hose which are the same； and the combining is essential to it； the functions of connecting and uniting being a mark of fire； while the separating is incidental。 For the expulsion of the foreign body is an incident in the compacting of the homogeneous。 In choosing the shape； then； they should have thought either of both functions or preferably of the combining function。 In addition； since hot and cold are contrary powers； it is impossible to allot any shape to the cold。 For the shape given must be the contrary of that given to the hot； but there is no contrariety between figures。 That is why they have all left the cold out； though properly either all or none should have their distinguishing figures。 Some of them； however； do attempt to explain this power； and they contradict themselves。 A body of large particles； they say； is cold because instead of penetrating through the passages it crushes。 Clearly； then； that which is hot is that which penetrates these passages； or in other words that which has fine particles。 It results that hot and cold are distinguished not by the figure but by the size of the particles。 Again； if the pyramids are unequal in size； the large ones will not be fire； and that figure will produce not combustion but its contrary。 From what has been said it is clear that the difference of the elements does not depend upon their shape。 Now their most important differences are those of property； function； and power； for every natural body has； we maintain； its own functions； properties； and powers。 Our first business； then； will be to speak of these； and that inquiry will enable us to explain the differences of each from each。
Book IV 1
WE have now to consider the terms 'heavy' and 'light'。 We must ask what the bodies so called are； how they are constituted； and what is the reason of their possessing these powers。 The consideration of these questions is a proper part of the theory of movement； since we call things heavy and light because they have the power of being moved naturally in a certain way。 The activities corresponding to these powers have not been given any name； unless it is thought that 'impetus' is such a name。 But because the inquiry into nature is concerned with movement； and these things have in themselves some spark （as it were） of movement； all inquirers avail themselves of these powers； though in all but a few cases without exact discrimination。 We must then first look at whatever others have said； and formulate the questions which require settlement in the interests of this inquiry； before we go on to state our own view of the matter。 Language recognizes （a） an absolute； （b） a relative heavy and light。 Of two heavy things； such as wood and bronze； we say that the one is relatively light； the other relatively heavy。 Our predecessors have not dealt at all with the absolute use； of the terms； but only with the relative。 I mean； they do not explain what the heavy is or what the light is； but only the relative heaviness and lightness of things possessing weight。 This can be made clearer as follows。 There are things whose constant nature it is to move away from the centre； while others move constantly towards the centre； and of these movements that which is away from the centre I call upward movement and that which is towards it I call downward movement。 （The view； urged by some； that there is no up and no down in the heaven； is absurd。 There can be； they say； no up and no down； since the universe is similar every way； and from any point on the earth's surface a man by advancing far enough will come to stand foot to foot with himself。 But the extremity of the whole； which we call 'above'； is in position above and in nature primary。 And since the universe has an extremity and a centre； it must clearly have an up and down。 Common usage is thus correct； though inadequate。 And the reason of its inadequacy is that men think that the universe is not similar every way。 They recognize only the hemisphere which is over us。 But if they went on to think of the world as formed on this pattern all round； with a centre identically related to each point on the extremity； they would have to admit that the extremity was above and the centre below。） By absolutely light； then； we mean that which moves upward or to the extremity； and by absolutely heavy that which moves downward or to the centre。 By lighter or relatively light we mean that one； of two bodies endowed with weight and equal in bulk； which is exceeded by the other in the speed of its natural downward movement。
2
Those of our predecessors who have entered upon this inquiry have for the most part spoken of light and heavy things only in the sense in which one of two things both endowed with weight is said to be the lighter。 And this treatment they consider a sufficient analysis also of the notions of absolute heaviness； to which their account does not apply。 This； however； will become clearer as we advance。 One use of the terms 'lighter' and 'heavier' is that which is set forth in writing in the Timaeus； that the body which is composed of the greater number of identical parts is relatively heavy； while that which is composed of a smaller number is relatively light。 As a larger quantity of lead or of bronze is heavier than a smaller…and this holds good of all homogeneous masses； the superior weight always depending upon a numerical superiority of equal parts…in precisely the same way； they assert； lead is heavier than wood。 For all bodies； in spite of the general opinion to the contrary； are composed of identical parts and of a single material。 But this analysis says nothing of the absolutely heavy and light。 The facts are that fire is always light and moves upward； while earth and all earthy things move downwards or towards the centre。 It cannot then be the fewness of the triangles （of which； in their view； all these bodies are composed） which disposes fire to move upward。 If it were； the greater the quantity of fire the slower it would move； owing to the increase of weight due to the increased number of triangles。 But the palpable fact； on the contrary； is that the greater the quantity； the lighter the mass is and the quicker its upward movement： and； similarly； in the reverse movement from above downward； the small mass will move quicker and the large slower。 Further； since to be lighter is to have fewer of these homogeneous parts and to be heavier is to have more； and air； water； and fire are composed of the same triangles； the only difference being in the number of such parts； which must therefore explain any distinction of relatively light and heavy between these bodies； it follows that there must be a certain quantum of air which is heavier than water。 But the facts are directly opposed to this。 The larger the quantity of air the more readily it moves upward； and any portion of air without exception will rise up out of the water。 So much for one view of the distinction between light and heavy。 To others the analysis seems insufficient； and their views on the subject； though they belong to an older generation than ours； have an air of novelty。 It is apparent that there are bodies which； when smaller in bulk than others； yet exceed them in weight。 It is therefore obviously insufficient to say that bodies of equal weight are composed of an equal number of primary parts： for that would give equality of bulk。 Those who maintain that the primary or atomic parts； of which bodies endowed with weight are composed； are planes； cannot so speak without absurdity； but those who regard them as solids are in a better position to assert that of such bodies the larger is the heavier。 But since in composite bodies the weight obviously does not correspond in this way to the bulk； the lesser bulk being often superior in weight （as； for instance； if one be wool and the other bronze）； there are some who think and say that the cause is to be found elsewhere。 The void； they say； which is imprisoned in bodies； lightens them and sometimes makes the larger body the lighter。 The reason is that there is more void。 And this would also account for the fact that a body composed of a number of solid parts equal to； or even smaller than； that of another is sometimes larger in bulk than it。 In short； generally and in every case a body is relatively light when it contains a relatively large amount of void。 This is the way they put it themselves； but their account requires an addition。 Relative lightness must depend not only on an excess of void； but also an a defect of solid： for if the ratio of solid to void exceeds a certain proportion； the relative lightness will disappear。 Thus fire； they say； is the lightest of things just for this reason that it has the most void。 But it would follow that a large mass of gold； as containing more void than a small mass of fire； is lighter than it； unless it also contains many times as much solid。 The addition is therefore necessary。 Of those who deny the existence of a void some； like Anaxagoras and Empedocles； have not tried to analyse the notions of light and heavy at all； and those who； while still denying the existence of a void； have attempted this； have failed to explain why there are bodies which are absolutely heavy and light； or in other words why some move upward and others downward。 The fact； again； that the body of greater bulk is sometimes lighter than smaller bodies is one which they have passed over in silence； and what they have said gives no obvious suggestion for reconciling their views with the observed facts。 But those who attribute the lightness of fire to its containing so much void are necessarily involved in practically the same difficulties。 For though fire be supposed to contain less solid than any other body； as well as more void； yet there will be a certain quantum of fire in which the amount of solid or plenum is in excess of the solids contained in some small quantity of earth。 They may reply that there is an excess of void also。 But the question is； how will they discriminate the absolutely heavy？ Presumably； either by its excess of solid or by its defect of void。 On the former view there could be an amount of eart