William Hogarth's self portrait
CANVAS & STRETCHER 
Page 1 
William Hogarth's selfportrait William Hogarth was interested in balance and proportion in his pictures. This is shown very clearly in his selfportrait. Look at the original picture carefully  you will need to do the measuring activities using the sketch of the picture on page 2. All the measurements are approximate, so make your measurements to the nearest centimetre. Your sketch of the picture is approximately square, each side being 21 cm long. The edges of the paper are the edges of the picture  the letters show points on the edge of the picture (your printer won't print right to the edge but you need to measure from the edge, not where the letter is printed). 
Selfportrait 
Hogarth has painted something bright and shiny half way across his selfportrait, at the level of his feet  what is it?
Now look at the diagonals, from corner to corner of the selfportrait  what has Hogarth put approximately in the middle of the picture? 
Page 2 
Page 3 
Hogarth uses other proportions, besides halves. Measure across the sketch from A to the far edge of the palette and then on to B. 
A to far edge of palette is  cm  
edge of palette to B is  cm  
Measure down from C to Hogarth's collar and then on to D  
C to collar is  cm  
collar to D is  cm 
Do you notice anything about these two sets of measurements? 
Measure from E up to the buckle on Hogarth's shoe.  
From E to the shoe is  cm  
Measure down from F to the tip of his paint brush and then from F to the bottom corner of the canvas on the easel.  
From F to paint brush is  cm  
F to bottom of canvas is  cm  
Measure down from G to the top corner of the canvas on the easel.  
From G to top of the canvas is  cm 
Page 4 

Now look at the picture Hogarth is working on; the woman is meant to be Comedy and is holding the comic mask. The same sort of measurements can be made on this picture  your sketch of it is 8 cm square. 
Measure from A to her right eye and then on to B.  
From A to right eye is  cm  
From right eye to B is  cm  
Measure from C to the highest small curve in the background and then on to D.  
From C to curve is  cm  
From curve to D is  cm 
Even though most of the woman's figure is placed in one half of the canvas the picture looks well balanced because Hogarth has thought carefully about the proportions he is using. All the measurements you have made appear somewhere in this number sequence (the first part has been given in brackets to help you) [1, 1, 2] 3, 5, 8, 13, 21
Look at the sequence and find how it works. 
What are the next 3 numbers in it? 
21 
It is called the Fibonacci series after a medieval mathematician Leonardo Fibonacci, but long before that the Greeks used numbers in the sequence to give their statues and buildings graceful proportions. The Greeks called these numbers the Golden Section or the Golden Ratio. 
Page 5 
Extension Start with a large sheet of squared paper and draw a small square (1 cm x 1 cm) roughly in the centre of the paper (a). Draw another square of the same size above the first and joined to it (b). Now draw a square which has one side equal to and touching the lefthand side of the two little squares (c). This square will be 2 cm x 2 cm. Go on drawing bigger and bigger squares, as in the picture below, until you run out of paper. Now measure one side of each square, starting with the smallest, and write the answers in a line. Compare this pattern with the Fibonacci series on page 4. 
a  b 

e  
c  d  f 
Start again with the 1 cm square. Repeat the stages of drawing squares until you have drawn five in all. The five squares, when drawn this way, together make the shape of a rectangle. If you measure the lengths of this rectangle it should be 5 cm by 8 cm. Add to this picture a curved line starting in the first square and passing through opposite corners of each of the squares (f). You will discover that you have drawn a spiral, like those in sunflowers, shells and pinecones. Hogarth also liked curved shapes. Where can you see some in his selfportrait? 
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