837 



INCREMENT. 



INDEPENDENTS. 



S3S 



with no scale, therefore are disagreeable to the ear, and never used in 

 any kind of composition. 



INCREMENT and DECREMENT. When two quantities are con- 

 sidered together, one of which is greater or less than the second, the 

 latter is said to be the former with an increment or decrement. In 

 the older English writings the calculus of differences is called the 

 method of increments. This phraseology refers to the supposition of 

 magnitudes being generated by continued increase or decrease as in 

 the method of fluxions, so that two different magnitudes are spoken of 

 aa the same thing in different states, and of course at different times. 

 Some difficulty to the beginner may be occasionally avoided by his 

 stopping to interpret " let x become x + h " as follows : " let us, having 

 considered the value of a function of x, proceed to consider the 

 alteration which will arise if x + k be written instead of x." 



INCUBATION, ARTIFICIAL. [POULTRY.] 



INCUMBENT. [BENEFICE.] 



INDEFINITE means " not given or defined in magnitude." Thus, 

 a definite straight line is that of which the extremities are known ; an 

 iudefinite straight line (in length) is one of which the direction is 

 given, and which may be supposed to have any length, or which can be 

 lengthened if necessary, without contravening any of the conditions of 

 the problem. Thus, Euclid, in the first book, constructs an equilateral 

 triangle upon a definite straight line, and shows how to draw two lines 

 making with one another the same angle as that made by two given 

 indefinite straight lines. 



There is, however, a reprehensible use of the word indefinite, which 

 is found hi many mathematical works ; namely, the employment of it 

 to avoid the odium which attaches to the word infinite. Thus we hear 

 of making a magnitude indefinitely great, of an indefinitely small arc 

 being equal to its chord, of the circle being a polygon of an indefinitely 

 great number of sides. In all these cases it would be better, with a 

 proper definition, to use the word infinite at once. 



A want of proper distinction between definite and indefinite some- 

 times leads to confusion. For instance, it is said that if a straight line 

 be halved, if its half be then halved, and if fresh portions be continually 

 taken, each of which is the half of the preceding, the result will at last 

 become less than " any line which can be named." Thia is not true if 

 the line which is to be named be indefinite ; that is, if we may at any 

 part of the process make it as small as we please ; for it is obvious that 

 whatever a line may be, a smaller line can be named. But it is true of 

 a definite line, made definite, or given in length, at the beginning of 

 the process : name any line, however small, but such as you name let 

 it remain ; then, by continually halving any other line, however great, 

 you must at last arrive at a line which is less than the length you 

 named. The phraseology of a line " less than any line which can bo 

 named " has often caused a difficulty by not specifying the time at 

 which it is to be named. The language used by Euclid himself is as 

 follows (book x., prop. 1), and is free from the ambiguity in question : 

 " Two unequal magnitudes being given, if from the greater be taken 

 away its half, and from what is left its half, and if this be done con- 

 tinually, a magnitude will at last be found which is less than the lesser 

 of the two given magnitudes." 



INDELIBROME. [INDIGO.] 



INDENTURE. [Dem] 



INDEPENDENTS, or CONGREGATIONALISTS, the name of a 

 sect, class, or denomination of English Protestant Dissenters, one of 

 the three who united form the Three Denominations, the other two 

 being the Presbyterians and the Baptists. 



When the principle of resistance to the power which maintained at 

 least an outward and specious 4miformity of Christian practice and 

 opinion had received encouragement and was successful, it was not to 

 be expected that nations who recognised that principle would agree 

 among themselves respecting what should be done in their new con- 

 dition of religious freedom. In England the politicians of the time soon 

 succeeded in establishing a national church with pastors and bishops, 

 and the church has been maintained in that form and order from the 

 time of the Reformation, with the slight exception of the period of the 

 Commonwealth. But there were many people in England who ob- 

 jected to several things which made a part of the constitution of that 

 church ; and as their objections consisted very much in the desire of 

 what they considered a greater degree of purity in its forms, they were 

 called in derision Puritans and Precisians, in which allusion was also 

 included to the greater strictness with which they observed their 

 religious duties, and their supposed peculiar preciseness in respect at 

 onoe to an exactness of conformity to scripture precedent and to the 

 obligations of a severe morality. 



These persons were not all of one mind within themselves. Many 

 uniting with these distinguishing characteristics the principle that, 

 there being no scriptural authority for the Episcopal order, the govern- 

 ment of the church or the superintendence of its ministers ought to be 

 verted not in an individual, but in synods and presbyteries; these 

 formed the Presbyterians. There were others who would have no 

 union or government of the church, who regarded each congregation of 

 faithful men as being in itself a church, and when properly constituted 

 with deacons and a pastor forming a body which was independent of 

 every other, and competent to its own direction and government with- 

 out any interference from presbyteries, bishops, or from the state 

 itself ; this is the pure principle of English Independency. 



Robert Brown, a clergyman of the reign of Elizabeth, is generally 

 reputed to be the first person in England who publicly avowed this 

 opinion, and acted upon it by the establishment of various such separate 

 churches, which however had no enduring existence. There is some 

 question whether he retained his opinions to the last : but it is certain 

 that after he had given no small trouble to the authorities in the 

 church, he was presented to the living of Achurch in Northampton- 

 shire. He closed a long and very troxibled life in the jail at Northamp- 

 ton, or very soon after he had left it, in 1630. [BHOWN, ROBERT, in 



Bioo. Div 



ery 

 iv.] 



Puritans, 



by the laws then in force for maintaining the Church of England as 

 then established. But when Episcopacy was abolished and Monarchy 

 had been overcome, there was a large party of these Independents 

 which suddenly presented itself, who had a great share in the struggle 

 then being made, and who were the means of preventing the 

 establishment of a Presbyterian church in England, which it was the 

 object of by far the larger portion of the Puritan body taking part in 

 the contest to form. Cromwell belonged to the Independents. Dr. 

 John Owen, dean of Christ Church, who was also for a time vice- 

 chancellor of the University of Oxford, is considered as the chief 

 ornament of this denomination at the time (the Commonwealth) when 

 it first became considerable. [OwEN, DR. JOHN, in Bioo. Div.] 



What the issue might have been of the struggle between the prin- 

 ciple of Independency and the principle of Presbyterianism cannot now 

 be told, the king being soon restored, and with him the Episcopal 

 church. In 1662 the Act of Uniformity was passed, the object of 

 it being to exclude from the ministerial office in the Church of 

 England divines of either of those opinions. The act required a 

 direct acknowledgment of the principle of Episcopacy. The effect of 

 it was, that about 1900 ministers retired from the places they held in 

 the church. Some make them 2000. These are the ministers whom 

 Dissenters mean when they speak of " the illustrious two thousand," 

 " the ejected ministers," or " the Bartholomew worthies." During the 

 reign of Charles II. every effort was made to prevent these persons 

 continuing to exercise their ministry. But it was all in vain. They, or 

 at least the greater part of them, persisted in preaching, notwithstanding 

 the certain penalties of imprisonment and fine. However, the Revolu- 

 tion of 1688 freed them from these penalties ; one of the first acts of 

 the new government being to grant toleration to them, that is, to allow 

 them to open meeting-houses, or chapels, and to conduct the services 

 under the protection of the law. 



The Independents were inconsiderable r at that time as compared 

 with the Presbyterians. Both however (and the Baptists also) built 

 chapels for themselves and formed themselves into congregations, 

 called the Presbyterian congregations and the Independent congrega- 

 tions ; and each denomination had its own board or fund. 



The ' Act of Toleration ' was passed in 1689, and for the seventy 

 years succeeding that date the Independent denomination dwindled (as 

 indeed did the whole body of Dissenters), and it was in a very low con- 

 dition when the state of things arose which we have now to describe. 



About the middle of the 18th century there was an extraordinary 

 revival of religious zeal under the influence created especially by the 

 Wesleys and Whitefield. The Dissenters, like the Church, had adopted 

 pretty generally the principle that to inculcate the moral duties, to 

 present the paternal government of God as a source of consolation and of 

 hope, to hold out the prospect of future accountableness and of eternal 

 life, to show the evidence on which we receive Jesus Christ as the minis- 

 ter and messenger of his heavenly Father, were the principal subjects 

 on which it was the duty of Christian ministers to insist. This it was 

 easy to represent as an abandonment of the distinctive truths, as they 

 are sometimes regarded, of Christianity ; and many persons, under the 

 preaching above alluded to, were disposed so to regard it, and to seek 

 a ministry by whom these distinctive truths would be made more 

 prominent. Most of these persons joined themselves to the Wesleyan 

 Methodists, or to the Whitefieldian Methodists (since better known as 

 the Countess of Huntingdon's Connexion) ; but there were many who 

 declined to unite themselves with any of these bodies, and formed 

 themselves into separate churches upon the Independent principle. 

 These new societies incorporating with themselves the small remains 

 of the old Independents of England, who, in some instances had, 

 throughout the period by some called the period of Religious In- 

 difference, adhered to the original opinions of the Puritan body at 

 large, which were Calvinistic, and had continued to make those opinions 

 prominent in the public services, or joining themselves to such 

 decayed and decaying churches, gradually increased in numbers and 

 influence, and constitute at the present day the large body of Dis- 

 senters called Independents or Congregationalists. 



From the accession of George I., in 1714, when the London dissent- 

 ing ministers of the three denominations (Presbyterian, Independent, 

 and Baptist) presented an address to the king [WILLIAMS, DANIEL, 

 D.D., in Bioo. Div.], the three bodies have been accustomed to act 

 together, by their appointed deputies, in reference to great public 

 questions. Most of the old Presbyterian denomination in England 

 having in the course of time adopted Unitarian sentiments, their repre- 

 sentatives at length withdrew from the board. The distinctive 

 appellation of " The Three Denominations " is however still kept up, the 



