Intelligence and Miscellaneous Articles, 545 



presslbility of the unit of volume have hitherto been but Httle 

 studied. It is true, however, that Wertheim has demonstrated, or 

 at least has shown it to be very probable, that for horaog-eneous 

 bodies the coefficients of cubic extension or compression are the 

 same as those of linear extension or compression. He has, moreover, 

 shown that this opinion was confirmed by M. Regnault's experiments 

 on the compressibility of copper, of brass, and of glass. 



Probability is also in favour of the accuracy of Wertheim's law. 

 For if the two coefficients of extensibility, Hnear and cubic, were not 

 the same, this ought also to be the case with the two coefficients of 

 elasticity ; and it would follow that the velocity of propagation of 

 sound is not the same in a rod and a ball, both of the same substance 

 and perfectly homogeneous in all directions. 



It being, then, admitted that the two coefficients of extensibiHty 

 are equal, the coefficient of cubic extensibility of iron, for example, 

 referred to the miUimetre as unit of length, is a =0*0000481. That is 

 to say, a cube of iron of 1 cub. centim., drawn normal to its six faces 

 by a force of extension of 1 kilom. per square millimetre, has its 

 volume increased 0'0000481 cubic centimetre. 



The coefficient of cubic dilatation of iron between 0°and 100" is, 

 for 1° C, /3 = 00000350. x\ cubic centim. of iron passing from 0° 

 to 1° increases therefore 0'0000350 centim. Consequently, to pro- 

 duce the same augmentation of volume as a tension equal to 100 

 kilogrs. distributed to the six faces, an increase of temperature 



_ =1°'374 would be required. 



The mechanical work produced by the heat in this rise of tem- 

 perature (l°-374) of the cube of iron corresponds to the effect neces- 

 sary to raise 100 kil. 0"000081 gramme-centimetre. Indeed, 

 since each of the three faces of the cube advances during the traction 

 — g — centim., this is equivalent, for the augmentation of volume, 

 to only one of the three faces advancing 0*000048 1 centimetre. 



The expression of the quantity of heat which a cubic centim. of iron 

 niust absorb to be able to produce this work is obtained by multiplying 

 its weight in grammes B=7'757 by its specific heat s=0" 1.098 and by 



_ = 1*374. We then take for unit the quantity of heat necessary 



to raise one gramme of water from 0° to 1°. 



The quantity thus obtained, 2s — =1*170, is the amount of heat 



necessary in order to give to a mass of iron of 1 cub. centim. a force 

 producing the same expansion as a traction-force of 100 kilogrammes. 

 Only a very small quantity of this heat is used for the dilatation 

 itself, or for the production of the work above estimated, and 

 becomes latent. 



If we take in round numbers 42000 grammes as the mechanical 

 effect of the unit of heat adopted, we shall have as the work of 1 • 1 7 unit 

 of heat 49140 gramme-centimetres. The effective work of the heat 

 in the dilating cube of iron is equal, as we have seen, to 4*8 1 gr.-c. 



Phil. Mag. S. 4. No. 296. SuppL Vol 44. 2 N 



