http://www.phys.uu.nl/~vgent/venus/venus_text2.htm#black%20drop
Bibliography: The Black Drop and Related Phenomena, from R.H. van Gent

http://www.transitofvenus.org/faq/298-what-causes-the-black-drop-effect
FAQ: What causes the Black Drop Effect? A simplified explanation of limb darkening and point-spread function, courtesy of Jay Pasachoff.

http://nicmosis.as.arizona.edu:8000/POSTERS/TOM1999.jpg
Poster on the 1999 transit of Mercury "definitively solves the problem of the black-drop effect that plagued past transits of Venus;" by Jay Pasachoff, Glenn Schneider and Leon Golub; from the American Astronomical Society's Division of Planetary Science meeting in 2001.

http://arxiv.org/pdf/astro-ph/0310379
Report by Schneider, Pasachoff, and Golub (see poster above) "separates the primary contributors to [the "Black Drop" Effect], solar limb darkening and broadening due to the instrumental point spread function...for the 1999 transit of Mercury, seen in high spatial resolution optical imaging with NASA's TRACE spacecraft."

http://www.aas.org/publications/baas/v32n4/aas197/785.htm
Abstract describes physical cause of "black drop" effect; B. E. Schaefer (Univ. Texas Austin) at 2001 AAS meeting.

From footnote 28 of  Chapter 7 of Sky and Ocean Joined: U.S. Naval Observatory, 1830-2000, by Steven J. Dick, (Cambridge University Press, 2003):

"The physical cause of the black drop phenomenon has been the subject of considerable controversy. Bradley Schaefer reviews the controversy in “The Transit of Venus and the Notorious Black Drop,” BAAS, 32 (2000), 1383-1384. He concludes that the phenomenon is not caused by diffraction, illusion or atmospheric refraction, but by terrestrial atmospheric smearing that blurs the image."

http://www.bo.astro.it/~biblio/Horn/Blackdrop.htm
Origin and Phases of the "Black Drop" Phenomenon, a paper on the understanding of the black drop effect as of 1922.  Also available in Italian; from Guido Horn D'Arturo of Università di Bologna, Dipartmento di Astronomia, 1922. 

http://skyandtelescope.com/news/article_1277_1.asp
Sky & Telescope magazine asks, "Where Was the Black Drop?" after the 2004 transit of Venus.

To simulate the appearance of the "black drop" effect, almost pinch your thumb and forefinger together against a bright background.  Near contact the ligament between them appears.

http://vestige.lmsal.com/TRACE/transits/venus_2004/
Images and movies from the TRACE spacecraft are among many new perspectives of the 2004 transit of Venus.

At the critical moment when observers try to time when Venus touches the inside edge of the sun, strange phenomena such as the black drop effect suddenly emerge.  This site guides observers in discerning at what instant internal contact occurs; from Steven van Roode.

http://star.arm.ac.uk/history/transit.html
Drawings of the Transit of Venus by Captain James Cook and Charles Green; from the Armagh Observatory.

http://www.metaresearch.org/home/Viewpoint/blackdrop.asp
In noting "an irradiation effect – the apparent spreading of light from bright areas onto any adjacent dark areas," author Tom Van Flandern asserts that the well-understood black drop effect "provides a timing advantage rather than a disadvantage." 

http://www.bo.astro.it/~biblio/sma/page/venere_05_06_1761.html
Bibliographical and archival records from the Department of Astronomy of the University of Bologna (Italy), featuring manuscripts of observations made in Bologna by Eustachio Zanotti; includes images and resources from transits in addition to the 1761 records.  (Italian; a link with some English translation is at http://www.bo.astro.it/~biblio/Archives/copertina.html.)

http://www.bo.astro.it/~biblio/Horn/Blackdrop.htm
A detailed 1922 assessment of the black drop effect suggests "instrumental astigmatism should be considered the cause of some aspects of the photographedGUIDO HORN D’ARTURO The “black drop” phenomenon and astigmatism. Università di Bologna, Dipartimento di Astronomia, (Pubblicazioni dell’Osservatorio astronomico della R. Università di Bologna, vol. I, n.3, 1922). ligaments." 

http://carnap.umd.edu/phil250/transits/transits.html
Images related to determining the distance of the earth to the sun; "black drop" effect illustrations.  Shown at left is "Close-up of Bergman's Drawing of the Blackdrop Effect;" from The Astronomical Unit, Stellar Parallax, & the Transits of Venus, Determining the Distance of the Earth from the Sun, From Eudoxus of Cnidos to Harold Spencer Jones.

http://carnap.umd.edu/phil250/transits/images/blackdrop.gif
"The Black Drop Effect at the Limb of the Sun."

http://carnap.umd.edu/phil250/transits/images/bergman_drawing.gif
"Torbern Bergman's Drawings of the 1769 Venus Transit."

http://carnap.umd.edu/phil250/transits/images/losmonov_drawing.gif. 
" Lomonosov's Drawings of the 1769 Venus Transit."

Original publications scanned by Stanford University Libraries & Academic Information Resources and offered online, including the following from http://dlib.stanford.edu:6520/text1/dd-ill/transit-1874-2.pdf:

http://dlib.stanford.edu:6520/text1/dd-ill/transit-1874-2.pdf
"Point Coton, Rodriguez, by Commander W.J.L. Wharton, RN, with a telescope 2 3/4 inches aperture, power 160."

http://dlib.stanford.edu:6520/text1/dd-ill/transit-1874-2.pdf
"Transit of Venus 1874 Dec. 8.  Diagram relating to the Egress of Venus as observed at Mokattam;" observations by Capt. Browne. (Mokattam Hills is near Cairo.)

http://dlib.stanford.edu:6520/text1/dd-ill/transit-1874-2.pdf
"Transit of Venus 1874 Dec. 8.  Diagram relating to the Egress of Venus as observed at Mokattam;" observations by Miss Newton and Mr. Newton.

http://dlib.stanford.edu:6520/text1/dd-ill/transit-1874-2.pdf
"Transit of Venus 1874 at Suez;" figures 1 & 2 (left) and figures 3 & 4 (right).

http://dlib.stanford.edu:6520/text1/dd-ill/transit-1874-2.pdf
"Transit of Venus 1874 Dec. 8; Observations at Point Venus, Rodriguez by Lieutenant Neate, R.N. with a Telescope of 6 inches aperture power 152."  Ingress Fig. 1 and 2 (left); Ingress Fig. 3 and Egress Fig. 1 & 2 (right).

http://dlib.stanford.edu:6520/text1/dd-ill/transit-1874-2.pdf
"Transit of Venus 1874 December 8.  Observations at Hermitage Islet, Rodriguez by Lieutenant R. Hoggan, R.N. with a telescope of 4 inches aperure, power 120 ingress, 160 egress."  Ingress figures 1, 2, & 3 (left); egress figures 1, 2, 3, & 4 (right).

http://dlib.stanford.edu:6520/text1/dd-ill/transit-1874-2.pdf
"Transit of Venus 1874 December 8.  Observations at Supply Bay, Kerguelen's Island by Lieut. C Corbel witha telescope of 4 1/2  inches aperture, power 145."  Ingress figures 1, 2, & 3.

http://dlib.stanford.edu:6520/text1/dd-ill/transit-1874-2.pdf
Observations at Supply Bay, Kerguelen's Island by Lieutenant G.E. Coke, R.N., with a telescope of 3 1/2 inches aperutre, power 150."  Ingress figures 4 & 5.

Observations at Supply Bay, Kerguelen's Island by Lieutenant G.E. Coke, R.N., with a telescope of 3 1/2 inches aperutre, power 150."  Ingress figures 4 & 5.

bde-honolulu.gif
Illustration of internal contact, 1874 December 8, Honolulu; Tupman 6-inch refractor; 20h, 46m, 14.5s; from Account of Observations of the Transit of Venus...; edited by Sir George Biddell Airy, K.C.B.

bde-honolulu2.gif
Illustration of internal contact, 1874 December 8, Honolulu; Tupman 6-inch refractor; 20h, 46m, 32.5s; from Account of Observations of the Transit of Venus...; edited by Sir George Biddell Airy, K.C.B.

bde-artificial.gif
"Front elevation of the Model artificially representing the circumstances of the Transit of Venus when place a the distance of 400 feet.  One-fourth natural size.  The planet is represented in the position of Internal Contact with Sun's limb (nearby); its motion is from left to right."   1874 December 8, Honolulu; G.L. Tupman.

http://www.vt-2004.org/Background/Infol2/EIS-F7.html
Belgian astronomers view "black drop" effect from Chile in 1874; from Hilmar W. Duerbeck.

From email:

• "Has anyone given thought to how the shadow of a sphere wrapping around the edge of a significantly larger sphere would be shaped?  Try it.  It is not such a mystery."    -Siteartist

• Having just watched the UK TV coverage of yesterday's Transit of Venus, which discussed the "black drop effect" I tried an experiment using my graphics program. Placing a small black circle inside and just in contact with a large white one (on a black background), I found that the degree of black drop increased when I zoomed out and decreased when I zoomed in.  Likewise, viewing the screen from a distance I found that the black drop effect increased as I moved further away. I then reversed the colours of the image and produced an corresponding "white drop effect". To me the cause seems obvious. Namely that the eye's resolution is limited, so that the smaller the image the less discernible is the boundary between adjacent objects. The same probably applies to optical apparatus; if not to the lenses themselves, then certainly to the media upon which images are displayed. My conclusions lead me to believe that the effect is not caused by cosmic interventions, but simply by our powers of perception.

  Try this test: open the blackdrop.gif file. If you zoom in you will see that there is a distinct white separation between the two circles. As you zoom out this becomes less visible, and by zooming out (say) 8 times a marked black drop effect appears. Alternatively, have the image on your screen at a zoom level that makes the separation just perceptible, then view the screen from, say, 15-20 feet away.             -John Rushby-Smith

  
  

The black drop effect for the 1878 transit of mercury is attributed to "a very variable amount of irradiation of bright images on the retina," though with caveats.