Page:Encyclopædia Britannica, Ninth Edition, v. 6.djvu/343

Rh where o&amp;gt; is the interval of time reckoned backwards from the actual time t to the time t - w, when the strain 6 t -ui existed, and i/^w) is some function of that interval. We may describe this method of deducing the actual state from the previous states as the historical method, be cause it involves a knowledge of the previous history of the body. But this method may be transformed into another, in which the present state is not regarded as in fluenced by any state which has ceased to exist. For if we expand Ot-u by Taylor s theorem,

d& o* cFO 0,_ w = &__+_ -j-j-Ac.,

and if we also write

/&quot; /. r x ia A=/ lMW B = / &amp;lt;aiL((a)dta, C = / ,715 $(&amp;lt;i&amp;gt;)dw , &C. , - o &amp;gt;/ o - o - 1 ^

then equation (1) becomes

where no symbols of time are subscribed, because all the quantities refer to the present time. This expression of Boltzinann s, however, is not in any sense a physical theory of the phenomena ; it is merely a mathematical formula which, though it represents some of the observed phenomena, fails to express the phenomenon of permanent deformation. Now we know that several substances, such as gutta-percha, India-rubber, &amp;lt;ic., may be permanently stretched when cold, and yet when afterwards heated to a certain temperature they recover their original form. Gelatine also may be dried when in a state of strain, and may recover its form by absorbing water. We know that the molecules of all bodies are in motion. In gases and liquids the motion is such that there is not hing to prevent any molecule from passing from any part of the mass to any other part ; but in solids we must suppose that some, at least, of the molecules merely oscillate about a certain mean position, so that, if we consider a certain group of molecules, its configuration is never very different from a certain stable configuration, about which it oscillates. This will be the case even when the solid is in a state of strain, provided the amplitude of the oscillations does not exceed a certain limit, but if it exceeds this limit the group does not tend to return to its former configuration, but begins to oscillate about a new configuration of stability, the strain in which is either zero, or at least less than in the original configuration. The condition of this breaking up of a configuration must depend partly on the amplitude of the oscillations, and partly on the amount of strain in the original configuration ; and we may suppose that different groups of molecules, even in a homogeneous solid, are not in similar circumstances in this respect. Thus we may suppose that in a certain number of groups the ordinary agitation of the molecules is liable to accumulate so much that every now and then the con figuration of one of the groups breaks up, and this whether it is in a state of strain or not. We may in this case assume that in every second a certain proportion of these groups break up, and assume configurations corresponding to a strain uniform in all directions. If all the groups were of this kind, the medium would be a viscous fluid. But we may suppose that there are other groups, the configuration of which is so stable that they will not break up under the ordinary agitation of the molecules unless the average strain excaeds a certain limit, and this limit may be different for different systems of these groups. Now if such groups of greater stability are disseminated through the substance in such abundance as to build up a solid framework, the substance will be a solid, which will not be permanently deformed except by a stress greater than a certain given stress. But if the solid also contains groups of smaller stability and also groups of the first kind which break up of them selves, then when a strain is applied the resistance to it will gradually diminish as the groups of the first kind break up, and this will go on till the stress is reduced to that due to the more permanent groups. If the body is now left to itself, it will not at once return to its original form, but will only do so when the groups of the first kind have broken up so often as to get back to their original state of strain. This view of the constitution o^&quot; a solid, as consisting of groups of molecules some of which are in different circum stances from others, also helps to explain the state of the solid after a permanent deformation has been given to it. In this case some of the less stable groups have broken up and assumed new configurations, but it is quite possible that others, more stable, may still retain their original configurations, so that the form of the body is determined by the equilibrium between these two sets of groups ; but if, on account of rise of temperature, increase of moisture, violent vibration, or any other cause, the breaking up of the less stable groups is facilitated, the more stable groups may again assert their swav, and tend to restore the body to the shape it had before its deformation.  CONSUEGRA, a town of Spain, on the Amarguilla, in the province of Toledo, and 36 miles south-east of the city of that name. It contains about 7000 inhabitants, princi- pally engaged in the manufacture of coarse woollens. Roman inscriptions and other remains bear witness to the antiquity of the town, which was formerly known as Consabrum ; and on a neighbouring hill are the ruins of its ancient castle.  CONSUL (ucraroc), the highest magistrate of the republic of ancient Rome. It is probable that the word is compounded of con and salio, so that consules signifies those who go together. They were in early times called prwtores, imperatores, ovjudices. From the abuse of the power which had been vested in the kings, the Romans were induced not only to expel the hated Tarquins from the city, but even to abolish the monarchical form of government altogether. Brutus and his companions, after the rape of Lucretia, made the people swear that no king should ever again reign at Rome. The ttate was henceforth ruled by two supreme magistrates called consuls. The consular office was instituted after the expulsion of the kings, 510 b.c., and continued, with few interruptions, till the establishment of the empire a period of nearly 500 years. The leaders of the revolution which had expelled the kings were first raised to this rank. All the royal insignia were preserved except the crown. Twelve lictors preceded them alternately. The elder of the two, or he who had most children, or who had been first elected, Lad the fasces fir^t, the other meanwhile being preceded by a public officer called accensus, and followed by the lictors. Sometimes they agreed to enjoy ibe fasces on alternate days, but generally for alternate months. By the law of Poplicola, the axe was taken from them and their fasces were lowered when they entered the assemblies of the people. A cloak with a scarlet border, and an ivory staff, were badges of their office. On public occasions they used a seat of ornamented ivory called the curule chair. From the great power which their order originally possessed in the state, the patricians succeeded for a long time in retaining the consulship among themselves. It was not till the year 445 B.C. that the plebeians acquired sufficient courage and strength to make any attempts to acquire the right of being elected to this office. Having once begun the struggle, however, they maintained it for 