Chinese Astronomical methods adopted by Toscanelli. European determination of Latitude

 

On 7^th August 1421 catcalls, whistles and coarse Florentine jokes cheered a barrel of brown bread, smoked ham, parmesan cheese and wine as it bumped up the side walls of the great dome of Florence Cathedral which the celebrated architect Brunelleschi had designed and was building.

 

His revolutionary design for the dome resembled a lemon with its bottom sliced off, positioned upright. The curve increased as the dome got higher –initially the bricks rose vertically then curved more and more until at the top the dome surface was horizontal. The dome was not supported whilst being built either internally or externally. The forty four thousand tons of bricks which made up the dome did not collapse inwards because they were laid horizontally and vertically as determined by extremely complex three dimensional mathematics perfected by Brunelleschi with Toscanelli’s help. This incredible architectural masterpiece was inaugurated by Pope Eugenius IV in 1434.

 

Of relevance to our story is that it was possible to stand on the flat surface at the top of the dome and peer down into it – from there one saw a perfect circular floor down below. Likewise the sun could shine through this aperture and cast shadows on the floor below.

 

In about 1465 Toscanelli supervised the erection of a marble slab at the height of 277 feet within the dome. A small opening, a camera obscura was cut into it. The pinhole camera has several advantages when measuring shadows cast by the sun’s rays. The edges of the circle receive less exposure than the centre and the focal length was greater at the edges making the centre of the shadow ‘zoomed’ in. In short shadows appeared sharper, thinner and clearer. As explained in Appendix 2 of ‘1421-The Year China Discovered The World’, by the early Ming dynasty, Chinese observers had invented this camera obscura and used it with the result that the width of a long shadow of the sun could be measured within one hundredth of an inch. Toscanelli’s identical device enabled him to determine midday (when the sun’s shadow is at it’s shortest) to within a second.

 

Now that Toscanelli could so accurately determine precisely when the sun was at its maximum height he could also measure south – which is also determined when the sun is at its maximum height.  He had a hundred metre line, a gnomon incised in the cathedral exactly north and south – this gave him the local meridian which he could use to determine when stars passed by precisely at due north.

 

Next Toscanelli had bronze markers placed around the circumference of the dome – both on the windowsills and on the marble floor which can be seen today. These were at the cardinal points N,E,S,W and intermediate points between these.

 

Using Toscanelli’s markers the observer on the cathedral notices the sun’s maximum height on March and September 21^st was 46 degrees. Subtracting this from 90 degrees gave the latitude of Florence at 44 North. The observer uses Toscanelli’s camera obscura to note the sun’s height (by length of it’s shadow) on midsummer’s day – it is now 69 degrees – a further 23 degrees 45 minutes has to be added to get the latitude of Florence. Similarly on midwinter’s day a further 23 degrees 45 minutes has to be subtracted – this is on account of the earth’s tilted of 23 degrees 45 minutes.

 

As Toscanelli’s bronze pegs show, the system can be refined to give the sun’s declination for every day of the year. Imagine the floor of the cathedral like a compass rose (see diagram). Midsummer day being at 180º, midwinter at 0º and March 21^st at 90º, May 6^th is thus at 135º. The radius on the north south axis is the sun’s declination viz plus 23º 45’ in summer and minus 23º 45 minutes in winter. Taking May 6^th as an example draw a horizontal line as shown to the N/S radius.  The ratio of little R/big R x 23º 45’ is the sun’s declination for May 6^th viz 16.6 degrees.  To find his latitude on May 6^th the observer takes the sun’s maximum altitude at noon (62 degrees) subtracted from 90 equals 28 degrees plus 16 degrees = 44 degrees.

 

So going round the circumference of the floor of Florence Cathedral we can now obtain declination of the sun for any day of the year and hence latitude for every day of the year by measuring the sun’s height and using declination tables.

 

The introduction to Appendix 2 of my book under ‘The Chinese determination of elapsed time’ explains how the Chinese measured the sun’s altitude at midday for every day of the year and corrected these measurements for latitudes between 17º and 40º.  They also compensated for the difference known as the equation of time. In short Toscanelli used the Chinese method – it is in my submission significant that he inserted his camera obscura, placed the bronze markers and incised his north south gnomon after he had met the Chinese who to use his description were ‘men of learning and ingenuity… as well in religion as in all the other sciences’. He could have had all these modifications made whilst the cathedral was being built but did not do so.

 

Toscanelli did not produce tables of the sun’s declination but Regiomontanus who collaborated with Toscanelli did. Regiomontanus published his tables of declination in 1474. They were immediately used by the Portuguese ‘Junta dos Mathematicos’ who issued them to Portuguese captains exploring South Africa. Diego Cão was one of the first to use them and Dias did so to determine the precise latitude of the Cape of Good Hope at 35 degrees south. It is thus arguable that Chinese astronomers showed (through Toscanelli) Europeans how to determine latitude, which enabled Europeans to determine latitudes of new discoveries and be able to return home to the latitude of Lisbon – all hugely important.

 

This was not the only astronomical discovery which I believe Toscanelli adopted from the Chinese during his ‘long conversations… on many subjects’. Toscanelli predicted and made accurate observations on Halley’s comet which passed by the earth between 8 June and 8 July 1456.

 

The Chinese had charted every arrival of Halley’s comet from 240 BC and by 1432 had over 2000 years experience of recording events in the night sky – a new star in 1300 BC and the remnants of the Supernova explosion known as the Crab Nebula in 1054. Recording comets was commonplace to the Chinese. Toscanelli was the first European to observe comets in 1433, 1449-50, 1456 (Halley), two in 1457 and 1472. Again it is significant he only observed them after the Chinese visit although there were plenty for him to observe before then.

 

Taking all these astronomical events together, that is Toscanelli’s obvious admiration for Chinese men of learning, his use of identical methods of measuring the sun’s shadow to determine date and time, his observation of comets – all of which were after the Chinese visit – makes it a reasonable assumption that he did indeed absorb Chinese knowledge.