374 Mr. A. Cayley on the Analytical Forms called Trees. 



intermediate in composition between ordinary carbonates and 

 ortho- or dicarbonates, precisely as the pyrophosphates are in- 

 termediate between metaphosphates and normal phosphates. 

 Thus Fritzsche has described a carbonate of magnesium having 

 the formula Mg*"' C^ 0' . SH^O. According to Mulder and 

 Hochstetter, white lead has the formula Pb^ C^ 0^ . H^ 0. Moun- 

 tain blue, a crystalline mineral, has the formula Cu^ C^ 0' . H^ 0, 

 and carbonate of bismuth the formula Bi'"'^ C^ 0'. IP 0. These 

 last three compounds may also be represented as orthocarbon- 

 ates, with the respective formulEe Pb^ HCO*, Cu^ HCO'', and 

 Bi'" HCO'*. 



The following Table illustrates the relations of the meta- and 

 ortho-salts above spoken of, to one another and to other similar 

 salts. 



Hence it appears that a certain relation which exists between 

 the terbasic and monobasic groups, is paralleled by a similar 

 relation between the tetrabasic and bibasic groups. In phos- 

 phates and silicates, the dominant tendency is to form ortho- 

 salts with four atoms of oxygen ; in nitrates and carbonates the 

 dominant tendency is to form metasalts with three atoms of 

 oxygen ; but each class manifests both tendencies. Metaphos- 

 phates and metasilicates on the one hand approximate to an- 

 hydro-salts, while orthonitrates and orthocarbonateson the other 

 hand resemble super-basic salts. It is observable that both 

 metaphosphates and nitrates, metasilicates and carbonates, differ 

 from normal ter-oxysalts such as chlorates, sulphites, and phos- 

 phites, in their absolute inoxidizability. 



LVIII. On the Analytical Fo?-ms called Trees. — Part II. 

 By A. Cayley, Esq. 



[Continued from vol. xiii. p. 176.] 



THE following class of " trees " presented itself to me in 

 some researches relating to functional symbols ; viz., attend- 

 ing only to the terminal knots, the trees with one knot, two 



