570 CEMENTS, LIMES, AND PLASTERS. 



in which CaO, Si0 2 , A1 2 3 , Fe 2 3 represent not the equivalent weights 

 but the number of equivalents of these substances present; that is to 

 say, the quotients of the weights of the substances divided by their 

 equivalent weights.* This proportion of lime must never, on the other 

 hand, reach the relation indicated by the following formula: 



Ca 



SiO 2 +Al 2 3 -Fe 2 3 



which corresponds to the exclusive formation of aluminate of calcium. 

 It is necessary, by reason of the inevitable imperfection of the mix- 

 ture, to keep always well below this limit, beyond which there will 

 remain uncombined lime. In the use of this formula, magnesia should 

 be added to the lime and sulphuric acid to the denominator after dividing 

 its number of equivalents by 3." 



On a later page Le Chatelier states that Portland cements of good 

 quality would give a value between 3.5 and 4.0 for formula 1, and 

 between 2.5 and 2.7 for formula 2. 



The Newberrys, working on synthetic cements prepared from pure 

 raw materials, obtained results differing from those of Le Chatelier in 

 one important particular. They agreed with him that the lime and 

 silica combined in the form of the tricalcic silicate 3CaO.Si02,' but in 

 regard to the lime-alumina compound they decided that it was present 

 as the dicalcic aluminate 2CaO.Al 2 O3 instead of in the tricalcic form 

 given by Le Chatelier. These results gave, as the general formula for 

 a pure Portland, 



z(3CaO.SiO 2 ) +^(2CaO.Al 2 3 ). 



No allowance is made for magnesia, as the experimenters decided 

 that it could not give a hydraulic product if present in Portland cement; 

 while iron is neglected because of the small percentage in which it usu- 

 ally occurs. 



Richardson, working both with the microscope and with synthetic 

 preparations, has evolved a theory of much ingenuity and complexity 

 by treating the investigation as a study in solid solutions. For the 

 details of this remarkable and important work reference should be 

 made to his original papers.f In the present place only a brief sum- 

 mary of his principal conclusions can be given. 



He believes that the two principal constituents of a good Portland- 



* For a table of combining weights, see p. 11 of this volume. 

 t See list on p. 575. 



