As Easy as PI(E)
By Ted Nicholls
To a cook, pie means pastry and rhubarb, apples or some sort of fruit or meat. To a printer it means that someone has upset his type. But to a mathematician it is the Greek letter symbol referred to in this article as Pi. It is the ratio of the length of the perimeter of a circle to the length of its diameter. About 1600, the English mathematician, William Oughtred, used the Greek letter (π) Pi to symbolise the perimeter, (perimetron being Greek for "the measurement around"), and Delta for the diameter (diametron - "the measurement through"). Nowadays it is customary to use the Latin word "circumference" when speaking of circles - thus successfully obscuring the reason for Pi. The first top-flight man to use this symbol was the Swiss Leonard Euler in 1757 - and what was good enough for Euler was good enough for everyone else.
Having settled how pi came to be used, let us consider how the value was obtained. To find the circumference of a wheel, wheelwrights presumably wrapped some sort of cord around it, marked it where a circle was completed, and then straightened it out and re-measured it. Modern theoretical mathematicians frown at this and make haughty remarks like - "but you are making an unwarranted assumption that the line is the same length when straight as when curved". The above honest workman would probably have solved matters by throwing the objector into the nearest cut.
When it came to the actual value, this varied enormously in ancient times. The Hebrews refused to be bothered with troublesome fractions and considered Pi to be equal to exactly 3. (Some years ago a bill was introduced in Tennessee to make Pi legally equal to 3 inside the state borders: fortunately it didn't pass!) Mostly the ancients used 3, which is only 1 part in 2,500 high. However, along came the Greeks - and they would have nothing to do with the vile lay-down-a-string-and-measure-it-with-a-ruler business. Archimedes used the "Method of Exhaustion", trapping the circumference of a circle between a polygon of 96 sides with the corners touching the circle inside it, and a 96 sided polygon with the sides tangential to the circle outside it. The figure he obtained, 3123/994, is only high by 1 part in 12,500.
Nothing better than this was obtained until the 16th century, when the fraction 355/113 was first used - and this is the best approximation that can be expressed as a simple fraction, being high by 1 part in 12,500,000. If we imagined that the Earth was a perfect sphere of exactly 8,000 miles diameter, by using 355/115 we get an equator of 25,132.7433 miles. The true value of Pi gives us 25,132.7412 miles - an error therefore of about 11 feet. This is good enough for most people, but mathematicians weren't satisfied!
The key step was taken by Francois Vieta, a 16th century French mathematician considered the Father of Algebra. He performed the algebraic equivalent of Archimedes geometric method of exhaustion, involving square roots, square roots of square roots, and square roots of square roots of square roots. In 1593 he used his own series to calculate Pi to 17 decimal places. In 1615 the German Ludolf von Ceulen used an infinite series to calculate Pi to 35 places (Pi is sometimes called "Ludolf's Number" in German textbooks). 1717 the Englishman Abraham Sharp went several times better by working it out to 72 decimal places.
Was this really necessary? Well, if we drew a circle 10 billion miles across, with the Sun at the centre to enclose the entire Solar System - using 355/113 as Pi the circumference of over 31 billion miles would be out by less than 3,000. Using Ludolf's 35 places the error would be equivalent to a millionth of the diameter of a proton. If we want the circumference of the known Universe (approximate diameter 80 thousand million light years) then this value of roughly 150,000,000,000,000.000,000,000 (150 sextillion) miles, using Ludolf's value to 55 places, would be off by a millionth of an inch! Obviously Sharp's value to 72 places was far beyond the accuracy needed now or in the future.
Did this stop mathematicians working it out to further decimal places? Not a bit of it: the improvers being George Vega (140 places); Zacharias Dase (200 places); Recher (500 places). Finally, in 1873 William Shanks reported the value of Pi to 707 places. It was the record until 1949 ~ and small wonder that it took him 15 years to make the calculation. However, in 1949; with computers coming into their own, one of the unending series was pumped into Eniac, and after 70 hours Pi was worked out to 2,035 places. In the process it was found that Shanks had made an error and well over a hundred of his last digits were wrong.
It seems that no-one had ever taken the trouble to check his calculations!
A Survey of Bright Galaxies (Part 2)
By Richard Barrett
The band of sky from Camelopardus, through Ursa Major, Canes Venatici and Coma Berenices, into Virgo hold a wealth of galaxies. Sadly, most of these are too faint for small telescopes (ie. under 6" aperture. Two of the brighter ones, M 81 & 82, have already been discussed (see MIRA 6) - but there are still a few more of interest.
In the large, barren constellation of Camelopardus lies the galaxy NGC 2403. It is odd that Messier did not include it in his list, and that few reference works give much space to it. NGC 2403 is only slightly fainter than M 81 (mag 8.8) and about the same size. It too can be seen in binoculars on a clear night, and is unmistakably nebulous. The object lies about one degree West of the 6th mag star 51 Cam. - but due to the lack of finder stars close study of the charts is needed. In Norton's it is designated 44/5.
Returning to Ursa Major we look for M 101. This galaxy is very large (22'x20') and, with a magnitude of 9.0, it has a rather low surface brightness. This means it is best viewed with a low magnification. In fact, after many months searching for it in the relatively poor conditions of Coventry with my telescope, I first saw it in the clear skies of North Wales through 10x50 binoculars. Through my telescope though it was almost invisible, appearing at lowest magnification as a faint diffuse glow. M 101 is easily found by tracing the line of 5th mag stars Eastwards from Mizar & Alcor. When 86 UMa is reached look 1½ degrees North-East of this. M 101 should then be in the field of view. In a telescope of less than 4" aperture it will be very difficult to see. If the skies are very clear, 10x50 binoculars will reveal this object, provided they are held very still.
In the same area of sky as M 101, though just inside the neighbouring constellation of Canes Venatici, is M 51 - the famous "Whirlpool" galaxy. This is the first of the so-called "spiral nebulae" in our survey. Lord Rosse detected its spiral structure in 1845 with his 72" reflector. Unfortunately this structure is only revealed by a large amateur telescope (at least 12") - and it needs a professional sized telescope to really show its full splendour visually. M 51 can be found 3½ degrees Southwest of the end star in the tail of the Bear. This object is also rather diffuse and hence is best seen (with small telescopes) using low powers. This is a problem with many galaxies. The more you would like to be able to see structure, the less chance there will be of using high powers (Murphy's Law!) As an example, take M 32 (see MIRA 6). This is a bright, compact elliptical galaxy which will take high powers - but it has no structure, and will always -appear as a circular patch of light. Compare this to a spiral galaxy of equivalent magnitude. As spirals tend to have a large angular size they are diffuse, and cannot take high powers to show their interesting features. This is the case with M 51, which I have seen easily in 10x50 binoculars - while finding it rather faint in my 4" telescope at x32.
Still in Canes Venatici (which is high in the sky during Spring and Summer evenings) we find three more spirals, M 106, M 63 and M 94.
The first of these (M 106), is situated in an area of sky deficient in bright stars - the nearest being 4th mag Chi UMa. 5½ deg. to the East of Chi is M 106. It is a large, rather elongated object (19.5'x6.5'), which is faint as far as a 60mm refractor is concerned, but anyone with a 4" or larger should have little trouble. I have seen it once, but as I prepared to draw it my mirror dewed up!
M 63 is an unusual sight in that, although it is not particularly small (9'x4'), it appears remarkably stellar at low power. The reason for this is a small bright nuclear condensation (6" across) surrounded by tightly wound spiral arms (50" across). The rest of the galaxy is somewhat faint. The lack of "fuzziness" can be seen if the mag 9.8 galaxy is compared with the 8th mag star very close to it. To find this galaxy first look for a lop-sided 'T' shape of 5-6th mag stars about 4-5 degrees North-East of Alpha (Cor Caroli). From the base of this T move North for about 2 degrees. M 63 should then be in the field.
M 94 is a small bright spiral galaxy located 3 degrees East of Beta. Stars in its vicinity will show its slightly diffuse appearance, allowing identification so that higher magnifications can be used. M 94 also has a very bright central core (30" across) and rather fainter arms. These arms, when seen on photos taken with large telescopes, are ill-defined and seem to form a disc. This means that even a large instrument will reveal little more structure (visually) than a small one.
In the final part of this survey we move South into Coma Berenices - and encounter part of the great Virgo Cluster.
By Rob Moseley
A Mercurian Phase Anomaly?
In recent years a suspicion, has arisen among observers that Mercury may be showing a phase anomaly similar to the well-known "Schroter Effect" on Venus. This effect, now generally held to result from the "scattering" of the Sun's light through the Venusian atmosphere, takes the form of a difference between theoretical and observed dichotomy (ie half phase). This difference has been known to be as much as 10 days on some elongations, but normally falls between 5 and 6 days. In evening elongations the observed dichotomy is early, in morning elongations late. The mnemonic is "Evenings Early"
Mercury, however, is an essentially airless world - so the light scattering hypothesis is untenable, and alternative explanations have been thin on the ground. But to be fair to the theoreticians, the observed discrepancy is far from being an accepted fact.
As far as I know, the question first arose in 1966 with a series of observations by HC Nightingale. Although only using a 4½ inch refractor he had the advantage of observing from Nigeria, where Mercury is much better placed for most of its brief elongations than it is from Britain. He consistently recorded a phase below the theoretical value for eastern elongation.
Mercury is a notoriously difficult object to observe properly. It has a diminutive disc at best, and its proximity to the Sun means that in our latitudes there are only two elongations a year where any serious observational attempts are feasible. Even at these apparitions (in the evening in Spring, and morning in Autumn) for users of small to moderate apertures the planet must be observed at an inconveniently low altitude - with consequent "seeing" problems. Moreover, each apparition is short, with an optimum period of as little as ten days or so a inevitably (in this country) clouds will conspire to blank out this period - and the Mercury specialist may have to wait years for a good opportunity.
My own experience is a case in point. In the Spring of 1969 I was exceptionally fortunate to get four telescopic observations in the same elongation. This really is untypical co-operation from the weather! In the intervening 15 years I have made just 5 observations, all on separate elongations - and therefore almost useless. When it comes to observing Mercury "Sod" really does put the boot in.
However, the series from 1969 may provide some interest, as one so rarely comes across any observational material on Mercury. The instrument used was a 2½ inch refractor. Although a small telescope the OG was well corrected, and it was portable enough to be carried to a site with a clear postern horizon. Of course, the small aperture used means that the results can carry very little weight.
My first view came on April 30th. (This was quite a late Spring apparition, this year's occurred in late March/early April). With a power of 112 the tiny pinkish disc - only 6.6" in diameter - trembled in the field of view. After 20 minutes I was convinced, even allowing for the inevitably poor conditions, that the terminator was very slightly concave. The human eye is surpassingly good at detecting departure from a straight line.
The following evening (May 1st) produced a crystal clear sky. Again I recorded the terminator as slightly concave. At this time the disc should have been 58% illuminated. Clouds then intervened, and I kicked my heels for nearly a week. On May 6th the phase was definitely past dichotomy, and a tentative estimate of .4 was made.
On the 9th the disc had grown to 8.6" as Mercury swung in rapidly between the Earth and Sun. Now the pale yellow disc (indicative of good transparency) was a definite crescent. The phase was estimated at .3, tallying well with the calculated value of .292, which I looked up afterwards in the BAA Handbook. Mercury was again located on May 11th, but cloud ruined what could have been a crucial phase estimate.
Again, these observations are not put forward as serious support for the mystery of the Mercurian phase anomaly. Decades of work with adequate equipment, including a micrometer, would be necessary before any conclusions could be drawn. To quote Richard Baum, the eminent amateur planetary observer, "Mercury may be difficult, but it has possibilities for those able to grasp them."
Luckily, the atrocious weather of March this year broke just in time for Mercury's Spring apparitions. Several members have reported sighting the planet on the evenings of April 1st and 2nd. Regular searches were made at the College Observatory, but several promising situations were spoilt by banks of horizon cloud and haze. However, the Cooke refractor was brought to bear on the evening of April 2nd. Independent drawings were made by R Moseley and P Porter - which show good agreement. The phase was seen to be just past dichotomy, conforming to its calculated value. Both observers recorded a terminator feature towards the N cusp. Paul's sketch also shows a hint of cusp extension. Cloud and haze hampered early location - but between 19.30 and 20.00 UT Mercury was comfortably visible to the naked eye, although a slight haze made it dimmer than normal.
The correct magnitude sequence for the Plough (see MIRA 6) is :
Epsilon ε 1.77 (white),
Alpha α 1.79 (yellow),
Eta η 1.86 (blue/white),
Zeta ζ 2.27 (white),
Beta β 2.37 (white),
Gamma γ 2.44 (white),
Delta δ 3.31 (white).
Zeta ζ (Mizar) forms naked eye double with Alcor (mag 3.95)
Deep Sky Notes
Galaxies in Leo
By Tim Gouldstone
No planets being conveniently placed in April, I thought I would go to the other extreme and do some deep-sky observing in Leo, with its profusion of galaxies - Burnham's "Celestial Handbook" lists over 70 NGC objects in this constellation.
1984 April 1
216mm (8½ inch) spec. x33, x85 - the larger-magnification much better, NGC 3623 (M 65) and NGC 3627 (M 66) - As usual, these objects appear as blobs of fuzzy, white light, but M 65 has a much "flatter" appearance; it is in fact an edge-on spiral, whereas M 66 is more face on. Burnham gives the magnitude of M 66 as 9.7, but to my eyes M 65 gives the impression of being brighter. I subsequently found that this was exactly the description given in Burnham, p 1O73 - "some observers. . . find M 65 actually more conspicuous owing to its more elongated outline." Both galaxies in same field at x85.
NGC 3628 - An edge-on spiral 35 arcmins North of M 65/66. I cheated with this one as I looked up its position in the excellent photograph of this group in Burnham, p 1073, and just about (was it wishful thinking?) spotted it. Its magnitude is supposed to be 10.3, but seems to be fainter.
NGC 2903 - Found by sweeping South in Dec. from Lambda Leonis. An oval patch., brighter than M 65 or M 66. "Astronomy" (April 1984) gives its magnitude as 9.5. This shows that the Messier objects are not always the brightest deep-sky targets... it was possible to detect the outer, more nebulous regions in NGC 2903 (Norton's 56/1)
This was a good, transparent sky and Praesepae (M 44) in Cancer could be detected with the naked eye as a faint glow.
1984 April 16
(Same equipment) Working hard against a rising full moon! Not the best conditions for observing deep-sky objects, but there was a surprise. . .
NGC 3384 and NGC 3379 Whilst looking for M 95 and M 96, I found two blobs of light, very close, about 10 arcmins apart. Checked with "Astronomy" (April 1984) and found that M 95/96 are 42 arcmins apart, which is twice my field of view... The objects seen proved to be those labelled 17/1 and 18/1 in Norton's "Star Atlas". 17/1 is also M 105 (NGC 3379) and is given as magnitude 10.6 in Burnham's, and NGC 3384, its close neighbour, as mag. 11.0. There is also a mag. 12.2 within 10 arcmins of these two - but I failed to see it. 3384 and 3379 can be found by "star-hopping" from Regulus via Rho Leonis to
53 Leonis and then sweeping North in RA.
M 95 and M 96 - completely eluded me, and with a rising full Moon observing was discontinued.
NGC 3655 (Herschel 5/1) - I also searched for this near 81 Leonis but failed to find it.
NGC 3607 and 3608 (Herschel 50/2 & 49/2) - Sweeping Southwards from Dalta Leonis, these objects (within about 7 arcmins of each other) were also detected.
Although useful work on these objects is very limited (seen any supernovae lately?) there is some satisfaction in observing deep-sky objects thirty million light years away. But be wary about the quoted magnitudes. Dowdell (J. Brit. Astron. Assoc. 1984, 94, 3, p 132) states, "The revised New General Catalogue gives magnitudes which are almost meaningless and these need to be looked at and re-estimated using standard variable star and cornet observing techniques."
Incidentally, the NGC contains 7840 objects, two thirds of which are observable from Britain. Dowdell considers that there is nobody alive today who has "seen them all" - John Herschel was probably the last. So when there are no planets, and the Moon isn't around, there's plenty to get cracking on. . .
Sunrise over Ptolemaeus
By Vaughan Cooper
6" reflector x180
Date 9th February 1984
Time 8.30pm to 9.30pm GMT
Seeing Ant II
The Western floor was very striking with many and delicate variation of tone displaced far more than I've drawn. A total of 10 features noted on the floor of Ptolemaeus. Also sighted reflected Earth light just visible around the Western limb.
A Survey of Bright Galaxies (Part 3)
By Richard Barrett
Moving South into Coma Berenices we encounter part of the Virgo Galaxy Cluster. As previously mentioned most of these objects are rather faint - but there is one notable exception. This is the "Black-Eye" Galaxy (Messier 64). Its name is derived from the presence of a band of dark material below the nucleus, creating the appearance of a black-eye. This is the first galaxy mentioned in this series that I have not so far seen. It lies 1° ENE of the 5th mag. star 35 Comae. It is quite small (7½'x3½') and rated at mag 8.6. It can take quite high magnifications and with an 8-inch reflector the black eye itself should be visible.
while you are looking in the region of the Virgo Cluster, those with telescopes of 6-inch aperture or larger should sweep across the area centred on about RA 12h 25m, Dec. +13° - covering an area from 12h 05m to 13h, and from +18° down to +10°, or even to 0° if you wish, as the cluster does extend this far. However, the highest concentration is for about 5° around the co-ordinates given above.
There are galaxies littered all across the sky - only the brighter examples have been discussed here. The more advanced observer will be able to see many more (such as the galaxies M 65, M 66, M 95 and M 96 in Leo, each at around mag 10.5 - and many more examples within the Virgo Cluster.)
We end with a galaxy specially for those with binoculars, which you may like to attempt during Autumn evenings. M 33 in Triangulum has such a low surface brightness that it can only really be seen in binoculars or by using very low power, wide-field eyepieces. To find M 33 sweep around an area 4° WNW of α Triangulum. If the sky is clear and dark a glow will be seen, ¾° in diameter. This galaxy has an integrated magnitude of 6.5, but because of its size it is actually rather faint - especially when its-light is spread out by high magnification.
A List of Bright Galaxies
Designation Mag. Size Type Position
NGC 205 10.8 8'x3' Elliptical 0h 37m +41°25'
NGC 224 (M 31) 5.0 160'x40' Spiral 0h 40m +41°00'
NGC 221 (M 32) 9.5 3.6'x3.1' Elliptical 0h 40m +40°36'
NGC 2403 8.8 16'x10' Spiral 7h 52m +65°43'
NGC 4258 (M 106) 9.0 19'x6' Spiral 12h 16m +47°35'
NGC 4631 9.7 12'x1' Spiral 12h 39m +32°49'
NGC 4736 (M 94) 8.9 5'x3.5' Spiral 12h 48m +41°23'
NGC 5055 (M 65) 9.8 9'x4' Spiral 13h 13m +42°17'
NGC 5194 (M 51) 8.7 10x5' Spiral 13h 27m +47°27'
NGC 1068 (M 77) 10.0 2.5'x1.7' Seyfert 2h 40m -00°14'
NGC 4254 (M 99) 10.4 4'x4 Spiral 12h 16m +14°42'
NGC 4826 (M 64) 8.6 7'x3' Spiral 12h 54m +21°57'
NGC 2905 9.7 11'x4' Spiral 9h 29m +21°44'
NGC 3351 (M 95) 11.0 4'x5' Barred Sp. 10h 41m +11°58'
NGC 3368 (M 96) 10.2 6'x4' Spiral 10h 44m +12°05'
NGC 3625 (M 65) 10.3 7'x1' Spiral 11h 16m +13°23'
NGC 3627 (M 66) 9.7 8'x2 Spiral 11h 17m +13°17'
NGC 598 (M 33) 6.5 40'x60' Spiral 1h 31m +30°24'
NGC 3031 (M 81) 8.0 18'x10' Spiral 9h 51m +69°18'
NGC 3034 (M 82) 9.2 8'x3' Irregular 9h 51m +69°56'
NGC 5457 (M 101) 9.0 22'x20' Spiral 11h 01m +54°35'
Letters to the Editor
In the May issue of 'MIRA', Tim Gouldstone referred in his Deep Sky Notes to Alan Dowdell's remarks concerning the NGC and John Herschel.
According to the report of the Ordinary Meeting of the Association held on 1984 January 25th (JBAA 94 (3), 131 (1984)), Alan Dowdell stated that he was unaware of anyone who had seen all the NGC objects observable from this country, and that John Herschel could well have been the last. It seems doubtful that anyone would carry out such an extensive programme of observation without communicating their results. However, even John Herschel did not observe all these objects. His 'A General Catalogue of Nebulae and Clusters of Stars', on which the NGC was based, was published in the Philosophical Transactions in 1864, and contains 5079 objects discovered by himself and his father.
This Catalogue inevitably contained errors, and in 1876 JLE Dreyer commenced work on a list of corrections and a catalogue of the numerous nebulae discovered by various observers after 1864, for use at Lord Rosse's observatory. This work was published in the Transactions of the Royal Irish Academy in 1878, and in 1886 Dreyer submitted a second catalogue to the RAS, after which the Council proposed that a new General Catalogue be compiled. The result was the publication in 1888 of the NGC, containing 7840 objects, a great many of which were discovered after Herschel's death in 1871.
Except for occasional observations with a 7-foot instrument (the one with which his father discovered Uranus) Herschel's career as a practical astronomer virtually ceased after his return from the Cape in 1858, and as he was 72 when his General Catalogue was published it is unlikely that he saw any of the nebulae discovered during the ensuing seven years, especially as he suffered with gout and bronchitis. Of the 5079 objects in his Catalogue, about 450 were not observed by him or his father.
However, he observed 3989 of them, but as about 1020 of these have a north polar distance greater than 129°and were among the 1708 nebulae and clusters observed by him at the Cape, the greatest number of those visible from the south of England that he observed was about 2969, compared with about two thirds of the 7840 NGC objects.
A precedent would no doubt be set by observing all the NGC objects, and it would be an admirable achievement even to observe the 5000 or so visible from this country. And if anyone completing such an immense task should still not be satisfied, he could take on the 5386 objects in the two Index Catalogues, published in 1895 and 1908.
(This letter also appears in the current BAA Journal - but we received it first!) Ed.
At 25.15 UT on 1984 April 17th I was outside taking photos of the zenithal constellations when suddenly a brilliant object was seen climbing from the southern part of the sky. At first I had the impression that it was a UFO, but somehow I just couldn't come up with a decent answer.
I attempted taking a few photos of this object, but after two shots I had run out of film. The object was moving quite fast so I rushed into the house to change the film, but I forgot to wind it back to the beginning. I opened the camera in the kitchen light and it was then that I realised I had done something wrong! I closed the camera immediately and began to wind it back to the beginning. I guess I have ruined the film, but anyway I carried on doing what I had to do - loading in a fresh film.
In a matter of seconds the film was loaded. I rushed outside to take a few more snaps of the "mystery object", but it had disappeared below some houses. I rushed out into the street and dashed across the road without bothering about traffic. I then aimed my camera at the object as it was now getting very low. I pressed the shutter button for a normal exposure time - and it had gone, below the northern horizon. I went back into the house to write up my notes.
The object took around 40 - 50 seconds to cross the sky. It must have been around mag. -6 or -7, but it was definitely brighter than Venus. It was mainly white in colour with just a little hint of green - but the question remains the same... What was it?
(Anyone got any theories?) Ed.
The Catania 6-inch Cooke Refractor
By Paul Porter
In June 1 received a letter from the Osservatorio Astrofisico Di Catania, in Sicily. Also enclosed were some photographs of the 6-inch Cooke refractor in use there.
The telescope is a York built 6-inch.(15cm) F/14.8 refractor. Slung alongside is another telescope which wasn't mentioned in the letter. It looks like another 6-inch, evidently used for astrophotography. Looking at the photograph the mounting is seen to be very similar to the one we have here. The only difference that I can see is that the Catania telescope is fitted with, an electric drive and not the original weight driven clock.
The town of Catania is situated, on the coast of Sicily near to the active volcano Mt. Etna. With the dust and gases given off by Etna I presume that observations must sometimes be very difficult.
Deep Sky Notes
By Rob Moseley
A few items of interest from Summer skies, starting with some planetaries of varying difficulty. A 10-inch F6 reflector was used for all observations.
ε5 (NGC 6210) Hercules. 19/6/84 A small bright disc, very blue, with slightly ill-defined edges. Very similar to NGC 6543 in Draco. Norton gives the diameter as 8", which is too small. I estimated the mag at c.8. There is a star of comparable brightness f. by 5'. Another brighter orange star in field. x120
M 27 (NGC 6853) Vulpecula. 19/6/84 "The Dumb-bell" At first seen as a large vague rectangle, c.5'x3' with a star of 11th mag close p. After a while the bi-lobal structure became evident, "Butterfly" shaped. The central star, mag 13, could be glimpsed from time to time with averted vision. On 23/6/84 with better transparency the central star was obvious at x120 and several others spangled the rather greenish surface of the nebula.
NGC 6804 Aquila 22/6/84 Herschel gave the designation 38/6 and the reason is easy to see. The object gives the impression of a highly condensed but partially resolved cluster. It is not easy to pick up, taking the form of a faint oval nebulosity (2' diameter) with a star of 11/12th mag towards its Nf edge. At least one other star could be seen super-imposed with a/v. A glorious field, x120
ε6 (NGC 6572) Ophiuchus 23/6/84 Extraordinary! A tiny disc, under 10" across. Very bright, must be 7th mag. Vividly blue/green, almost turquoise. On 29/6/84 this object was re-examined with a full magnification range. It could be readily picked up at x60. The best general view, showing its vivid coloration was obtained at x120. At x240 a faint outer "shell" could be seen beyond the fuzzy edges of the disc. At this power the disc appeared a light blue/violet. Central star not seen.
These two globulars need very clear skies whilst on the meridian. . .
M 4 (NGC 6121) Scorpio 21/6/84 A loose scattering of faint stars, with four 9/10 mags lying to S. An amorphous suffused glow was seen, better with x60 than x120. A prominent N-S 'bar' crossed the central regions, on the threshold of resolution. Being so low in the sky (-26°24') excellent transparency and seeing are needed for a good view. A disappointing object from our latitudes.
M 80 (NGC 6093) Scorpio 22/6/84 A small (2' across) unresolved 8th mag glow. Circular, centre very condensed. Most comet-like.
M 57 (NGC 6720) "The Ring" Lyra 23/7/84 No apologies for another look at this most famous planetary. x300 A 4:3 oval, with a 12 mag star following. The nebula has a faint greenish caste, and the sides of the ring on its major axis "glisten". Two intense patches, possibly embedded stars, were suspected along the S edge. To my eyes the N edge often appears brighter. At high power the ring is seen to be extended on its major axis by areas of faint projecting nebulosity - the E projection being distinctly pointed. The central hole is "misty" and lighter than the background sky. No stars seen within.
Whilst looking for NGC 6572 I came across IC 4665, near β Ophiuchi. The drawing represents the field as seen with a x33 Erfle on the 8½ inch reflector.
IC 4665 8½" spec x33 1984 July 23. Very, very large sparse group: diam 55' mag 6, about 20 stars mag 7 (Burnham)
The night of July 23rd was indeed clear, with the central dark area in Cygnus in the Milky Way very conspicuous and the dark 'hole' in the vicinity of Deneb and 56 Cygni also clear - it seemed to me that it was possible to discern the shape of the "North America" nebula with the naked eye.
By Tim Gouldstone
1984 July 21 21h 45m
8½" Spec. x155 seeing poor
By Rob Moseley
1984 May 2. 00.00 - 00.30 UT
CM 265°0 6" Spec. x240
Short periods of Ant I, when surface features seemed as if "etched" on the disc.
The Syrtis Major was very impressive, just E of CM. Pale area centred on N Pole variable from night to night. This is not the Polar Cap itself, which was not sighted throughout this apparition.
By Tim Gouldstone
1984 Anpil 12, 20.30 UT Colong. 51.1
216mm spec. x155 Seeing - Poor.
Aristarchus & Environs
By Rob Moseley
1984 April 12, 21.55 UT Colong, 51.9
150mm spec. x120 Seeing Fair.
The two drawings shown here provide a short-term sequence showing the progress of sunrise over Aristarchus and associated features to the West (IAU). The sketches show good agreement, particularly in the account of the W wall of Herodotus, which is only just coming into view.
Aristarchus is a fascinating crater renowned for its TLP activity - but under high illumination its interior becomes so brilliant that study is difficult. Topographical features show up better under grazing illumination.
Both drawings show the two most prominent members of Aristarchus complex system of interior bands. The main bands are not difficult, and may be readily seen with a small refractor, if the air is steady.
Aristarchus: Herodotus: Schröter's Valley
By Bob Marriott
1984 March 14, 19.30 - 20.50 UT Colong, 57.8
8½" spec. x70-230
Bob Marriott's excellent sketch shows the scene about 12 hours on, although during a different lunation. The bands, crossed by interior terracing, are shown - as well as the small central peak. This peak is elusive, and can only be detected when the main body of interior shadow thrown by the E wall has just retreated from it.
Astronomical News & Views
Compiled by Geoff Johnstone
Much has been said about the Infra-Red Astronomy Satellite, but in the opinion of Dr. Emersen (Queen Mary College) far more remains to come out of future analysis of IRAS data than the results which have so far emerged.
During its active life IRAS observed 7 comets as faint as mag 17. A tail was detected on several, including Tempel (2) for which no tail had previously been recorded. The dust tail was not observed optically but was conspicuous in infra-red wavelengths. Emissions were also prominent from Zodiacal Light. Zodiacal light is visible optically due to reflection of sunlight by dust grains, but IRAS revealed the grains absorbing light and re-radiating it as heat.
Vega, intended as a calibration object, produced a surprise as it was surrounded by a dust cloud containing large particles. These were presumably material remaining from the initial formation which could still be accreting to form a planetary system. Other similar stars have been found, including Fomalhaut.
IRAS was able to study the structure of the Galaxy by recording features near the core, ionised hydrogen in the plane - and galactic "cirrus clouds". Some galactic features can be correlated with optical obscurations or gas clouds detected by radio emissions. Others could not be correlated with either optical or radio data. Stars in formation were also studied, as infra—red radiation is able to pass through the dust surrounding them.
Galaxies were also examined, and in general spirals were found to emit infra—red radiation - whereas ellipticals do not. Some faint spirals are 1OO times more powerful in the infra-red than normal galaxies which tend to be equally bright in both infra-red and optical wavelengths.
By February of this year 5 positional measurements had been made, mostly by the Danish 1.5m telescope in Chile, using a charged couple device (CCD). At present the comet is mag 25, lying 8 astronomical units from the Sun. By February 1985 it will be 4.7 au. distant — and brighten to mag 16.5.
An article in "Sky & Telescope" (April 1984) gives details of 12 quasars bright enough to be photographed by amateurs. The faintest is mag 16.9 with a red shift of 3.12. The most luminous quasar yet discovered is S5 OO14+81 in Cepheus. This quasar has a red shift of 3.4 and a mag of 16.9. . . within amateur grasp. Its distance is over 10,000 million lightyears - giving an absolute magnitude of -33, Which is incredibly bright particularly when compared to the famous 3C273.
M 33's Nucleus
Although the nucleus of the nearby spiral galaxy M 33 is small it probably contains the most powerful object in the local group of galaxies. The Einstein satellite detected it, together with 1O other sources of X-ray emission. The central source is 10,000 times stronger than our galaxy, and 1O times stronger than M 31 (The Andromeda Galaxy). The source may be a super-massive object such as a black hole. Another possibility is that the nucleus is showing activity similar to Seyfert galaxies and quasars. If this is the case then it must be a particularly faint example.
By Rob Moseley (Secretary)
A steady trickle of enquiries leading to several new members has been a pleasing feature of recent months. A sincere welcome to all new faces at our monthly meetings.
The Autumn programme has provided some quite singular meetings. In September Don Wallis provided graphic illustration of the scale of the Solar System with the aid of a roll of toilet paper! October saw Bob Marriott conduct a sort of cavalry charge into the history of astronomy which made the James Burke "Connections" format look rather facile! And in November we experienced some real shoulder rubbing when, after member's slide offerings, everyone crammed together into a heaving mass in order to spill coffee over computers - it all went down very well though!
On the observational front: Some members have made use of the College Observatory on Thursday evenings, though the weather has been quite foul during the Autumn so far. A quantity of Mylar has been obtained to enable direct viewing of the Sun with the refractor stopped down to 5 inches. The next thing we need is a Hydrogen Alpha filter to look at prominences — only a couple of thousand quid each! On October 20th a party went over to Ansley Vicarage as the guests of Tim Gouldstone and enjoyed some marvellous deep sky observing on an exceptional night - (a report on this excursion can be found below).
But the most significant item of news is that of a change-over in the position of Honorary President. After filling this post admirably for over twenty years the former College Principal, Mr Arcu1us, has now become an Honorary Vice-President. Far from losing him we hope that his retirement will give him more time to devote to his numerous
interests. Our new President is the present Principal, Mr John Temple - and we offer him a warm welcome, with the hope that our association will be as long and harmonious as it was with Mr Arculus.
There have, in fact, been no letters this quarter. However, I would like to reply to Shun Lea*s letter in the last issue, which was about a sighting of a strange object moving across the sky.
As I read Shaun's account, I looked out of the window, only to see the same phenomenon as was described in the letter. This was something I had seen many times before. It was a plane coming in to land. The very bright light is its landing light, and the subtle hint of green is probably due to the navigation lights, which flash, but are so overpowered by the landing light that they give the impression of a constant green hue, (there are actually two navigation lights, one red, one green, but the body of the plane may have obscured the red one, or it may have been too faint to see).
I hope Shaun finds this a satisfactory explanation of his strange sighting.
The Ansley Visit
By Richard Barrett
The Orionid meteor shower has its maximum on the 21st of October. This shower is associated with Halley's comet and as the comet nears perihelion its associated showers should (in theory) be more impressive. Observations of meteor showers are therefore particularly important during the next year or so.
On the night of the 20th - 21st October the Rev. Tim Gouldstone invited members of the society to visit the Ansley Vicarage, to observe the Orionids from a position with very clear skies.
As it turned out, the weather was excellent, (a little windy perhaps). Several members brought telescopes, and Tim had his own 8½ inch reflector set up. This gave magnificent views of several objects; I was particularly impressed by the views of the Ring Nebula (M 57 in Lyra) and NGC 7662 (a planetary nebula in Andromeda). A summary of the deep sky observations made is given below, courtesy of Vaughan Cooper. The weather was very cold, but hot fish and chips were available from a nearby shop, and Tim allowed us to use the warmth of the Vicarage to restore circulation when the cold got too much for us.
We stayed for about four hours (the cloud closed in at about eleven o'clock). Estimates of the number of meteors seen during this time varied between 0 and 1, (and that was a sporadic).
The lack of meteors did not spoil the occasion for any of us since there were plenty of deep sky objects on view, and the clear skies (not to mention the presence of Tim's 8½ inch reflector) meant that there was plenty to see and a great time was had by all.
Observations from the Ansley Site
26th October 1984 (20.30 to 23.15 UT)
by Vaughan Cooper
Square of Pegasus - naked eye 5 stars visible within square - limiting mag. 5.1 (the number of stars visible in the Square is a test of observing site - the more stars, the better the site. I could see 10; which makes the limiting mag 5.7 — I must have good eyesight. For more details of this transparency test see the September 1983 issue of MIRA 4, Ed.)
Epsilon Aurigae — naked eye. Its brightness seems to be equal to ETA Aurigae (mag 3), so the eclipse of Epsilon is over for another 27 years.
Fomalhaut (ALPHA Pisces Astrinus) — naked eye. This has been the first time I have seen this star -the most southerly 1st mag star visible from this latitude.
M 33 in Triangulum — 10x50 Bins. This galaxy was a faint, extended object. It looked like a stain within the field of view. First sighting of M 33, despite many attempts.
M 33 - 4 inch spec. x32. Very faint, just able to see it.
M 81 & M82 - 8½ inch spec. Both of these objects were well within the wide field of view. M 81 was elliptical and showed little structure. However, M 82 was clearly elongated and had a wispy quality at each end.
NOTICE would any members of the Society like to draw or photograph the following objects as a challenge.
M 97, The Owl Nebula (a difficult object for astrophotographers)
M 51, The Whirlpool Galaxy (drawings preferred)
Photos of a globular cluster
M 11 in Scutum
M 27 in Vulpecula
The Orion Nebula (drawings only - we have an excellent photo by Geoff Johnstone)
M 81 & M 82
I hope these objects cover all tastes and artistic abilities. The next issue will contain the beat efforts (if any). Do have a go, but don't forget about the usual lunar and planetary photos and drawings, or any other deep sky photos.
I have chosen these objects because they are not often drawn or photographed, despite the fact that they are very interesting subjects;there should be something for everyone to have a go at.
The Wonderful Star
by Rob Moseley
Although our bulletin is entitled "MIRA", (Latin for "the Wonderful". . . and strictly tongue in cheek!) very few, if any, of our members appear to observe and record variable stars. At least, nothing has turned up in these pages so far.
In view of this I thought I would redress the balance a little by taking a look at Mira (Omicron Ceti) itself - as it is one of the most celebrated stars in the firmament, and the type star of the long period variables (or LPVs).
This cool, low density, red "giant" varies between mag 5 and mag 9 in a period of 331 days. It must be stressed that these are average values. At some maxima the star struggles to brighten above mag 5, whereas in in 1799 Herschel rated it as equal to Aldebaran (ie mag 1). Its period too can vary by up to one month either side of 331 days.
All this only adds to the fascination of following Mira - it has been springing surprises since it was discovered (and then lost!) by David Fabricius in 1596.
Where is Mira? The star lies in the rather dull constellation of Cetus, the Sea Monster, which occupies much of the space between Pegasus and Orion. Norton's Star Atlas will direct you to the general area, but to identify Mira itself and make estimates of its brightness with binoculars or a small telescope you will need a slightly more detailed chart, (below).
The map shows the field around Mira Ceti with magnitudes given to enable comparisons with Mira to be made. Note that North is up.
This chart is based on one issued by the VS Section of the BAA, and shows a field 9 degrees around the variable. Numbers against some of the stars refer to Flamsteed's catalogue of 1726. Not all stars are given a magnitude as some are unsuitable for comparison.
At the moment Mira is approaching its minimum. According to Roy Panther its mag was 8.4 on 1984 Oct 30, it may fall by perhaps another magnitude and linger at this level for one or two months before rising again quite rapidly next Spring - but no one can be sure! A rather inconvenient factor in following Mira at the present time is that the maximum is tending to coincide with its conjunction with the Sun - rendering it invisible. However, this state of affairs won't last for long, as Mira's period will move it out of this phase within a few years.
The minima of Mira are easily followed with a moderate telescope, or even good binoculars under dark skies. Its strongly red tint will help in identification. There is also an interesting bonus attached to the minimum - for Mira is but one component of a double system. There is a close white attendant of around mag 10, only ever visible when the "Wonderful Star" is dim.
(Variable star observers would be most welcome to contribute to MIRA on the subject of variable stars in general. If there is sufficient interest variable stars will get a regular slot in MIRA — Ed).
FILM HYPERSENSITIZATION USING PURE HYDROGEN
By Geoff Johnstone
NB: Hydrogen is highly explosive (remember the Hindenburg?) and must be treated with great care. It would be safest to produce the hydrogen gas out of doors, where a build up of gas would be unlikely. Note that great care must also be taken with any chemicals used, they must be disposed of IMMEDIATELY after sufficient hydrogen has been produced, since they will continue to create hydrogen, which may build up to explosive concentrations.
This image of M27 was taken with a 10” newtonian telescope and was a 20 minutes exposure.
Hypersensitization of film for astrophotography has become a popular topic of discussion over the last few years, particularly since Kodak brought out their new 'Kodak 2415 Technical Pan’ film, which has very high resolution, is red sensitive but is rather slow for the purposes of astrophotography. Hypersensitization effectively increases the film’s speed, (increases of 3 to 50 times have been reported with 2415, which shows the greatest enhancement of all films after hypersensitization).
A cheap method of hypering film is described here. Its advantages are not only that it is cheap, but also that the chemicals used are easy to obtain and the necessary equipment is fairly simple.
A flat piece of ¼” inch (6mm) steel plate is used as a lid for a stainless steel developing tank. Such a tank is available from most photographic suppliers. The lid is drilled to take a caravan gas tap. Rubber seals are required, but can be made from an old inner tube. In the bottom of the tank is placed some drying agent to keep the contents free from moisture. The film is wound on to the spiral and placed in the tank, the lid is held in place with a 'G' clamp. The tank is now evacuated with a vacuum pump, which can be made by reversing the internal washer of a bicycle pump and screwing into the end a valve (which must be reversed) used for inflating footballs. The pump is connected to the tank with a short piece of GAZ tubing, and 50 to 100 quick strokes of the pump produces an adequate vacuum. The hydrogen used to sensitise the film is produced in very small quantities just prior to use. Hydrogen is recognised as a more effective sensitising agent than the more usually used forming gas (a nitrogen—hydrogen mixture). Hydrogen will sensitise more quickly, at a lower temperature and probably more effectively than any other agent. It can be made in a honey jar, the lid of which is drilled to take a caravan gas connector; suitable rubber seals are again required. The gas can be produced by the action of DILUTE hydrochloric acid on zinc or 10% sodium hydroxide on aluminium milk bottle tops. Sodium hydroxide is available from any hardware store. The gas is collected in a football bladder with its associated needle valve, which are available from good sports shops. When the bladder has inflated sufficiently, the hydrogen is transferred to the evacuated developing tank. The tank is now heated for a certain length of time. I use ft fish tank with heater/thermostat turned up full, i.e. about 38°C. At this temperature the film is sensitised in about 17 hours. At 25°C 24 hours are required; higher temps require shorter times, but are inclined to introduce uneven sensitisation.
After sensitisation the film is removed, wound back into its cassette and stored in the deep—freeze until required. Before loading into the camera the film, still in the plastic bag in which it should be placed before storage in the deep—freeze, is allowed to come to room temperature. I have found it to be valuable to perform quality control tests on the film before use (after sensitisation). This involves snipping a bit off the sensitised film before loading the cassette and developing it by the normal procedure, e.g. sensitised in D19 for 4 minutes. The negative should show slight but even fogging. If no fog is present you cannot be sure that the film is adequately sensitised, and if there is too much then some contrast has been lost.
I would maintain that this procedure is as safe as filling the car with petrol at a garage, (make sure there are no naked flames in the vicinity and there should be no problems if the rules above are adhered to).
A final caution about the solutions used; these are corrosive liquids and should be dilated with copious amounts of water before being discarded.
DEEP SKY NOTES
Some recent double star observations.
We start with two objects chosen as tests for the 6½" Cooke refractor at the College Observatory. As the drive is now operational I thought I would try to see just how good this instrument is. . .
π Aquilae (Σ2583) 1O/1O/84 Seeing - IV
A - mag 6, Yellow
B - mag 6.8, Greenish white
Separation - 1'.43 (Argyle, 28 inch OG, 1970)
Estimated PA - 125° (Argyle gives 108° 1970)
The pair was elongated at x204. As strong interference band seen at x245. Cleanly split at x390 and 526.
(Webb records great divergence as to colours - his own opinion being Yellow and Green)
This was a good performance in relatively poor seeing.
Σ 2723 (Delphinus) 25/10/84 Seeing III
A - mag 6, White
B - mag ?, ?
Estimated separation - 1'.OO
Estimated PA - 100°
Elongated at x246. At x526 just split in good moments.
(Duruy, 1944: - 110°, 1'.17, mags 7 & 8.7. Seen as round in 1958)
This pair possibly widening again? Observation confirmed by Paul Porter. Only about 0.3 above the theoretical resolving power of the 6½ inch. Needs checking with a larger aperture.
Two nuggets observed with my own 10-inch reflector:
α Pisciura (Σ 202) 2/10/84 Seeing - II/III
A - mag 3, Greenish white
B - mag 5?, Pale Violet
Estimated separation - ? (Very Close)
Estimated PA - 270°
The magnitudes were difficult to gauge due to the proximity of the components. The pair was elongated with x120 and definitely split in good moments with x280. There is great disagreement in my sources over the magnitudes and colours. In the last century with the pair separated by over 3 arcsecs. Webb gave the magnitudes as 2.8 and 3.9. The modern Webb Society Handbook gives 4.5 and 5.2! Webb quotes the primary as Greenish white, but describes the comes as blue, tawny and even brown (!), at different times.
I found the colour of both to be rather odd. The primary is indeed a strange tone of yellow, having a distinctly greenish caste. Perhaps "Lemon" would be the best description. At first the companion appears bluish, but after a while I could see a definite admixture of violet. (I should stress that Webb's descriptions were not consulted until after the observation — this being my invariable practice.)
The last measure I have is one by Duruy made in 1975 - "PA 286°, Sep 1'.79. The ephemerides for 1984 in the BAA Handbook gives 278°, 1968.
The pair has a period of c. 700 years, and is now closing.
Burnham 1 (Cassiopeia) 26/10/84 Seeing - III
The first entry in SW Burnham's catalogue of 1,274 discoveries (though not his first discovery - this being β 40). Finding objects among the rich Milky Way star fields of Cassiopeia is not easy as they are littered with beautiful pairs and triplets. However, this object is easily found lay centring the bright star α Cass in the field of view and waiting 12 minutes. If you have an equatorial mount (with the drive turned off β 1 will then be in the field.
Webb describes it as a "pretty quintuple". At first sight a fine triplet - then quadruple an the 12th mag comes to N is noted. Star A is double, but close (1.4) - so that B was not seen at x120.
A - mag 8, Yellowish A & C are separated by c. 3'.00
C - mag 8.5, Pale Blue There are two further comites (F & G), below 13th mag
D - mag 8.7, Purplish There is a wide pair South preceding
by Rob Moseley
Sunset aver Sabine & Ritter
1984 July 19 01.45 - 02.45 UT
Colong 158.4° - 158.9°
10" Spec. x120
Seeing - II/IV (Var) Trans - Good
Terminator shadows drawn 01.45 - 02.00
Shadow from Ritter 'B' almost at N wall of Ariadaeus at 02.20. E wall of Ariadaeus gone at 02.40.
Observational details as per drawing
Sabine and Ritter form a fine pair of craters lying near the Western (IAU) shoreline of the Mare Tranquillitatis, just North of the Moon's equator.
They are both just under 20 miles in diameter, Sabine being the marginally larger of the two. They lie in a most interesting region crossed toy delicate rilles which attempt to follow lines of crustal weakness between the great Ariadaeus Rille to the West and the Hypatia system to the East. (Ariadaeus itself is the larger of the two rather insignificant craters perched right on the shoreline of the Mare - at bottom right in the drawing).
The drawing was made an a test exercise for a new 10" mirror. The seeing throughout the observation was very variable and so the power was not pushed beyond x120. The two parallel rilles running between Ariadaeus and Ritter are visible in much smaller telescopes providing they lie near the terminator and that conditions are favourable.
Apollo 11, the first manned expedition to the Moon, landed just a few miles East (ie left in the drawing) of Sabine and Ritter, in 1969.
Astronomical News and Views
Compiled by Geoff Johnstone
Geminiga - the black hole near Calcutta?
The unusual gamma-ray source called Geminiga (2CG 195+04) continues to puzzle astronomers. Recent discussion that the object produces gravitational waves which are detectable has blown hot and cold.
A photograph taken in 1955 reveals an object 7 arc seconds north-west of Geminiga's proposed X-ray position. More recent photographs fail to show the object but do show another object 4 arc sec south-east which suggests that Geminiga could have moved at a rate of 0.37 arc seconds per year. This indicates that Geminiga is within 300 light-years of Earth. This evidence strengthens the argument that Geminiga may be the closest condensed object (neutron star or black hole) to the Earth.
A Double Gravitational Lens
Gravitational lenses are a result of General Relativity. This theory states that:
1) light rays follow the shortest paths between any two points in space
2) in the regions surrounding massive bodies space-time is appreciably curved
These rules mean that when light passes close to a massive object it is deflected from a straight line (since in curved space the shortest paths are curves). A well known example of this effect is the change in the observed position of a star seen close to the sun during an eclipse.
When a quasar (distant but very bright) is in line with a massive galaxy (closer but relatively dim) its light may be 'bent' by the intervening galaxy (according to General Relativity) so that multiple images are formed, (i.e. light travelling round either side of the galaxy may be bent so that two separate images of the quasar are formed. Often the galaxy is so dim as to be invisible). This is lensing. Quasi-stellar source Q 2345 +007 in Pisces may be the first case of a double gravitational lens. The problem has been that using a single lensing object its mass must be 10 times that of the Milk Way, with a red shift of only 0.4 (implying that it is close to us). This is unlikely as no such object is visible. A multiple lensing object such as a pair of galaxies or a cluster much further away fits the observations much more satisfactorily.
Big Eye on the Universe
In April, the University of California received 36 million dollars from the Marion D Hoffman trust for the construction of a 10 metre telescope, which covers about ½ of the estimated cost. It should reach first light in 1990, when it becomes the worlds largest telescope. The instrument is to be situated on Manna Kea, Hawaii, and will have a mirror consisting of 36 six—foot wide hexagons. Each mirror element will be individually controllable. Together they will form a paraboloid, (the usual shape of telescope mirrors). The telescope will have an altezimuth mount and will not look dissimilar to the British William Herschel Telescope at present under construction in La Palma.
The interlocking hexagon design has long been the chief contender for the role of the New Generation Telescope (other contenders are the multiple mirror design and the radio telescope style, which consists of a large paraboloidal dish from which the secondary supports emanate, giving it the appearance of a radio telescope). The advantage of the patchwork of mirrors is that a large aperture can be obtained without the difficult and expensive process of casting, figuring, polishing and aluminising such a large mirror also the need for many reflections (used in multi-mirror types) is dispensed with.