wide and deep fissures, but all become too tight or are blocked by boulders or debris before they are a further 30 feet deep. The official guidebook states that some of these fissures may extend to sea level, but as this is over 300 feet below it is most unlikely that anything more than the finest crack would exist at this depth; and also that this feature is of volcanic origin and dates back to the early days of the island's evolution.
Benson's Cave (NGR 142438)
This is situated about 300 feet above sea level, just below the remains of Marisco Castle on the south-east corner of the island where it narrows to a peninsula running down to the South Lighthouse and Rat Island. The castle itself was built subsequent to 1242 when the island was forfeited to the Crown on Sir William de Marisco being convicted of treason as a result of his piracy activities in the Bristol Channel. Some differ as to the age of the castle and the castle remains, and say that the latter only date from the 1800's (5).
The cave is named after Thomas Benson, MP who leased the island from Lord Gower for a few years around 1750. He was a merchant and shipowner who lived at Appledore on the mainland, and is reputed to have turned smuggler and to have constructed this cave for use in connection with smuggling. The cave is of almost uniform cross section throughout its 63 feet length, is almost straight in alignment as is shown by the accompanying survey; and is most certainly man-made having been hacked out of the granite cliff, thus confirming this part of its history at least. Anyone who has ever tried hammering pitons into granite will appreciate the work that must have gone into the excavation of this cave. The entrance is formed by the breasts and stone lintel of an open hearth fireplace, and the remains of the building outside the entrance confirm the legend that the cave was hidden behind a fireplace - but at present serves as a shelter for sheep.
The official guidebook states that wooden steps used to lead down to the beach from the cliff, and maybe a keg of brandy and bale of tobacco (on which excise had not been paid) were carried up and down those steps (5). The landing beach is only 100 yards to the north-east of the cave and the reputed unusual approach, although differing slightly in exact detail is confirmed by an extract from a letter written by a guest who accompanied Benson to the island in 1752 "The inhabitants, by assistance of a rope, climbed up a rock, in which steps were cut to place their feet, up to a cave or magazine where Benson lodged his goods." (2) Additional support for the existence of such a cave is provided by "Benson got into difficulties for smuggling, and what was then termed piracy, and was exchequered and fined in heavy penalties for duties to Government amounting to £5,000. A writ or fieri facias was directed to the Sheriff of Devon to levy the penalties under which the officers seized a large quantity of tobacco and other goods secreted in a magazine and caves cut out of the rock of Lundy." (3), (4) - this was in 1748.
Figure 1 – Survey of Benson's Cave
Sentinels Cave (NGR 144437)
This turned out to be the cave that had been mentioned to me before our visit, and is situated at the south end of the Landing Beach towards Rat Island and almost directly below the South Lighthouse. Access to the cave is from the Landing Beach at low tide. At the time of our visit there did not appear to be a local name for the cave and so we named it thus, after a group of large rock pinnacles at the south end of the Landing Beach and close to the entrance of the cave. The cave is situated in a portion of the 7% shale of which the remainder of the island (93% granite) is composed, the shale being said to correspond to the shale at Mortehoe and Ilfracombe on the mainland (5). The entrance is below a large impressive shale overhang and is entered over a heap of crumbling shale blocks beneath this - the entrance is clearly shown in the centre of a picture postcard on sale on the island and entitled "Lametor Peninsula, Lundy and the South Lighthouse".
The accompanying survey shows the nature and form the cave takes, which of the features on the island is the nearest to a limestone cave, as we know them. One resident informed us that at one time the cave connected through the headland to Hell's Gates (the shingle bar between Rat Island and the south-east corner of the island adjoining the South Lighthouse) a distance of between 100 and 200 yards. Although the end of the cave does give the appearance of having collapsed we were not convinced that the cave continued beyond, and the continuation may well only be local legend.
Figure 2 – Survey of Sentinels Cave
Devils Limekiln (NGR 134435)
This is the giant blowhole situated on the south-west corner of the island on Shutter Point and was the reason for our taking 400 feet of ladder to the island, as we had read (1), (5) that it was 370 feet deep and the thought of five feet more than Gaping Gill direct made a descent a must. A very severe footpath down the side of the cliff, which provides an approach to Great Shutter Rock, gave us access to the bottom of the chasm prior to laddering. At the bottom a sea cave passage / enlarged rift brought us to the bottom of the pitch and a further drop through the boulder floor of 24 feet led to another sea cave passage running out to sea at right angles to the first.
Subsequently we carried our ladders to the gouffre and after spending one and a half hours trying to find pitonable cracks in the granite pinnacle that is situated at the southern (seaward) end of the chasm, we managed to arrange sufficient for adequate belays. Lowering 405 feet of ladder down and then after arranging a coil of 390 feet of lifeline, Bill with whistle and rock helmet commenced the descent. The first 120 feet was easy and down a large smooth slab covered in lichen and inclined at about 80°. At the bottom of the slab a piton was put in as a tether for the ladder and the real descent commenced - going off the edge of the slab an impressive thirty to forty feet overhang shot away from the ladder and a free pitch of 110 feet appeared. Although wearing a "Beaudrier Alpin" for resting as necessary, this was not required as at about midway on this pitch a convenient ledge was within reach and Bill was able to swing over and step off for a rest. Half an hour after leaving the top Bill arrived back and taking over the lifeline from me I repeated the descent. At the bottom I found, as Bill had reported, about 150 feet or ladder heaped on the floor of the chasm, and subsequent measurement showed the pitch to be only 235 feet deep - disappointing but nevertheless most impressive and worthwhile. But from our point of laddering the ladder hung directly over the hole in the boulder floor leading to the lower passage, thus making a full descent 259 feet.
The depth of 370 feet must, we feel, refer to the height from sea level up to the north (landward) side of the chasm, which is about forty feet higher than the top of the southern side and our point of laddering. However a descent from this side would be down the very loose back wall and a far more serious undertaking. The 2½ inch OS map (6) shows the chasm starting below the 350 contour thus indicating the depth to be still less than the 370 feet claimed (1), (5).
The accompanying survey indicates the size of the two sea cave passages, whilst on the surface the chasm is roughly square in plan with sides of around 200 feet, looking rather like a giant funnel tapering into its depth - the passages below in the granite indicating its origin being as a result of sea erosion. At first the chasm is an awe inspiring sight; it is not difficult to understand why some years ago a young lady is said to have thrown herself down the chasm at night, whilst her mind was disturbed – her torch left on the cliff above serving to indicate her fate and whereabouts.
Even taking into account the tragic circumstances of this earlier descent, our satisfaction at having accomplished the first true descent was somewhat dispelled when we learnt that on his second visit to the island in 1927 (his first visit being in 1903 (1)) Dr Tom Longstaff, mountaineer and member of the 1922 Everest expedition, had descended to the bottom of the limekiln with his daughters by rope! A most adventurous feat of daring, but the line of descent was most likely via a series of stable ledges and a relatively easy chimney in the north-east corner.
Figure 3 – Survey of Devils Limekiln
Seal's Hole (NGR 136435)
Situated some 300 yards west towards the Devil's Limekiln from the beach opposite the Rattles Anchorage at the south end of the island, this cave is the only known place on the island of the Atlantic Grey Seal which is haunting the shores in increasing numbers (at the last census over 80). This sea cave is stated (5) to be a hundred yards long and terminating in a gravel floored chamber sixty feet high, which is not touched by the tide. Unfortunately time did not permit us to visit this cave, which is only accessible from the beach along the base of the cliffs at low tide; and to visit it during the breeding season is not advised.
On our visit to the island next year we are hoping to investigate the following:
- Signs of the continuation or the other end of Sentinels' Cave
- Mermaids Hole to the south of the South Lighthouse and on the opposite side of the Lamentor Peninsula to the Landing Beach
- Old Copper Mine adjoining Long Ruse which is on the west coast and slightly south of the North Lighthouse
- Visit and survey of Seal's Hole
- Mousehole and Trap just north of Brazen Ward in Gannets Bay and on the east side of the island
References
- RB Evans – Climbing on Lundy. Mountaincraft (62). (Winter 1963)
- S Thomas – The Nightingale Scandal (Gazette Printing Service, Bideford). (1959)
- JR Chanter – Lundy Island. Devon Assoc Trans, 4. (1871)
- WS Boundy – Bushell and Harman of Lundy (Gazette Printing Service, Bideford). (1959)
- FW Gade – Lundy, Bristol Channel The Official Guide (Gazette Printing Service, Bideford)
- Ordnance Survey – 2 ½ inch map, sheet SS44. (1960)
- Ordnance Survey – 1 inch map, sheet 163. (1960)
MT Mills
Traverse Closure (& Other Errors) in Cave Surveying
Abstract
Different methods of closing cave survey traverses are discussed and the results obtained by three different methods are compared. The conclusions reached are that in many cases it is not necessary to calculate corrections for traverse misclosures, and that when it is necessary it does not matter which of the methods is used. The simplest is recommended, therefore. The causes of errors in cave surveying, and therefore of misclosures, are discussed; as are methods of closing multiple traverses.
Sooner or later in cave surveying one finds a closed traverse has been made and you are back at some point that you have already surveyed. The trouble is that on calculating the co-ordinates for the survey station positions it is always found that the position calculated for the point at the end of the traverse is not the same as the position of the start. This difference is known as the "traverse closure error". The numerical size of this error will depend on the length of the traverse but the figures quoted by Warburton (1) for a large number of cave surveys show that for a reasonably accurate survey (ie CRG grades 4 to 6) it will usually be better than 2% of the traverse length. As one cannot have two points on a survey representing a single point in space (except on an extended section) the survey of the traverse must be adjusted so that it starts and finishes at the same point. How this should be done is a subject that has received little or no attention in the caving literature; it is completely ignored in the recent CRG publication on cave surveying (2) and the author cannot remember seeing any articles on this topic in any club journal.
For the sake of this discussion it will be assumed that the traverse closure error is always better than 2% of the traverse length; if it is larger than this then there is probably a gross error in the survey and the traverse should be re-surveyed. If the error is small due to a short traverse, good surveying or good luck (compensating errors) it may be possible to ignore the misclosure because the difference is too small to be shown at the scale to which the survey is being drawn. Similarly, if the error is small but slightly greater than that just considered, it may be possible to adjust the survey 'by eye'. That is the positions of the survey stations are moved slightly to fit without making any calculations on how far they should be moved.
If the smallest distance that can be shown on a drawing is 0.02 inches, and if we allow 'closure by eye' for cases when the station position is to be moved for distances of up to 0.05 inches on the plan, then with a closure error of 2%, no calculations will be necessary for fairly long traverses drawn at a reasonably small scale (eg for surveys drawn for reproduction on the page of a club journal). The lengths of these traverses at various scales are shown in Table 1.
Scale of Survey | Maximum traverse length to give a misclosure that | |
is too small to print | can be closed by eye | |
1/125 | 10 feet | 50 feet |
1/250 | 20 feet | 100 feet |
1/500 | 40 feet | 200 feet |
1/1000 | 85 feet | 425 feet |
1/2000 | 165 feet | 825 feet |
Table 1 – Maximum traverse length before misclosure errors are noticeable
With smaller closure errors these traverse lengths would be proportionately longer (e.g. with a 1% misclosure the traverse lengths given in Table 1 would be doubled) so it will be seen that except with long traverses or when plotting at large scales the calculations of corrections to close the traverse will not be necessary. Perhaps this is why the subject has been ignored in the past; the remainder of this article considers these calculations for those occasions when they are required and also for the sake of the purist.
Origins of Misclosure
Before discussing how to adjust the misclosure obtained after surveying a closed traverse it would be as well to look at the causes of the misclosure. In making the survey of the traverse three readings will have been taken on each survey leg to determine the position of the second station relative to the first. These were the sloping distance between the stations, the angle of inclination of the line between the stations, and the compass bearing of that line – we shall ignore theodolite traverses as the theodolite is an instrument designed for triangulation rather than traversing.
i) Measurement of distance
Provided that a good quality tape (steel or "Fibron") has been used, errors in the measurement of the distance should be negligible apart from any illegitimate errors caused by misreading the figures or writing down the wrong result. (Illegitimate errors are possible with all three readings, cannot be allowed for and must be prevented by taking care when making the survey.) The determinate errors likely in tape measurements will be due to inaccurate markings on the tape and to stretching of the tape. The former will be extremely unlikely in any commercially made tape and the latter will be negligible if a steel or "Fibron" tape is used. Catenary errors can be ignored for the standard of accuracy we are discussing provided that the tape is always pulled tight when making a reading.
ii) Measurement of inclination
Possible errors in the reading of a clinometer are more difficult to specify, especially as they may vary with different types of clinometer. Thus a Watkin clinometer is usually calibrated only between plus and minus 45°, whereas most, but not all, Abney Levels are calibrated from plus 90° to minus 90°. The ease of reading a Watkin clinometer, however, is the same whatever the angle, but it becomes progressively more difficult to read an Abney as the angle from the horizontal increases, until at angles of about 50° it is no longer possible to see the bubble in the mirror. (It is possible to read angles greater than this by setting the bubble externally but this can only be done if the instrument is tripod mounted and can be clamped in the sighting position.) The effect of an error in the clinometer reading is found when calculating the vertical change and the horizontal distance between the stations. From Table 2 it will be seen that errors made when reading a small angle of inclination (ie when errors are less likely to be made) have a larger effect on the calculation of the vertical change than they do on the value of the horizontal distance. The converse is also true; when considering an error made when reading a large angle – and this is when errors are most likely to occur – the effect is greater in the calculation of the horizontal distance.
Once again the possibility of error must be reduced by taking care in the cave, especially when making readings of high angles of inclination when errors are most likely to occur (if using an Abney Level).
If leg length is 10 feet then | ||
vertical change is | horizontal change is | |
True angle is 10° | 1.74 feet | 9.85 feet |
If read angle is 11° | 1.91 feet | 9.82 feet |
Difference | 0.17 feet (=10%) | 0.03 feet (=3%) |
True angle is 80° | 9.85 feet | 1.74 feet |
If read angle is 81° | 9.88 feet | 1.56 feet |
Difference | 0.03 feet (=3%) | 0.17 feet (=10%) |
Table 2 – Calculated errors in length for a given inclination misread
iii) Measurement of direction
The possibilities of error when taking compass bearings are different from those that have just been considered. There is no greater difficulty in reading a bearing of 90° then there is one of 37° or 261° – its ease of reading is independent of the numerical value. Where difficulty does arise is when one is attempting to read the direction of a steeply sloping line, that is when one station is considerably higher than the other. The angle of inclination at which difficulty will be experienced varies with different types of compass but irrespective of type the steeper the angle the greater will be the difficulty. (This can be overcome by fixing a sighting tube to the compass that rotates parallel to the sighting line of the compass.) The likelihood of error in compass bearings, therefore, is dependent on the angle of inclination and not on the numerical value of the bearing.
This is a determinate error but when considering compass readings there is one very important indeterminate error that must be mentioned. This is the error caused by variations in the direction of the earth's magnetic field. These errors are probably the largest that will be encountered in cave surveying and as their size is not known it is not possible to make corrections for them with any accuracy. For this reason, although it is possible to make precise compass readings, it is seldom that they will be very accurate.
Having considered the three sets of readings made in the cave and the possible sources of error, and having discounted illegitimate errors such as the misreading or misrecording of values, there is one further possible source of traverse closure error that must be considered.
iv) Station position error
This error is caused by changing the position of the survey station between readings and in particular will occur because readings to the third station are not taken from the same position as that to which they were taken from the first station. As an example of an extreme case, the readings may be taken from the first station to a candle on the floor at the second, while the readings from that second station are made by someone holding the instruments to his eye while standing approximately above the candle. In this extreme example the error is mainly vertical though there is likely to be a horizontal change of position, to a lesser extent, at the same time. Although this example is a very bad occasion when an error of five or six feet is introduced, errors in the order of one foot easily occur unless definite steps are taken to remove or minimise them. The error can be removed by the use of suitably mounted instruments (eg on tripods) or by methods such as marking both survey stations with candles and making all measurements through both flames. The error can be greatly reduced by using the leap-frog method of surveying.
To summarise these possible causes of error then, we have in order of importance:
- illegitimate errors - those must be removed by taking care and checking when in the cave and when calculating
- compass bearing errors - some of those increase with increasing angle of inclination; others are indeterminate
- station position errors - these can be removed or reduced by suitable surveying techniques
- clinometer reading errors - with an Abney Level these are more likely the larger the angle of inclination
- Tape errors - these are very unlikely if a good tape is used
(A method of mounting surveying instruments so that most of the legitimate errors that have been discussed are removed or reduced to a minimum was described in a recent issue of this journal (3).)
Traverse Misclosure
After that long diversion into the origins of traverse misclosures it is now necessary to consider the misclosure itself. At the end of the traverse there will be a three-dimensional failure to close that can be expressed as two horizontal components and one vertical component, all of them at right angles to each other.
Horizontal components
These two components are usually expressed as so many feet (positive or negative) to the east, and a number of feet (again positive or negative) to the north. It has already been mentioned that in making the survey three measurements have been made on each survey leg: distance, direction and slope. The horizontal position of each survey station, as calculated, is dependent on all three of those readings. At first glance it may well be wondered why the angle of slope between the stations will affect the calculation of the horizontal position of the second station. This is because it is the slope distance that is measured and the horizontal distance is calculated from this value and the slope. Therefore as all three measurements affect the result of the calculated horizontal station position, errors in any of them will give rise to a horizontal closure error.
Vertical component
This is expressed as a number of feet above or below the original position of the station. Of the three measurements taken on each survey leg, only two will affect the calculation of the vertical position of the second station. Those are the slope distance and angle of inclination. Therefore, not only are there less occasions for introducing an error in the vertical closure but the least accurate instrument, the compass, does not affect the result. For these reasons it is to be expected that the vertical misclosure will be smaller than the horizontal error. This is nearly always found to be the case (see Warburton).
Methods of Closing Traverses
Let us assume that a closed traverse has been surveyed and that it has failed to close by x feet too far to the east, y feet too far to the north and that it was z feet too low at the end. Assuming that the values of x, y and z are large enough to be discernible at the scale to which the survey is going to be drawn, these errors must be distributed somewhere in the traverse so that the final point is in the same position as the starting point.
First of all the traverse should be considered subjectively. Is there any part of it where the likelihood of error is greater? Was part surveyed less carefully? Perhaps along one part of the traverse back bearings did not agree very well with forward readings suggesting a local magnetic anomaly. From this subjective assessment a decision must be made as to whether the error should be distributed along the full length of the traverse or along only a part of it. It is usual to distribute the error over the full length but this is not always so. Having made this decision there is still the problem of how to distribute the error along the decided length of the traverse. It is not known where the errors occurred so any distribution can only be an approximation. Four possible methods of proportioning the error along the survey legs are considered.
i) Closure by eye
This method has already been mentioned at the start of this article. The surveyor looks at the misclosure and by guess and good (?) judgement decides how much the position of each station should be moved. This is a legitimate method if the distance each station has to be moved is very small, and is also suitable for the closure of a traverse on a low accuracy sketch plan. In the latter case any error introduced would be small compared to those caused by inaccurate surveying.
ii) Equal correction on each survey leg
In this method each of the three components of the misclosure is divided by the total number of survey legs and the position of the first station is altered by this amount, the second by twice this amount, and so on. At first glance this would appear to be only a rough and ready correction as it assumes that the same size of error resulted on each survey leg irrespective of the values of readings between stations. This is possible but very unlikely as any error made in reading an angle (compass or clinometer) will have a greater effect the greater the distance. We have seen that errors in measuring distance are unlikely, and the effect of leg length on an erroneous angle measurement is clearly shown in Figure 4 below.
Figure 4 – Effect of leg length on an erroneous angle measurement
If an angle is measured from A as shown by the line AB when the true angle is represented by the line AC, then if the distance is 'o' the error is 'l'. But if the distance is to 'o' + 'p' then the error is 'm', and 'm' is obviously much larger than 'l'.
iii) Correction proportional to the distance between survey stations
In this method each component of the misclosure is divided by the total distance between all the stations of the traverse. The error is then proportioned to each station depending on the total distance of that station from the beginning of the traverse. Expressed mathematically, the correction at the 'x'th station of the traverse of 'n' legs is:
where S_{1}, S_{2}, etc are the slope distances on the first, second, etc legs, and M is the component of the misclosure being considered. This method takes into account the fact that the longer the leg the greater the effect of an error, but nothing else.
iv) Correction proportional to the change in the direction of the component being considered
This sounds complicated and is in fact a more complicated version of the method just described. It is also more complicated to explain! When proportioning the vertical component of the misclosure it is done in the proportion of the total vertical change between stations along the traverse, to the total vertical change between stations along the traverse to the station being considered. Mathematically it is the same as in (iii) except that when taking the vertical component, S_{1}, S_{2}, etc are the vertical changes between stations irrespective of the mathematical sign of the change. Similarly, when considering the east - west component, S_{1}, S_{2}, etc are the changes east and west between stations. And the same for the north - south component. This method assumes that any misclosure in the east - west plane is proportional to the distance travelled in that plane.
Comparison of Methods
Although already stated, it must be remembered that no method of traverse closure can be accurate because it is not known where the errors occurred. Four methods have been described but none of them take into account all of the points that were raised when considering the origins of misclosure. Presumably it would be possible for a mathematician to consider the question fully and propose a method of distributing the error that covers all of the points in their correct proportions. To the author it appears that insufficient emphasis is given in the methods described above to the greater likelihood of error on steeply sloping legs. This would appear to be given more emphasis if method (iii) were modified so that each component was distributed in the ratio of the change in height between stations instead of the slope distance. Whether or not this would be better I must leave for a mathematician to decide. The point is that a mathematically sound method is almost certain to be more complicated than those described and will still only be an approximation. It is more likely that a few comparatively large errors were made than that a small error was made on every leg. Would this method, if devised, give answers appreciably different from those that have been discussed? It is unlikely.
The reason for that last statement is that the author took a short survey traverse made in a cave and modified it so that it contained extreme examples in the form of both horizontal and vertical survey legs. At the same time the closure error was increased to 1.7% so that it approached the limit of 2% that is to be expected. It contains a reasonable range of leg lengths though admittedly with an average leg length of only 13 feet this is a little on the short side. The misclosure on this traverse was proportioned according to the three mathematical methods that have been described in this paper and the results were compared. The three theoretical survey readings taken on the traverse and the corrections of station position to be applied by each of the methods are given in Table 3. The misclosures given in the table work out as 1.3% of the traverse length for the horizontal position, and 0.9% for the vertical; these together giving the three-dimensional figure of 1.7% quoted above. The interesting point to be seen from the table is the differences in the corrections to be applied as calculated by the three different methods. It will be seen that only four of the differences are greater than 0.1 feet for the horizontal planes. Two of the vertical plane differences are greater than 0.3 feet and these occur when there is a slope distance or clinometer reading far removed from the average values. The maximum difference in these adjustments is 0.33 feet, which at a scale of 20 feet to the inch would be represented by 0.0165 inches; this is about the minimum that can be drawn.
The conclusion to be drawn from this is that it does not appear to matter what method is used to distribute the error as the results will be indistinguishable unless there are a large number of vertical or steeply sloping legs amongst those of a more gentle angle, or if several of the leg lengths are disproportionately long. This being so the obvious choice is the simplest method, method (ii) where part of the misclosure is applied equally to each leg.
Table 3 – Comparison of three methods to calculate correction values
Multi-Traverse Closure
So far we have only considered the closure of a single traverse; there are further complications when two traverses close on a point and in maze type caves with large numbers of closed traverses. The method of distribution of the closure error will be the same but the decisions to be made from the subjective assessment will be more difficult. Examples of multi-traverse closure are shown diagrammatically in Figure 5. At (a) is shown two traverses having one point in common; (b) shows three traverses with two points in common; and (c) is a maze type, a complication of (b).
Figure 5 – Examples of Multi-traverse Closure
Considering the simplest of the three types first, that shown in (a), this is only a case of two simple traverses; first one would be closed on the starting point and then the other.
The second case is more difficult as there are several ways in which the traverses can be closed. First assume that the position of (A) is to be taken as the fixed point. Traverses (1) and (2) could first be closed, then traverse (3) closed between (A) and the amended position of (B); alternatively (2) and (3) are first closed followed by (1), or the third possibility is closing (1) and (3) followed by (2). Now assume that the position of (B) is to be taken as the fixed point. A decision must now be made as to which point is going to be taken as the far end of the traverse. Is it going to be closed on the end of one of the traverses (1), (2) or (3), the mean position between any two of these traverses, or the mean point of the ends of the three traverses? (The finding of this point is an interesting problem in three-dimensional geometry and is left as an exercise for the reader.) The decision on which way to close the traverses must be based on the subjective assessment of the relative accuracy of the three different traverses and then having decided which is probably the most, or least accurate, close the traverses by the method described above.
The maze type, represented by Figure 5(c), not only looks more complicated but is more complicated. The number of possible closed traverses is legion and the author has no intention of attempting to work out how many. Again, the first thing is to make a subjective assessment and if any of the traverses are thought to be more accurate than others they can be closed first and the others closed on to them. If all the traverses are of the same exрeсted accuracy the method favoured by the author is to close the outer traverse and then close the inner traverses successively. In the example shown the traverse ABCDA would be closed on A, then the traverse BEFA would be closed across the positions found for A and B, then the next traverse, CGE, would be closed across the values found for C and E, and so on. An alternative method is to work out the percentage misclosure on each of the major traverses and then close them in the order of increasing misclosures. It has not been checked but from the figures obtained by the different methods of closing a simple traverse it is thought doubtful whether these different methods of closing multiple traverses would give any significant differences. To repeat it for the last time, it must be remembered that any traverse closure is only an approximation.
References
- D Warburton – The Accuracy of a Cave Survey. Wessex CC Jnl, 7, (89), 161 - 181. (April 1963).
- AL Butcher and CL Railton – Cave Surveying. Cave Research Group Trans, 3, (2). (June 1966).
- BM Ellis – A Mounting for Cave Survey Instruments. Shepton Маllet CC Јnl, 3, (10), 3 - 8. (November 1965).
Postscript
Since the preceding article was submitted for publication, further thought has been given to the suggestion made that the most accurate "simple" method of distributing the traverse closure error would be to make the distribution proportional to the change in vertical height. It was shown that errors were more likely to be made with both a prismatic compass and an Abney Level when there is a large angle of inclination between stations. Also, that any error in angular measurement will have a greater effect the longer the survey leg length. To have obtained a large change in height means that the angle of inclination was steep, and/or that the leg length was long – the same two criteria. Therefore it appears that a larger correction applied where there is a large change in height would be a better approximation to the likely correct value than any of the others discussed. Because of this, corrections to be applied at each of the stations (in the traverse used to illustrate the article) were calculated using the formula given under method (iii) where S_{1}, S_{2} etc, are the change in height between stations. These corrections were :
Table 4 – Alternative method to calculate correction values
As this method uses the change in height on which to base the correction, which none of the other methods do, it is not surprising to find that there is now a bigger variation in the horizontal plane corrections that have to be applied. In fact the largest variation has now increased to 0.47 feet. This distance is still represented by only 0.024 inches at a scale of twenty feet to one inch, which can only just be differentiated in drawing.
Therefore, although this method is likely to give a more accurate result it is still not thought worth the extra effort involved. It is still recommended that the simplest method, equal correction to each survey leg, be used as it is sufficiently accurate.
BM Ellis
The Paignton Zoo Caves
In the summer of 1964 I was asked by Mr Les Neale of the Devon Speleological Society to survey some of the caves in Paignton Zoo. There are five caves in the zoo but only three were surveyed due to one being very, very tight and another very loose.
Notes on the Surveys
The surveys were made using a hand-held prismatic compass and a "Fibron" tape, a clinometer being used only when the slope of the floor was greater than five degrees.
Snake Cave
Since an extension was found in the floor of this cave it is the largest of the caves in the zoo grounds. A main survey line was taken down this passage but no details were measured so it is shown on the survey by dotted lines only.
Figure 6 – Survey of Snake Cave
Lynx Cave
This cave has by far the largest chamber to be found in the zoo caves, and there is an aven in the roof which has a vocal connection with the third cave surveyed, though I have not checked this connection for myself. There is a third chamber in this cave which is shown on the survey as a jumble of rocks - it was found difficult to locate the walls here.
Figure 7 – Survey of Lynx Cave
Quarry Face Cave
This cave is the only one having a floor that consists entirely of rock as opposed to mud as found in the others. A dig was started in this cave but after getting into a very small chamber (1 x 2 x 3 feet) the way on was found to continue along a passage only three inches wide - interest has since been lost in this exploit.
Figure 8 – Survey of Quarry Face Cave
Additional Notes
These caves are on private property and anyone wishing to visit them must make arrangements for the trip with Paignton Zoo well in advance.
WN Tolfree
Review: Journal of the Mendip Nature Research Committee
Volume 2, Number 1 (November 1965) price 5/- (plus postage)
and Number 2 (August 1966) price 5/- (plus postage)
Available from BM Ellis, Knockauns, Combwich, Bridgwater, Somerset.
These two numbers are devoted entirely to the history and other aspects of Lamb Leer Cavern; they provide in a readily available form much of the material that has been published on the cave in various past publications, together with original articles.
Number One covers the years from the middle of the seventeenth century to the Second World War. There are quotations from the Philosophical Collections of 1681 (already reprinted in the Proceedings of the University of Bristol Spelaeological Society, Vol. 9, No. 3), from 'The Times' for 1882 and the Downside Review of 1884. These are connected by original contributions. Then follow reprints of articles from the caving publications of the 1930's which give a description and historical sketch of the cave. There is also a description of the cableway from the same period and the 1938 geo-electrical survey by Professor Palmer. The volume ends with general articles on the cave covering points already discussed but adding further information, and a comprehensive bibliography of references to Lamb Leer.
Number Two principally covers the post-war years though there are a few pages devoted to further information on the earlier period. There are also short, original contributions on the fauna and basic geology; these are followed by extracts on digging activities in 1957 and 1949. There is then a summary of digging trips in the period 1959 – 1966 that is given in log-book form. Articles on the reaching of Valentine's Landing, climbing to the '75ft Grotto' and on radio experiments in the cave follow. Finally there are some pointers for future work, notes on the survey (which survey is not stated) and a continuation of the bibliography. In the back cover are two sheets showing a plan and sections of the complete cave.
Compared with the prices of other caving publications these days, these two numbers are outstanding value for money. Each contains approximately 60 pages, half a dozen photographs (mainly historical) and several maps and diagrams. And the survey is included in Number Two. The volumes are a mine of information, the only trouble being that at times it is difficult to find what you want. They give the impression of not having been edited or checked; this would have made them even better, as would have a more consistent layout - some pages are printed, some duplicated and others off-set lithographed. Despite this, I repeat that they are outstanding value for money and should be interesting to every caver.
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