COM 



Ctmmon to, the unit, or which do not differ from one another 

 Measures, D y m0 re than this unit, or by some fraction of it ; and 

 ^■""■"Y""""' hence the great advantage of a series of large numbers, 

 like €12 in the VIII. But multiplication can only cor- 

 rectly be performed on these artificial commas in some 

 cases, and division in still fewer cases, and only where 

 there are no remainders after such divisions ; and, ge- 

 nerally, where fractions of intervals arise, as in all tem- 

 pered systems must be the case, they cannot be relied 

 on, or used, except as a rough check on more correct 

 and difficult calculations ; but in all such cases, either 

 the tlnee columns, as 2, f, and m, or logarithms of 

 some sort, (as the decimals of any one interval always 

 are,) to a sufficient number of places, must be used in 

 all calculations relating to temperaments, or other frac- 

 tional intervals. See Aridoxenian Common Measures. 



(?) 



COMMON Measures, Aristoxenian.m music. These 

 were, as Dr Holder expresses it, {Treatise, 1st edit. 

 p. 149,) ". Irrational contrivances for expressing the se- 

 veral intervals." Aristoxenus, and many others among 

 the ancients, having vainly imagined, that by dividing 

 all the principal degrees of the scale, or consonances, 

 into all their aliquot parts, that some one, in each of 

 all these sets of parts, would be found exactly equal to 

 each other ; and this small interval, to be found in the 

 nliquot part3 of every other one, was the least common 

 measure of all the intervals, which they laboured in- 

 cessantly to find. Had the ancients been able as quick- 



33 



COM 



ly and accurately to extract the 12th, 30th, 72d, &c. 

 roots of numbers, as we now can, and even of still 

 higher numbers, almost without limit, by the help of 

 a Table of Logarithms, as we have shewn, as to the 

 104th, 197th, 358th, and 612th parts of the T, III, V, 

 and VIII respectively, in our article Common Mea- 

 sures above, this delusion must quickly have vanished; 

 and it would have appeared, as we have shewn in the 

 article above referred to, that an artificial comma has a 

 different value in every different interval to which it is . 

 applied. But owing to the tedious and difficult labour 

 of extracting the roots of the terms of musical ration 

 by arithmetical operations, and the impossibility almost 

 of avoiding errors therein, it was not difficult for those 

 engaged in these calculations, to persuade themselves 

 and their followers, that they had made out certain of 

 their roots, thus obtained, to agree exactly. And thus 

 it should seem, that the 1 2th part of the major tone, the 

 30th part of the diatessaron, or fourth, and the 72d part 

 of the octave, Avere known by the common name of the 

 Arisloxenian common measure, and were supposed by 

 many to be equal, and adapted accurately to measure 

 these and all other intervals ; and though others showed 

 the absurdity and impossibility of this abstractedly, or 

 in some particular cases, yet the doctrine could not be 

 exploded entirely, until after the invention of logarithms, . 

 when it quickly vanished, like a mist before the sun. 

 We shall, however, subjoin the most useful particulars 

 of these measures, viz,. 



7 ' 5 th of the 4th = 

 ^d of the VHIth = 

 T \th of the T = 



Which Table may prove of considerable use to those 

 who wish to examine the ancient musical writings, and 

 see the extent of the errors into which such authors may 

 have been led, by assuming the three intervals above to 

 be one and the same. The last of the above intervals has 

 been called theduodecimalof 'atone, and supposed to equal 

 the first of them ; from which it differs nearly 1 in the 

 fourth place of com. logs, or not much more than .f 2: 

 the middle one appears -to be less than an arithmetical 

 mean between the other two. (?) 



COMMON Law, is that branch or department of the 

 municipal law of any state which is opposed to the edic- 

 tal, legislative, or other written constitutions. It con- 

 sists of those maxims, customs, and established usages, 

 which, originating in the peculiar genius, local situation, 

 military institutions, or other circumstances of a peo- 

 ple, take root and gradually spring up in every country. 

 . Hence the different parts of it are not of equal antiquity, 

 but have been successively recognised, as the maxim, 

 custom, or usage was found to be consonant to the pub- 

 lic sentiment, and had received a general adoption. 

 What, therefore, formed no part of the common law of 

 a country at one period of its history, came afterwards 

 to be acknowledged as an important feature of it ; and 

 thus passing from one acquisition to another, as the 

 changes in society produced correspondent changes in 

 the public sentiments and manners, the common law of 

 most countries has insensibly accumulated into an ex- 

 tensive system. The gradual departure, however, from 

 ancient manners, has, in some instances, undermined 

 this department of Jaw ; Avhile in others it has been 

 directly overtlu-own by positive enactment. A history, 

 therefore, of the common law of any country, must fur- 



\01,. VII. part I, 



2 m 



2 



Com. Logs. 



VIII. Logs; 



C.'Logs. 



489514+ 1 



8.497376 



.9958353,7545 



.0-1 38346 



.771937 



.522869 -f 1 



8.530731 



-9958190,2784 



.0138889 



.774967 



.689645 + 1 



8.697507 



' -9957372,8980 



.0141603 



.790117 



nish information of no ordinary interest and importances 

 since it is nothing else than a developement of the 

 changes which take place on the sense of justice and 

 morality among any particular people, in consequence 

 of the changes which have taken place on their condi- 

 tion. 



It is opposed to the lex serif la, or written law of' a 

 country, not because it cannot absolutely be said to be 

 unwritten itself, but because, unlike the edicts ol em- 

 perors, or the legislative enactments of free states, it is 

 not originally promulgated in a written form. It gra- 

 dually comes, however, to be firmly embodied in the 

 same form ; and the recorded decisions of the supreme 

 courts are the authentic and mighty volumes in which 

 it is chiefly to be read. A labour so impracticable, in- 

 deed, no understanding, however undaunted or absurd, 

 could be expected to undertake ; so that in most states 

 where the study of the law is not obstructed from views 

 of oppression, recourse has been had at an early period, 

 and afterwards successively continued, to " reported 

 cases," or abridgments of the most important decision-;. 

 These, when disputed, are of course authenticated by 

 reference to the records themselves. 



We have said, that the common law is chiefly to be 

 found in the records of the supreme courts ; for there 

 are other repositories of it, though greatly inferior in 

 extent, and also to a certain degree, in authority. These 

 are the ancient sages of the law, whose writings either 

 precede the time at which the decisions of the courts 

 began to be regularly recorded and preserved ; or which 

 supply the deficiences of the records ; or, by the wis- 

 dom and analogy of the observations they contain, have 

 acquired an authoritative respect bordering on venera- 



