1.4 Describe and explain experiments to investigate the small size of particles and their movement

I) dilution of coloured solutions
Dilution is when you add something to a mixture of a substance, meaning that the total fraction of the original substance out of the whole mixture is decreased.   This is a very long, confusing definition, but usually it will be in the context of a solution, where more solvent is being added.
For example: Say you have 3g table salt (NaCl) dissolved in 20ml of water.  As 20ml distilled water weighs 20g, the overall weight of the solution would be 23g.  This means that 3/23g was salt.  If you diluted the substance by adding 40ml distilled water, the slat would now be 3/63g of water.

There is a technique for trying to figure out the mass of substances using dilution, but it is very inaccurate. 

Suppose you dissolve 0.1g of potassium manganate in 10ml of water to get a purple solution.
You could then dilute this by 10 times by taking 1ml of the solution and mixing it with 10ml more water.  Continue doing this process until the colour is too faint to see.  Perhaps you could see the purple colour still after 5 dilutions but not 6. 
By the time of the fifth dilution, each 0.001ml drop would only contain a billionth of a gram of potassium manganate.  If you only need one 'particle' of potassium manganate per drop in order to see the colour, the 'particle' can't weigh more than a billionth of a gram.
This is not a very good answer:  The 'particle' actually weighs 0.00000000000000000000026g!  But the textbook seemed to think that this technique was important to know. 

ii) Diffusion experiments

Diffusion is the intermingling of substances by the natural movement of their particles.  Diffusion experiments can be set up to see which substances have a greater mass. 
An example of an experiment is the one above.  If a substance diffuses faster than another substance, then it weigh less.  The ammonia diffused faster that the HCl, as it got further before it met and reacted with the HCL.