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The Historical Development of the methodologies employed in rights to light cases

''’I may have a passion for looking at the sea, whereas to some people it is a hateful sight, but access to light from the sky is essential to every normal person’s normal enjoyment of the use of rooms having apertures admitting light, and hence it is with access to sky visibility that the easement to light is essentially concerned.’ Anstey, B. 1963''

Introduction In this chapter the key events relating to the assessment of daylight in ‘Rights to Light’ calculations during the twentieth century are identified, discussed and analysed in chronological order but, as will be seen, there was a great tendency amongst the experts of the early twentieth century, to simply reiterate that which had been stated previously rather than to reinvestigate, or examine the validity of, the original bases of assessment. 1907 to 1919 There are a number of events, which have lead to the current methodologies for calculating the availability of daylight for ‘Rights to Light’ cases. Probably the first of these to be recorded was when Percy Waldram undertook measurements of existing daylight conditions in a variety of public and private buildings, using the ‘Trotter’ photometer, in 1907 (figure 2.04). The results of these measurements were published in 1909 when Waldram recommended that 1 foot-candle should be used as a ‘rough working rule’ to measure the adequacy of interior daylight and that interior daylight illumination should be expressed as a proportion of that which is simultaneously available from the dome of an unobstructed sky (Waldram 1909a). It should be noted that, at this point, Waldram was advocating that all parts of a room should have a minimum illumination of 1 foot-candle on the basis that the assumed sky luminance was estimated to be 1000 foot-candles and the ‘grumble point’ i.e. the point within a room where the occupant would start to complain that there was insufficient light for normal purposes, would be where 0.1% of the sky was visible. It will be seen later in this chapter that there is an inbuilt contradiction in this approach. Very little direct documentary evidence of the 1907 measurements remains. Such information as is available consists mainly of sections incorporated by Waldram into subsequent publications and invariably the information is lacking in the detail, which might make it useable for comparison. For example, there is no information about the appearance of the rooms tested. Did they have wooden panelled walls? What colour were the finishes etc. In his other publication that year entitled ‘The Measurement of Illumination; Daylight and Artificial: With Special Reference to Ancient Light Disputes’ (Waldram 1909b; p135) he was proposing that interior daylight illumination should be expressed not as an absolute value, but as a proportion of that simultaneously available from the dome of the unobstructed sky. It was not until 1914 that the Illuminating and Engineering Society produced their report on daylight illumination in schools (Gaster 1914) and the Home Office followed this in 1915 with their report on lighting conditions in factories. (Home Office 1915) which, whilst adding to the body of knowledge of lighting levels and the measuring instruments available, did little to add to or define how the courts might be advised as to adequacy. 1920 to 1929 It is widely accepted, by practitioners, that after the decision in Charles Semon & Co v Bradford Corporation in 1922 when Waldram’s use of the 0.2% sky factor as a measure of the grumble point received judicial approval, his publication in the Illuminating Engineer 1923 entitled ‘Window Design and Measurement and Predetermination of Daylight’ (Waldram 1923) was his first seminal paper. The second seminal paper was published in The Illuminating Engineer and presented to the RIBA in 1925 and entitled ‘The Natural and Artificial Lighting of Buildings’. (Waldram 1925) In this second paper, Waldram (1925:5) stated that ‘in towns the zenith sky is nearly always brighter than sky nearer to the horizon where the light from the sky has to pierce a greater thickness of smoke belt'. He stated that it was of even more importance that obstructing buildings almost invariably block out sky from low angles and so the light through the upper panes of glass provided the most sky visibility and it was this that was the dominating factor in natural illumination. On page 9 he reproduced the graphic representation of the results from the Home Office Report on Factory Lighting 1914 showing the Seasonal Variations of Noon Daylight and the Diurnal Variations of Daylight, Midsummer, Equinoxes, and Midwinter. The values given represent the apparent brightness of a white card lying horizontally under an unobstructed sky and he stated that this would be double what would be recorded if the card were laid on a window cill where it could only receive half the amount of light. This of course is an oversimplification and it is understood that the direction of the sun can affect the amount of light available even for an overcast sky.

'Figure 2.01 Seasonal Variations of Noon Daylight (1914) Home Office Report on Factory Lighting'

Figure 2.02 Diurnal Variations of Daylight, Midsummer, Equinoxes and Midwinter. (1914) Home Office Report on Factory Lighting

Waldram then compared the combined results of a full year’s observation at Teddington, with the values in the Home Office report and, whilst emphasising that he believed it to be an exceptional year in Teddington, it is quite clear that the combined results significantly exceed the predicted vales. Figure 2.03 Seasonal Variations of Noon Daylight, Teddington 1924

At page 14 of the paper, Waldram observed that it is necessary to determine the proportion of light admitted through the windows on a moderately dull day but not abnormally so, when people would not reasonably expect to have enough light for ordinary purposes. He went on to state that he had adopted, for some years, a reading of 500 foot-candles as representing the amount of light from the sky on an ordinary wet day in spring or autumn, in the country rather than in a town or city. He also stated that it is rarely exceeded throughout the day in winter in towns. (Note that this differs from his original use of 1000 foot-candles). When Waldram, (1925 p5) referred to the zenith sky being nearly always brighter than sky nearer to the horizon he may have been alluding to the theory behind the CIE sky which suggests that the value of light from the sky at the zenith is three times that at the horizon and which is expressed as Lα=0.33Lz(1+2Sin(α)). However, the adjustment, which he used, was supposed to have been based on Lambert’s formula, which recognised that diffuse reflection redirects light equally in all directions and is common for dull surfaces. Lamberts formula is stated as E = p E0cos(θ) where p describes how dull/ shiny the surface is, E0 is the intensity of the light source and θ is the angle between the light direction and the surface normal. It appears that Waldram used neither of these formulae to produce his diagram but he used the formula 1-cos2 θ for the vertical adjustment of the chart and the rationale for this is discussed later in this chapter. At the end of his presentation to the RIBA in 1925, there was the opportunity for questions and comments from the audience during which Mr J W T Walsh, of the National Physical Laboratory (NPL), voiced his concern that Mr Waldram had alluded to the comparative unimportance of diffused light in rooms and argued that in some cases over 50% of the natural illumination of a room comes from the internally reflected component. He did not agree with Mr Waldram that people could manage with less daylight than artificial light and he pointed out that, where Mr Waldram mentioned the figure of one foot-candle as being probably satisfactory for clerical work in daylight, the recommended intensity for artificial light was three times the figure. He asserted that the idea of minimum illumination of one foot-candle being satisfactory, probably arose from the fact that it was used only for a brief period when the light was failing i.e. at twilight. In the section of the paper entitled Principles of Measuring Daylight, Waldram commented that the difference between the amount of daylight externally and the amount of light internally can be different by several hundred times. He stated however that with a sky that is uniformly bright, the ratio between the external light and the internal will remain constant at all times. In 1927, the Department of Scientific and Industrial Research published their technical paper number 17 entitled ‘Penetration of daylight and sunlight into buildings’. The research committee contributing to the paper included both P J Waldram and J W Walsh and their chairman C C Paterson who, in his prefatory note, referred to ‘the establishment of a ratio generally known as the daylight factor or sill ratio as a recognised criterion of interior lighting and the tendency towards the establishment of a given sill ratio as indicating the borderline between the sufficiently and insufficiently lighted portion of a room’. (In fact the daylight factor and sill ratio are not the same – see appendix one) He also referred to the development of methods of measuring the sill ratio in cases of existing buildings and of calculating it in the case of a proposed building. The paper sought to set out the current state of knowledge at that time and described how ‘the sill ratio would be affected by the amount of sky visible from the point in question, the transmission of the window glass, external reflected components and internal reflected components’. The first diagram used in this paper is the rectangular diagram described by Waldram described as ‘diagram for the calculation of sill ratio’ but apart from the vertical adjustment referred to later in this chapter, there was no adjustment for the transmission value of the glass. The paper went on to express the committee’s opinion that the fixing of a ‘minimum tolerable’ value for the sill ratio was ‘arbitrary and depended on the opinion of reasonable people as to what constitutes adequate lighting’. They referred again to the ‘extensive series of measurements of sill ratios that had been made in offices and in the footnote commented that these measurements were made in a number of clerical offices at points selected by a committee of four architects as having ‘only just adequate lighting’. It also reaffirmed the principle that the sill ratios should be ‘expressed in terms of illumination which is derived in dull but not abnormally dull weather during the period from 9.00 a.m. to 3 p.m. GMT between February and October’. Much of the remainder of the text is a reiteration of previous publications and provides no new evidence. On the 5th March 1928, P J Waldram gave a paper to The Surveyors Institution (now the Royal Institution of Chartered Surveyors) at 12 Great George Street, entitled “The Estimation of Damage in Ancient Light Disputes” (Waldram 1928) where he described the circumstances whereby a neighbourly dispute about light could be resolved by the use of ‘modern methods of ascertaining and of presenting the facts of any case’. This paper was subsequently published by the International Illumination Congress; Commission Internationale de L’Eclairage in September 1928 entitled ‘Daylight and Public Health’. In this paper, he described how, twenty years previously, ‘any expert report was mere guesswork but that this was no longer the case as standards of good and adequate light had now been established’ and he referred to the critical investigations undertaken by the National Physical Laboratory at Teddington and to the Government Report (Technical Paper No.7, Illumination Research Committee, Department of Scientific and Industrial Research) which, he said, ‘places them beyond dispute’. He also referred to material in the papers read before the Illuminating Engineering Society in May 1923 and the RIBA in 1925. The principles espoused by Waldram were as follows: 1	That the material illumination of any interior position can never be other than a proportion, generally a surprisingly small proportion, of the light existing simultaneously out of doors, and can only be expressed as such. Natural illumination cannot be expressed as being of any fixed value, as is the case with an interior lit from artificial sources such as 1-foot-candle (the illumination obtained from 1 candle at a distance of 1 foot) or 2, 5 or 20 foot-candles. Whatever it may be at one moment, it will almost certainly be something quite different an hour or so later. Sometimes in windy changeable weather it will vary by several hundreds per cent from one minute to the next. 2	That the light by which objects are rendered visible is not the light, which falls on them, but the light, which is reflected from them into the eyes of the observer. The useful light in an office is not the light which an observer notes when he walks into the room and looks out of the window; nor is it merely the light which falls on the table. It is the light, which can be reflected from books, papers, drawings etc into the eyes. 3	That the human eye is generally quite unconscious of huge percentage differences in daylight. 4	That with a given sky brightness the useful light at any interior position depends primarily upon how much sky can be seen from that position through the windows, and how high that sky is above the horizon. Light reflected from external objects and from walls and ceilings of interiors is very seldom sufficient per se to supply light reasonably adequate for ordinary purposes. 5	That any definition of adequacy in daylight illumination must of necessity cover the condition of moderately dull weather such as a wet day in summer, when the visible sky is fortunately uniform at all aspects. In so far therefore as adequacy can be defined as adequacy in moderately dull weather – and no other criterion would appear possible – we may neglect aspect and sun and pre-suppose a uniformly grey sky. Thus, in those few short passages, Waldram jumped from the identification of the problem to a solution, which ruled out many of the factors, which are now taken into account when calculating daylight availability for planning purposes. It may be a coincidence but, by this time, the National Physical Laboratory had, rather helpfully, established that the brightness of the sky on the moderately dull day in England, proposed by Waldram, would amount to 500 foot-candles (approximately 5,000 Lux) measured on a horizontal surface with no obstructions in any direction or 250 foot-candles (2,500 Lux) falling on the sill of an otherwise unobstructed window. Waldram actually produced charts of his assessment of the amount of daylight in some of the rooms of the Surveyors Institution (Now the Royal Institution of Chartered Surveyors (RICS)). Those at the front still exist and could provide an opportunity to check his results. (Waldram 1928, figures 4 and 5). At figure 2 of paper 512, Waldram (1928) referred to his first version of the now famous Waldram diagram, which represented the light from the sky in a rectangular diagram where the spacing between lines of altitude nearer to the horizon and the zenith are reduced for reasons explained elsewhere and he described the sill ratio as the ratio between the amount of light falling on a table to the amount of light falling on an unobstructed sill and stated that a sill ratio of 1 per cent would always represent 2½ foot-candles and that the “fairly well known ‘grumble point’ of 0.4 per cent sill ratio would always mean one foot- candle. Waldram stated that the theoretical possibility that interior daylight illumination could be expressed as a proportion of the light obtainable simultaneously externally was first suggested by a Mr Trotter who had been an adviser to the Board of Trade. At that point in time there were no instruments such as portable photometers and the only instrument available was the Trotter photometer (Figure 2.04), which measured the brightness of daylight against the brightness of a lamp seen through separate slots. This instrument would only register up to 12 foot-candles whereas it was stated that daylight could reach 10,000 foot-candles. To deal with this they fitted a tube of known length, which would reduce the amount of light getting through in proportion to its length. (Walsh 1922; p157). Figure 2.04 The Trotter Photometer Waldram reported that, from this development, progress was rapid and daylight ratios were measured in many buildings and results were published from time to time (although very few have been found by the author). He asserted that the system for measuring light was adopted by the Home Office for factory inspectors and by 1914 was adopted by the National Physical Laboratory. He went on to state that despite intensive scientific investigation both in England and other countries, and in hundreds of ‘ancient lights cases’ the standards arrived at had not been altered from the levels established by ‘the laborious process of noting the opinions of ordinary people and then measuring the light which they had judged as 1% cill ratio and above was good, 1% to 0.4% adequate and 0.4% and under inadequate’. At this point, one percent sill ratio was deemed to be the equivalent of 2.5 foot-candles (25 Lux) and 0.4% sill ratio would be equal to 1 foot-candle (10 Lux). He acknowledged however that these values appeared low according to text books on artificial lighting but argued that in view of comprehensive tests in Government offices he did not expect to find the original standards varied. Later that same year, Waldram presented another paper, in September 1928, entitled ‘Daylight and Public Health’ to the Commission Internationale de L’Eclairage in which he summed up by stating that: a)	the positions from which no sky at all is visible at table height are inadequately lit for ordinary purposes, such as continued clerical work, and b) it is undesirable that rooms should be constructed, or used for habitancy (sic), or for clerical or other ordinary work over long periods, unless they have at least some sky visible from table height over some reasonable portion of their area.’ He further advised the members of that forum that ‘whitened obstructions, light walls and ceilings and other expedients for mitigating gloom were no longer beneficial once the surfaces became dirty and especially on dull days. Prior to this he had also stated that the human eye could not be trusted when dealing with light levels and gave an example where the light in an ordinary room lit by windows on one side only, fell away very quickly indeed as the distance from the window increased as the amount of visible sky decreased rapidly but the human eye was not necessarily aware of this. He concluded by stating, amongst other things, that the light must be direct from the sky, and not from artificial light or from reflected surfaces. 1930 – 1939 In 1931 the Department of Scientific and Industrial Research published a report on the daylight illumination required in offices (Taylor 1931), which described the research in various government offices and confirmed, in their view, the validity of the 0.2 sky factor, although it is important to note that the Commission Internationale de L’Eclairage (CIE), later that year, refused to recognise it as an appropriate standard. In this report, the Chairman, Clifford C Paterson, referred to work by the Illumination Research Committee and concluded that the paper supported the previously adopted figures with particular reference to the work by PJ and JM Waldram in the Illuminating Engineer of 1923, where it was stated that over a wide range of illumination values, the adequacy or inadequacy of the lighting at a point was closely correlated with the daylight factor at that point. The paper went on to describe how they had established the levels of light necessary by engaging a ‘jury’ to visit several offices and establish where in the rooms they each thought that there was sufficient light. However, Waldram had previously stated that the human eye could not be trusted when dealing with light levels and the validity of this jury approach has to be questioned. The author then took these results and produced them in graphical and tabular form and gave the answer, which he said best suited the results and replicated the methodology suggested in the 1923 paper. Prior to the visit by the jury, the daylight factor contour plans had been prepared for a number of clerical offices in the new government building in Whitehall. Each room was surveyed photometrically (It is assumed that this was accomplished using the Trotter device but no explanation is given on this) and plans were prepared to show the contour lines corresponding to the daylight factors of 0.5, 0.25 and 0.1 percent at a level of 2 feet 6 inches from the floor, which equates to 762 mm. It is known that the jury consisted of seven members for the first part and six for the second part of the experiment. In addition, for the second part, the occupier of each room was asked to give an opinion and each observer was asked to plot onto the plan the line which in his (no mention of her) opinion divided the room between the adequately daylit and the inadequately daylit. It was noted that the contours between observers did not agree but were thought to be comparatively close. The author noted that the first set of assessments were all carried out on the same day which was bright with a certain amount of sunshine and that only two observers (JMW and JWTW) made allowance for the effect of either direct sunlight or of reflection. From the initials provided it is possible to determine that the jury included both of the Waldrams, father and son, and J W T Walsh. In the second part of the experiment the observations were made on different days with the weather conditions being dull on most occasions. The tables (Tables 2.01 and 2.02), reproduced below, show the results as they were presented. What is clear from these is that there is a wide spread of perception as to adequacy in each room and that it cannot even be said that the occupiers always required more, or less, than the jury members. What can also be seen is that the average daylight factor required on a bright day, measured over all twenty rooms, is half that required on a dull day. Unfortunately, without information regarding the external conditions it is impossible to determine the value represented by the average of 0.26% on the dull day. An external value of 7,500 Lux (which is consistent with an averagely dull day) would produce an illuminance of 19.5 Lux compared with only 13 Lux under a 5,000 Lux external value. This however is only an average and it may be argued that the same principles should apply as those used in assessing the availability of daylight where the value selected was that which was achieved on all but the dullest of days. In this instance perhaps it may have been valid to assess the daylight factor required by all but those with the poorest eyesight. By reviewing the readings for each room against the numbers of people requiring daylight factors in 0.1% increments, on the dull day, the highest requirement was by the occupier in room 4, 3rd floor, at 1% which represents the value which would satisfy 100% of the occupants. Table 2.03 shows an analysis of the percentage satisfaction at the various levels. From this is can be seen that 80% satisfaction is only reached at 0.3% to 0.4% daylight factor but even this is unreliable as the illuminance would have changed frequently during the process meaning that, even for a single observer, the points where there was sufficient illuminance would change if they carried out a reassessment within a matter of minutes. The tables also make clear that at least some of the windows were obstructed externally and were benefiting from reflection off glazed tiles and mirrors, which means that external reflectance will have been a factor. TABLE 2.01 Summary of Observations by Seven Observers on a Bright Day Room Number	4 --    2nd F. 4   --  3rd F	4A --    G.F. 6 --    1st F. 64 --   1st F. 69a --   G.F. 69a --  3rd F. 72 --   G.F. 72A --   S.G.F	73 --   1st F. 73 --   2nd F. 73A --   S.G.F. 	Per cent	Per cent	Per cent	Per cent	Per cent	Per cent	Per cent	Per cent	Per cent	Per cent	Per cent	Per cent P.W.J	0.05	0.10	0.04	0.02	0.10	0.05	0.07	0.05	0.05	0.08	0.05	0.03 J.M	0.05	0.10	0.05	0.02	0.15	0.05	0.08	0.10	0.10	0.05	0.05	0.05 A.E.M	0.05	0.20	0.05	0.03	0.25	0.15	0.15	0.30	0.50	0.05	0.20	0.05 J.M.W	0.15	0.20	0.05	0.25	0.35	0.10	0.20	0.20	0.50	0.25	0.20	0.02 P.J.W	0.15	0.60	0.20	0.25	0.50	0.10	0.15	0.22	0.17	0.20	0.05	0.25 J.W.T.W	0.25	0.35	0.10	0.08	0.50	0.10	0.15	0.10	0.08	0.25	0.15	0.03 J.G.W	0.05	0.25	0.03	0.03	0.10	0.03	0.05	0.05	0.10	0.05	0.05	0.05 Mean for each room	0.10	0.25	0.07	0.10	0.28	0.08	0.12	0.15	0.21	0.13	0.11	0.07 Room Number	74 --   S.G.F. 74   -- 3rd F	74 --   G.F	130 --    3rd F. 133 -- S.G.F	133 --  G.F	133 --   1st F. 133 --  2nd F.	 Mean for 20 Rooms	Weather Conditions Per cent	Per cent	Per cent	Per cent	Per cent	Per cent	Per cent	Per cent	Per cent	Generally Fair P.W.J	0.02	0.20	0.03	0.15	0.03	0.02	0.03	0.05	0.06 J.M	0.03	0.15	0.02	0.15	0.07	0.03	0.02	0.07	0.07 A.E.M	0.05	0.35	0.05	0.30	0.05	0.05	0.05	0.10	0.15 J.M.W	0.03	0.35	0.07	0.45	0.25	0.20	0.10	0.10	0.20 P.J.W	0.02	0.25	0.15	0.25	0.20	0.20	0.05	0.25	0.20 J.W.T.W	0.03	0.35	0.25	0.25	0.10	0.05	0.05	0.08	0.16 J.G.W	0.02	0.10	0.10	0.10	0.01	0.03	0.05	0.05	0.06 Mean for each room	0.03	0.25	0.10	0.24	0.10	0.08	0.05	0.10	0.13	Generally Fair Corrected	0.03	0.25	0.10	0.24	0.10	0.08	0.05	0.10	0.13 Denotes sun shining on wall opposite		 	Denotes sun shining into room NOTE - The figures in the columns give the Daylight Factor Contours approximately in agreement with the line separating adequately from inadequately lighted portions of the corresponding rooms as determined by the several observers. TABLE 2.02 Summary of Observations by Six Observers on a Dull Day and by Occupiers Room Number	4 --   2nd F. 4   -- 3rd F	4A --    G.F. 6 --   1st F. 64 --   1st F. 69a --   G.F. 69a --  3rd F. 72 --   G.F. 72A --   S.G.F	73 --   1st F. 73 --   2nd F. 73A --   S.G.F.	Per cent	Per cent	Per cent	Per cent	Per cent	Per cent	Per cent	Per cent	Per cent	Per cent	Per cent	Per cent P.W.J	0.60	0.60	0.45	0.20	0.50	0.50	0.25	0.25	0.20	0.20	0.25	0.45 J.M	0.25	0.35	0.05	0.10	0.20	0.15	0.15	0.50	0.20	0.25	0.15	0.10 J.M.W	0.10	0.75	0.45	0.20	0.15	0.20	0.25	0.20	0.10	0.25	0.15	0.15 P.J.W	0.25	0.75	0.40	0.25	0.20	0.35	0.25	0.10	0.05	0.15	0.10	0.25 J.W.T.W	0.05	0.10	0.25	0.20	0.35	0.10	0.10	0.20	0.10	0.25	0.12	0.20 J.G.W	0.50	0.65	0.10	0.25	0.30	0.65	0.50	0.50	0.10	0.20	0.20	0.40 Mean for each room	0.29	0.53	0.28	0.20	0.28	0.32	0.25	0.29	0.13	0.22	0.16	0.26 Occupier	0.50	1.00	0.50	0.10	0.30	0.10	0.25	0.25	0.50	0.25	0.08	0.40 Room Number	74 --   S.G.F. 74   -- 3rd F	74 --   G.F	130 --    3rd F. 133 -- S.G.F	133 --  G.F	133 --   1st F. 133 --  2nd F.	Mean for 20 Rooms	Weather Conditions Per cent	Per cent	Per cent	Per cent	Per cent	Per cent	Per cent	Per cent	Per cent P.W.J	0.15	0.60	0.55	0.25	0.05	0.15	0.10	0.25	0.32	Blue Sky, White Clouds J.M	0.10	0.30	0.20	0.35	0.10	0.07	0.08	0.15	0.19	Moderately Dull J.M.W	0.15	0.45	0.15	0.40	0.03	0.10	0.08	0.05	0.21	Dull weather and Overcast Sky P.J.W	0.40	0.50	0.10	0.40	0.05	0.10	0.08	0.10	0.24 J.W.T.W	0.20	0.10	0.50	0.20	0.25	0.25	0.20	0.20	0.20	Dull J.G.W	0.50	0.85	0.10	0.50	0.10	0.25	0.25	0.30	0.36	Generally Dull Mean for each room	0.25	0.47	0.27	0.35	0.10	0.15	0.13	0.18	0.26 Occupier	0.15	0.20	0.05	0.30	0.20	0.20	0.10	0.05	0.27 Denotes very clean white glazed tiles			Denotes dull weather Denotes Mirror fitted in front of window

Df	satisfaction 0-0.1	27.86% 0.1-0.2	52.14% 0.2-0.3	74.29% 0.3-0.4	81.43% 0.4-0.5	92.86% 0.5-0.6	96.43% 0.6-0.7	97.14% 0.7-0.8	98.57% 0.8-0.9	99.29% 0.9-1	100.00% Table 2.03 Percentage satisfaction at various levels of daylight factor At page 5 of the paper, there is a plan of room 4A G.F. showing the contours produced using the measuring device. The no sky line, i.e. the line representing the series of points in the room from which the last remnant of sky visibility disappears, is also shown on the plan and this falls mainly between the 0.1% and 0.25% contours. The only possible interpretation of this is that the daylight factor, measured, must have been reliant upon reflection from internal and possibly external sources. The chart, reproduced below at Figure 2.05, shows the contour lines. What is not explained is why the ‘no sky line’ contour is nearer the window than the point at which at least 5 jury members, on the bright day, and 2, on the dull day, indicated that they had sufficient light to work by. From this, it can be deduced that at least some of the jury members were unable to distinguish between direct light and reflected light and this casts doubt on the subjective nature of the measurement process and how this may have been used to justify the use of the 0.2% sky factor by Waldram.

Figure 2.05 - Room 4A GF, Taylor A K 1931

In this room, the average of the minimum daylight factor required by the jury on the bright day was 0.07%, compared with 0.28% on a dull day, although the occupier on that same day expressed a requirement of 0.50%. Unfortunately there is no information upon how the daylight factors were calculated and neither are the contours shown for each of the jury members’ observations. If it were to be assumed that the average minimum daylight factor required by the jury members was in fact measured at the series of points which represented the minimum value required then it might be argued that the room between this contour and the window benefited from an average amount of direct sky light and thus a contour line drawn midway between the two could be correlated to the amount of sky visible at each point on that contour. With this it might have been possible to justify Waldram’s use of the 0.2% sky factor but without it, as has been stated above, this is not possible. From the discussion above it can be seen that this ‘experiment’ was of extremely limited value. The range of readings between the rooms and with differing external lighting conditions and the failure to relate any of the readings to the external value, which would have permitted comparison with the sky factor, makes the results unusable in justification of any methodology; nevertheless this appears to be what happened at the time. In 1932, the Commission Internationale de L’Eclairage (CIE) (International Commission on Illumination 1932) met at Cambridge and set out the parameters, which have been adopted ever since by ‘Rights to Light’ Surveyors, and these were as follows: 1	The use of contour lines should be adopted in all cases. 2	That table height should be regarded as 85 centimetres or 2 ft 9 in 3	That less than 0.2% sky factor should be regarded as inadequate for work involving visual discrimination. The one new fact introduced at this point was the acceptance of ‘table height’ which is between 7.5 and 10 centimetres higher than previously recognised and which other forms of calculation normally use and it is also higher than most work surfaces which does not make sense since it is supposed to relate to the amount of light needed for work. The significance is that a work surface at a lower level may benefit from light at a higher altitude, which comes through the top of the window, and lose light from lower angles; particularly where the cill height is above work surface height. It was not until 1937 that the Department of Scientific and Industrial Research published the results of further research on the daylight illumination in offices, which concluded that the previous recommendation was too low. (Department of Scientific and Industrial Research 1937) 1940 to 1960 Towards the end of the second world war the ‘Post-War Building Studies No. 12, The Lighting of Buildings’ (Building Research Board 1944) recommended a minimum sky factor value of 1 per cent for domestic living rooms and in 1952 ‘Post-War Building Studies No.30 The Lighting of Office Buildings’ also confirmed that a sky factor of 1 per cent was recommended for office floor areas relying exclusively on daylight illumination. (Ministry of Public Building and Works 1952). In these cases the sky factor was reported to be the direct ratio of the internal illuminance to the unobstructed external illuminance but this is appears to be incorrect as this would equate to the daylight factor. 1961 to 1980 Whilst Walsh was undoubtedly a contemporary of Waldram, he was also the author of the more recent publication, ‘The Science of Daylight’ which, in Chapter 5 entitled ‘Daylight Calculations by Graphical Methods’ (Walsh 1961), discussed the ‘Unit-Sphere Principle’ (Figure 2.06) and described the relationship between the illumination on the horizontal plane due to a small element of sky, the luminance of that element and its angle of elevation or altitude, at the point where the illumination is measured.

Figure 2.06 The principle of the unit sphere from Walsh 1961 The mathematics involves the use calculus but in simple terms, the illumination at point P due to the light received from S is proportional to the luminance of S and the area of S”. (Figure 2.07) According to Walsh, “If Z is a very narrow zone of sky of angular breadth  and constant angle of altitude  then Z’ is a zone of H whose breadth is . Its inclination to the vertical is  and so Z” is an annulus whose breadth is  Sin  and radius Cos . If S is a small section of Z whose angular breadth projected onto the horizontal plane through P, is , the area of S” is . Sin  multiplied by  Cos , i.e. it is ½ Sin 2. . .”

Figure 2.07 The illumination from an element of sky

He then asserted that this calculation leads on to the calculation, which justifies the rectangular diagram described by Waldram. “The network constructed with abscissae proportional to  but with co-ordinates in which the distance between two adjacent divisions (+ ) is proportional to  multiplied by Sin 2, then areas on the network are proportional to the values of illuminance produced by the corresponding areas of sky of uniform illuminance. The scale of the abscissae is uniform so that the abscissa corresponding to any angle  is proportional to  while the ordinate corresponding to any given angle of  is proportional to Sin 2 d which converts to 1-Cos 2 ,” This formula undoubtedly produces the chart at Figure 2.08 below although in practice the results are converted such that the maximum value of the ordinates is 1 rather than 2 (since 1-Cos 180 = 2), but the ratios remain the same. This equation and its derivation are examined below.

The Construction of the Waldram Diagram The following charts have all been produced, using the original formulae, in Excel spreadsheets and charts and so may not exactly match the original drawn versions but they serve to demonstrate the points being made. Figure 2.08 shows how the original Waldram Diagram adjusted the distance between the horizontal angles of altitude as has been explained previously in this chapter.

Figure 2.08 Waldram diagram original form (The rectangular diagram described by Waldram) The more familiar ‘droop’ version of the Waldram diagram is constructed using basic trigonometry. The diagram below shows how the vertical angle of a fixed point decreases as it is moved away from the normal and it is the relationship between the vertical angle in the normal position to its angle either side that creates the droop lines. Figure 2.09 Geometry of the Waldram Diagram

Tan  = a/b; Cos = b/c; Tan θ = d/c Since the droop lines represent a horizontal line, d = a and therefore Tan θ = b Tan /b/Cos  = Tan  * Cos  If this formula is used for each angle of altitude it would create a droop diagram where the spacing between each line of altitude is equal. This is best understood by looking at the spacing on the vertical line at 0 degrees azimuth in the figure below. (Figure 2.10)

Figure 2.10 Equivalent Vertical Angles

However, according to the initial Waldram diagram, the value of the luminance near the horizon and near to the zenith should be lower and therefore the adjustment factor of 1- Cos 2θ should be applied to the equivalent vertical angle for each point. The chart for this at Figure 2.11 shows how the lines are closer together near the zenith and horizon but open out in the mid sky zone centred around 45 degrees.

Figure 2.11 Basic Waldram diagram with Droop lines

It is possible to construct this diagram using Microsoft Excel although the mathematics has to be adjusted to convert through radians using the following formula: P = 1-(COS((2*(DEGREES(ATAN(TAN(()*PI/180)*COS(()*PI/180))*PI/180))))) This formula creates a chart, which looks essentially the same as the above with the exception that the value at 90 degrees Azimuth and 90 degrees altitude is not quite at the edge of the chart. This is purely the result of the complex mathematics. This chart is now referred to by ‘Rights to Light’ surveyors as “The Waldram Diagram” and for years this was printed by the BRE/HMSO with the main modification being the inclusion of droop lines for obstructions at right angles to the window wall (these lines are effectively the same droop lines moved across horizontally through 90 degrees) and vertical guidelines to assist hand drawing of perpendicular surfaces or edges such as window frames, together with a grid divided into 500 squares to make calculations easier. Figure 2.12 shows how this now appears Figure 2.12 Waldram Diagram with 90 degree droop lines and grid Note that the size of the diagram has been modified to measure a total of 500 square units. This will be discussed later in this paper but the value of the units is actually irrelevant if the grid, which is used as an overlay, uses the same units. The Waldram diagram, above, still pre-supposes a sky of uniform luminance to provide a sky factor but an overcast sky has a different luminance distribution and this was described by Walsh as being represented by the formula Lγ=Lz(1+sinγ)/3 where γ is the angle above the horizon and, if this were used, it would have the effect of modifying the rectangular diagram described by Waldram and thus the Waldram Diagram at Figure 2.12, and this modification will be explored in a later chapter. Heights of Ordinates in the Waldram Diagram Angle (deg)	Uniform sky	Overcast sky	Angle (deg)	Uniform sky	Overcast sky 5	0.008	0.004	50	0.587	0.508 10	0.030	0.015	55	0.671	0.602 15	0.067	0.039	60	0.750	0.693 20	0.117	0.073	65	0.821	0.777 25	0.179	0.120	70	0.883	0.853 30	0.250	0.179	75	0.933	0.915 35	0.329	0.249	80	0.970	0.961 40	0.413	0.329	85	0.992	0.990 45	0.500	0.416	90	1.000	1.000

Figure 2.13 Comparison of ordinate heights for uniform and overcast skies (Anstey 1963)

Figure 2.13 above illustrates the comparison between the heights of the ordinates for uniform and overcast skies. It can be seen that the lower levels benefit most from the uniform sky approach but that all levels differ slightly and thus results using the overcast sky would always be different from those using a uniform sky. In summary, the concerns, which arise out of the existing methodology, are with the following assumptions. •	total amount of light provided by the Sky Dome should be assumed to result in an illuminance of 500 foot-candles to an unobstructed point on the horizontal plane •	a Uniform Sky can be assumed for the purposes of these calculations •	Lambert’s Formula can be used to define the adjustment factor for low angle light and that there needs to be an equal adjustment to the chart for the value of light from a higher altitude •	the Waldram Diagram can be adjusted to 20 units in height and 25 units in width so that a grid of 500 equal squares can be used without affecting the result •	the appropriate height for the measurement of available light is 850 mm above floor level •	1 foot-candle illuminance adequate •	it is appropriate to ignore window frames and glazing •	internal reflectance should be ignored In part B of this thesis, the use of the Waldram Diagram is explored in chapter three, showing how the results produced by the use of the diagram are translated into a contour plan showing the ‘grumble line’ and then how this relates to the presently available alternatives methods. Chapter four will then examine two of the fundamental factors leading to the development of the Waldram Diagram i.e. how much light is needed and how much is available.