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Ernest Kazakov
Ernest Kazakov

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Past reports indicate that some nanoparticles (NPs) affect seed germination; however, the biotransformation of metal NPs is still not well understood. This study investigated the toxicity on seed germination/root elongation and the uptake of ZnO NPs and Zn2+ in alfalfa (Medicago sativa), cucumber (Cucumis sativus), and tomato (Solanum lycopersicum) seedlings. Seeds were treated with ZnO NPs at 0–1600 mg L–1 as well as 0–250 mg L–1 Zn2+ for comparison purposes. Results showed that at 1600 mg L–1 ZnO NPs, germination in cucumber increased by 10 %, and alfalfa and tomato germination were reduced by 40 and 20 %, respectively. At 250 mg Zn2+ L–1, only tomato germination was reduced with respect to controls. The highest Zn content was of 4700 and 3500 mg kg–1 dry weight (DW), for alfalfa seedlings germinated in 1600 mg L–1 ZnO NPs and 250 mg L–1 Zn2+, respectively. Bulk X-ray absorption spectroscopy (XAS) results indicated that ZnO NPs were probably biotransformed by plants. The edge energy positions of NP-treated samples were at the same position as Zn(NO3)2, which indicated that Zn in all plant species was as Zn(II).


The recent exhibition at the Science Museum, Leonardo da Vinci: The Mechanics of Genius (10 February–4 September 2016) included among 39 models based on Leonardo’s drawings one that was described as a ‘worktable for friction experiments’. It is the purpose of this article to examine the history of this exhibit, to scrutinise the original drawings on which it is based, and to ask what information it really conveys about Leonardo’s studies of friction.There are two generally accepted ‘laws of friction’, which are broad guidelines rather than fundamental physical laws (Hutchings, 1992). These state that:the force of friction acting between two sliding surfaces is proportional to the force pressing the surfaces together (i.e. the two forces have a constant ratio, often called the coefficient of friction), and;the force of friction is independent of the apparent area of contact between the two surfaces.These statements are usually attributed to Guillaume Amontons (1663–1705) and were published by him in 1699. They are often referred to as ‘Amontons’ Laws’, but it is widely known that they were first enunciated by Leonardo da Vinci some 200 years earlier. In a recent chronological study of Leonardo’s notes and sketches relating to friction (Hutchings, 2016) I have shown that his first statement of these laws dates from 1493–1494, and that sketches that are often reproduced and described as showing his ‘friction experiments’ were in fact drawn considerably later. Furthermore, as discussed below, these sketches show experiments that could not realistically have been used to deduce the laws of friction. It was on these sketches that the present ‘worktable’ model, created by Giovanni Canestrini, was based.

The exhibit from the 2016 Leonardo exhibition in London is shown in Figure 1, together with a schematic diagram. The accompanying display board stated ‘Leonardo systematically studied friction, which he considered would be important for the functioning of machines. This bench allowed him to experiment with the contact between different surfaces, by distinguishing between sliding and rolling.’ The same exhibit had also been included in related exhibitions in Paris (Cité des Sciences et de l’Industrie, 23 October 2012–18 August 2013), Munich (Deutsches Museum, 11 October 2013–3 August 2014) and São Paulo (Federação das Indústrias do Estado de São Paulo, 11 November 2014–10 May 2015). It belongs, as did many of the other models on display in this loan exhibition, to the Museo Nazionale della Scienza e della Tecnologia ‘Leonardo da Vinci’ (MUST) in Milan where it has inventory number 392.

Giovanni Canestrini (1893–1975) had a long career as a motor racing journalist, and is famous as one of the founders of the Mille Miglia road race in 1926. He also wrote three substantial pieces on the contributions of Leonardo da Vinci to mechanics, particularly in the context of the development of the motor car. His first essay (Canestrini, 1938) was contained in a volume on the Italian contribution to the evolution and development of the motor vehicle, published by the Reale Automobile Club d’Italia (RACI). It was a detailed account which showed familiarity with much of Leonardo’s writing as well as evidence of wide reading of other sources, and despite the apparent narrowness of the chapter title (‘Leonardo da Vinci and the problems of locomotion’) attempted to show that Leonardo’s contributions had pre-dated and indeed informed the work of later inventors in many fields ranging from geometry and optics, to statics and dynamics, fluid mechanics and hydraulics, military engineering, mechanical devices, metalworking and other areas. In discussing Leonardo’s studies on friction, Canestrini reproduced MS L f. 11v and identified it as showing ‘studies of rolling friction’[1], but while he quoted a statement about friction from Codex Arundel f. 41r[2], he did not reproduce any sketches from that folio.

The second model was not illustrated in the exhibition guide or catalogue, but an image is to be found in Canestrini (1939b, p 160), shown here as Figure 6(a), with a caption that closely parallels the entries in both the exhibition guide and the catalogue: ‘Reconstructed model – from drawing by Leonardo – for the study of the action of forces and friction in a rotary system’[12]. This model, which we shall call Model E, is also shown in a leaflet advertising the exhibition (Leaflet, 1939) and depicted in Figure 6(b). The accompanying caption reads misleadingly ‘Cylinder clutch’ or more literally, ‘Clutch made from cylindrical elements’[13]. Model E was based on the sketch in the Codex Atlanticus (f. 1081v) shown in Figure 7, which Canestrini also reproduced in two of his publications. In Canestrini (1938) he described this diagram as ‘thrust rollers in a drawing by Leonardo’[14], while in Canestrini (1939a) it was a ‘system of rotating bearings with thrust rollers on spindles’[15].

Figure 6(a) shows an illustration of Model E from Canestrini (1939b) captioned ‘Modello ricostruito – su disegno di Leonardo – per lo studio dell’azione delle forze e dell’attrito in un sistema rotoide’. Figure 6(b) shows an illustration of model E from a booklet advertising the 1939 exhibition, captioned ‘Frizione a cilindri’ (Leaflet, 1939)

The ‘table’ of Model A is based on the two central sketches from Codex Arundel f. 41r (see Figure 3) and was first created (as Model A*) in 1939. These sketches date from 1500–1505[16] and show two separate and distinct pieces of apparatus. The notes written on the same page of the notebook, some of which extend on to the facing page (f. 40v), consist of a general statement on the origins of variation of friction, detailed quantitative attempts to evaluate the effects of friction on rotors carrying various hanging weights, and the statement ‘circular friction is equal to linear friction’[17]. But there is no text that relates explicitly or implicitly to the sketches on which Model A is based, and we must therefore interpret them in the context of what we now know about Leonardo’s investigations of friction (Hutchings, 2016).

Leonardo’s first definitive statement on sliding friction (in Codex Forster III f. 72r, 1493–4) pre-dates the diagrams of Figure 3 by some 7–12 years, and by the time he made the sketches on which Model A was based his understanding of friction was well developed. His earliest sketch of a friction ‘experiment’ in the Forster notebook, whether intended to represent a real arrangement or a thought experiment, appears to show a string passing over a pulley. So also do several other later diagrams, rather than the roller that is very clearly drawn in the left-hand central sketch of Figure 3 and embodied in Model A. There is no similar sketch of a string attached to a block and passing over a roller elsewhere in the notebooks, and one can only speculate as to Leonardo’s purpose in drawing the roller in this case. By changing the position of the roller on the slope, the height of the string above the horizontal plane could easily be adjusted to allow blocks with different heights to be accommodated, and this may well have been his intention; the two simpler sketches lower down the page, of blocks on planes with horizontal strings, do indeed show progressively thinner blocks, and are consistent with this interpretation. Alternatively, or possibly additionally, Leonardo may have wished to avoid the effect of friction from a pulley that would otherwise add to the tension in the string that he was trying to measure. The use of a roller on a horizontal plane would certainly have that advantage, but a roller on a sloping plane as shown in the sketch would also add a contribution to the string tension from the weight of the roller. It is not clear from the sketch whether the roller was intended to be a solid or a thin-walled cylinder; the diagonal stroke across the top-left corner of the complete circle could be construed as (inaccurately-drawn) completion of the distal end of an open tube, but the absence of any shading on the ‘inside’ of the tube, as used to show depth elsewhere in the drawing, argues away from that reading. Even if it were a tube with negligible weight, its introduction would have added considerable complexity to Leonardo’s analysis of the experimental results, and we know from his earlier sketches and statements (summarised in Hutchings, 2016) that in his previous investigations of friction he had almost certainly used the much simpler arrangement of a pulley.


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