324« Prof. Johnston on the received 



of new corners. But the additional polygon is one new face ; 

 therefore the addition of each new polygon increases the faces 

 and corners together as much as the edges ; consequently the 

 initial relation, namely, 



No. of faces + No. of corners = No. of edges + 1 

 remains undisturbed. 



The preceding is equally true if the faces be not all in one 

 plane, and consequently it is true of any portion of a solid 

 figure which is not the whole. It is true then of a solid figure 

 from which one face is omitted, the edges of that face answer- 

 ing to the exterior contour in the preceding theorem. Con- 

 sequently, including the face just omitted, and thus com- 

 pleting the solid, we have 



No. of faces + No. of corners = No. of edges + 2. 



LI. On the received Equivalents of Potash, Soda, and Silver, 

 By James F. W.Johnston, AM., F.RS. L.Si'E., Professor 

 of Chemistry, University of Durham.* 



TN the progress of the sciences of observation it is interesting 

 -*- to remark how the establishment of every new principle is 

 opposed by certain apparent exceptions or anomalies, yet 

 how these anomalies all ultimately disappear, and how the 

 removal of each is necessarily preceded either by some cor- 

 rection of received opinions, or by fresh additions to our ac- 

 tual knowledge. 



The researches of Dulong and Petit into the specific heats 

 of the metals rendered it extremely probable that the atoms 

 or equivalents of these elementary bodies had the same spe- 

 cific heat. This relation was found to hold with remarkable 

 exactness in the case of a considerable number of metals ; but 

 to bring silver, gold, and mercury into conformity with the 

 law, it was found necessary to reduce by one half the atomic 

 weights of these metals as generally received among chemists. 

 The result of these beautiful researches therefore, though 

 they pointed to and rendered probable the existence of a very 

 simple relation among the specific heats of the metals as a law 

 of nature, yet being opposed by so many apparent exceptions, 

 have not been generally received with that confidence to which 

 they may ultimately prove to be entitled. Chemists have been 

 unwilling to alter the received atomic weights of so many 

 metals for the sole purpose of bringing them into conformity 

 with a relation still considered hypothetical. 



• Communicated by the Author. 



