Sketch of The Analytical Engine
Augusta Ada, Countess of Lovelace 鐃熟ワ申鐃緒申鐃緒申鐃夙リア朝鐃緒申鐃緒申留儿鐃塾緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃叔緒申離廛鐃緒申鐃緒申鐃殉でわ申鐃緒申塙佑鐃緒申鐃緒申討鐃緒申泙鐃緒申鐃緒申鐃緒申鐃淑醐申鐃緒申 L. F. Menabrea 鐃夙わ申鐃緒申鐃緒申鐃緒申鐃所ア鐃緒申鐃緒申鐃緒申 (鐃緒申離鐃緒申鐃緒申螢�鐃緒申鐃緒申) 鐃緒申 Charles Babbage 鐃緒申鐃粛案わ申鐃緒申鐃緒申鐃熟居申鐃舜わ申匆陲垢襪随申鐃祝書いわ申鐃緒申文鐃緒申 Ada 鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申里任鐃緒申鐃�Ada 鐃緒申鐃緒申鐃緒申鐃祝わ申鐃緒申鐃所、A 鐃緒申 G 鐃塾ワ申鐃緒申鐃夙ルが鐃春わ申譴随申痢鐃緒申箸鐃緒申鐃緒申箸鐃緒申鐃緒申媛辰鐃緒申泙鐃緒申鐃緒申鐃�Note G 鐃祝は駕申鐃熟居申鐃舜わ申鐃緒申僂鐃緒申謄戰鐃縮￥申鐃緒申鐃緒申鐃緒申彁鐃緒申鐃緒申鐃緒申鐃祝￥申鐃緒申颪�わ申討鐃緒申泙鐃緒申鐃�
Ada 鐃塾計誌申鐃緒申鐃淑学への貢醐申鐃祝つわ申鐃銃わ申鐃粛￥申鐃淑居申鐃緒申鐃緒申鐃緒申鐃緒申泙鐃緒申鐃�Brian Randall 鐃緒申 "The Origin of Digital Computer" 鐃緒申鐃緒申如鐃緒申戰鐃縮￥申鐃緒申鐃緒申鐃竣誌申鐃竣ワ申鐃緒申鐃緒申鐃熟￥申鐃叔緒申 Babbage 鐃緒申 Ada 鐃塾駈申鐃熟にわ申鐃書き駕申鐃緒申鐃緒申鐃緒申鐃夙種申張鐃緒申鐃銃わ申鐃殉わ申鐃緒申Note G 鐃緒申 Ada 鐃緒申 Babbage 鐃塾間でなわ申匹鐃緒申鐃緒申蠅居申鐃殉わ申鐃緒申鐃緒申Babbage 鐃緒申鐃緒申鐃楯￥申鐃夙わ申鐃銃わ申鐃緒申鐃塾は間違い鐃淑わ申鐃塾でわ申鐃緒申鐃緒申鐃熟緒申 Ada 鐃緒申導鐃叔種申筆鐃緒申鐃淑わ申鐃曙た鐃処う鐃叔わ申鐃緒申Ada 鐃緒申 Babbage 鐃緒申鐃緒申命的鐃淑ミワ申鐃緒申鐃重�鐃緒申鐃銃わ申鐃殉わ申 (Joan Baum鐃緒申Calculating Passion of Ada Byron)
Ada 鐃緒申鐃緒申鐃緒申鐃緒申 Note 鐃緒申 1843 年 9鐃庶、Richard Taylor 鐃緒申発鐃峻わ申鐃緒申 Scientific Memoirs 鐃祝掲載わ申鐃緒申泙鐃緒申鐃緒申鐃�Ada 鐃塾器申望鐃祝わ申鐃緒申鐃緒申鐃緒申圓鐃銃震常申鐃緒申鐃緒申鐃� A.A.L 鐃夙わ申鐃緒申鐃書かわ申泙鐃緒申鐃緒申鐃�
鐃緒申鐃緒申鐃叔わ申 Ada 鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申文鐃緒申鐃緒申鐃緒申鐃緒申悩椶鐃緒申泙鐃緒申鐃緒申鐃緒申箸覆辰討鐃� Note 鐃緒申鐃緒申戮洞鐃縮ｏ申鐃緒申鐃緒申鐃緒申鐃銃ではなわ申鐃塾でわ申鐃緒申鐃緒申鐃淑わ申鐃潤く鐃緒申鐃緒申鐃塾な計誌申鐃緒申鐃緒申必鐃竣とわ申鐃曙た鐃塾わ申鐃夙わ申鐃獣わ申鐃緒申鐃緒申鐃舜景わ申鐃塾わ申砲鐃緒申匹鐃緒申匹鐃淑�鐃緒申鐃夙思わ申鐃殉わ申鐃緒申鐃殉わ申鐃緒申文鐃祝わ申 Ada 鐃緒申鐃緒申鐃緒申鐃緒申鐃縦わ申鐃銃わ申鐃緒申里任鐃緒申鐃緒申泙鐃銃わ申鐃殉わ申鐃藷。誌申鐃瞬わ申鐃緒申鐃緒申鐃緒申媛辰鐃緒申鐃緒申鐃緒申隼廚鐃緒申泙鐃緒申鐃�
Invented by Charles Babbage
By L. F. MENABREA of Turin, Officer of the Military Engineers
from the Bibliotheque Universelle de Geneve, October, 1842, No. 82
With notes upon the Memoir by the Translator ADA AUGUSTA, COUNTESS OF LOVELACE
Those labours which belong to the various branches of the mathematical sciences, although on first consideration they seem to be the exclusive province of intellect, may, nevertheless, be divided into two distinct sections;one of which may be called the mechanical, because it is subjected to precise and invariable laws, that are capable of being expressed by means of the operations of matter;while the other, demanding the intervention of reasoning, belongs more specially to the domain of the understanding. This admitted, we may propose to execute, by means of machinery, the mechanical branch of these labours, reserving for pure intellect that which depends on the reasoning faculties. Thus the rigid exactness of those laws which regulate numerical calculations must frequently have suggested the employment of material instruments, either for executing the whole of such calculations or for abridging them;and thence have arisen several inventions having this object in view, but which have in general but partially attained it. For instance, the much-admired machine of Pascal is now simply an object of curiosity, which, whilst it displays the powerful intellect of its inventor, is yet of little utility in itself. Its powers extended no further than the execution of the first four operations of arithmetic, and indeed were in reality confined to that of the first two, since multiplication and division were the result of a series of additions and subtractions. The chief drawback hitherto on most of such machines is, that they require the continual intervention of a human agent to regulate their movements, and thence arises a source of errors;so that, if their use has not become general for large numerical calculations, it is because they have not in fact resolved the double problem which the question presents, that of correctness in the results, united with economy of time.
鐃緒申鐃舜わ申鐃粛￥申鐃緒申分鐃緒申鐃渋逸申鐃緒申鐃緒申箸蓮鐃緒申鐃緒申譴常申譴�鐃緒申鐃緒申鐃緒申鐃緒申的鐃緒申鐃塾種申鐃緒申鐃獣駕申鐃緒申鐃緒申鐃緒申里任鐃緒申襦ｏ申鐃緒申鐃叔わ申鐃順き鐃緒申鐃緒申弔鐃淑�鐃緒申鐃暑こ鐃夙わ申鐃叔わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃旬は居申鐃緒申的鐃淑削申箸砲鐃緒申鐃塾で￥申鐃緒申鐃緒申鐃緒申鐃夙逸申鐃緒申鐃祝‖э申忙鐃緒申曚鐃緒申鐃緒申分鐃庶。鐃瞬計誌申鐃竣に関わ申鐃暑こ鐃夙と醐申鐃緒申鐃緒申鐃夙わ申任鐃緒申襦ｏ申發�鐃緒申弔蓮鐃緒申鐃緒申鐃緒申鐃緒申弋瓩刻申鐃淑�鐃庶。鐃緒申鐃緒申鐃緒申的鐃祝醐申鐃緒申鐃夙「考わ申鐃緒申廚箸鐃緒申鐃緒申琉鐃緒申属鐃緒申鐃緒申分鐃緒申任鐃緒申襦ｏ申罅刻申蓮鐃緒申鐃緒申鐃重�鐃淑削申箸狼鐃緒申鐃重�鐃淑種申鐃淑にわ申辰匿鐃峻わ申鐃緒申鐃緒申鐃緒申鐃緒申能鐃熟に逸申存鐃緒申鐃暑、鐃緒申鐃淑思考わ申鐃緒申鐃熟わ申鐃駿わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃粛計誌申鐃緒申鐃所す鐃緒申法則鐃塾醐申密鐃緒申鐃緒申鐃緒申鐃緒申鐃熟￥申鐃竣誌申鐃緒申鐃緒申鐃銃もし鐃緒申鐃熟逸申鐃緒申鐃緒申鐃峻わ申鐃暑た鐃緒申法鐃緒申鐃緒申蕕�鐃緒申道鐃緒申鐃夙わ申鐃緒申鐃夙を、人￥申鐃緒申鐃駿￥申鐃竣わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃祝違い鐃淑わ申鐃緒申鐃緒申鐃緒申鐃銃￥申鐃緒申鐃緒申鐃緒申鐃初い鐃緒申鐃縦わ申鐃塾考案わ申鐃淑わ申鐃曙た鐃緒申鐃緒申鐃緒申呂鐃緒申鐃緒申鐃緒申鐃緒申鐃重�鐃緒申達鐃緒申鐃緒申鐃塾わ申鐃獣わ申鐃緒申鐃緒申鐃殉わ申鐃峻緒申分鐃緒申鐃獣わ申鐃緒申鐃純え鐃出￥申鐃順い鐃祝賞誌申鐃緒申鐃緒申咾鐃緒申僖鐃緒申鐃緒申鐃塾居申鐃緒申鐃淑パワ申鐃緒申鐃所ー鐃縮のわ申鐃夙と思わ申鐃緒申砲蓮鐃緒申鐃緒申任鐃獣縁申帽鐃緒申鐃緒申鐃出象でわ申鐃緒申鐃淑わ申鐃緒申発鐃緒申鐃峻わ申鐃緒申鐃緒申鐃初し鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申里任呂鐃緒申辰討癲�鐃緒申呂笋緒申鐃熟わ申鐃緒申鐃渋わ申譴随申鐃緒申箸砲鐃緒申鐃緒申箸鐃緒申覆鐃緒申鐃淑�鐃緒申鐃緒申鐃緒申鐃緒申能鐃熟は誌申則鐃初算鐃緒申超鐃緒申鐃淑わ申鐃緒申鐃処算鐃夙緒申鐃緒申鐃熟加誌申鐃夙醐申鐃緒申鐃緒申鐃夙み刻申錣誌申納存鐃緒申鐃緒申討鐃緒申鐃緒申里如鐃緒申尊櫃浪短鐃緒申噺鐃緒申鐃緒申鐃緒申鐃緒申鐃準し鐃緒申鐃叔わ申鐃淑わ申鐃獣わ申鐃塾わ申鐃緒申鐃緒申鐃殉で削申鐃曙た鐃緒申鐃緒申鐃塾種申竜鐃緒申鐃緒申里曚箸鐃宿は￥申動鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申襪随申鐃祝人の駕申鐃緒申鐃緒申必鐃竣とわ申鐃緒申鐃緒申鐃緒申鐃緒申鐃獣てわ申鐃暑。鐃緒申鐃緒申鐃銃わ申鐃緒申聾鐃緒申鐃塾醐申鐃緒申鐃夙なる。鐃緒申鐃曙が鐃順き鐃淑随申鐃緒申彁鐃緒申鐃緒申鐃緒申鐃緒申的鐃緒申鐃緒申法鐃祝なってわ申鐃淑わ申鐃夙わ申鐃緒申弌鐃�鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃瞬わ申鐃緒申鐃緒申鐃夙わ申鐃緒申密鐃旬わ申鐃緒申鐃淳刻申辰鐃緒申鐃緒申鐃緒申鐃処し鐃銃わ申鐃淑わ申鐃塾わ申鐃緒申由鐃叔わ申鐃暑。
Struck with similar reflections, Mr. Babbage has devoted some years to the realization of a gigantic idea. He proposed to himself nothing less than the construction of a machine capable of executing not merely arithmetical calculations, but even all those of analysis, if their laws are known. The imagination is at first astounded at the idea of such an undertaking;but the more calm reflection we bestow on it, the less impossible does success appear, and it is felt that it may depend on the discovery of some principle so general, that, if applied to machinery, the latter may be capable of mechanically translating the operations which may be indicated to it by algebraical notation. The illustrious inventor having been kind enough to communicate to me some of his views on this subject during a visit he made at Turin, I have, with his approbation, thrown together the impressions they have left on my mind. But the reader must not expect to find a description of Mr. Babbage's engine;the comprehension of this would entail studies of much length;and I shall endeavour merely to give an insight into the end proposed, and to develop the principles on which its attainment depends.
同鐃粛の考わ申鐃緒申鐃緒申辰鐃緒申丱戰奪鐃緒申鐃熟￥申鐃緒申年鐃塾歳件申鐃緒申鐃緒申鐃緒申鐃淑わ申鐃粛わ申鐃塾実醐申鐃祝つわ申鐃緒申鐃緒申鐃緒申鐃緒申鐃熟￥申鐃緒申鐃淑わ申鐃夙も、鐃緒申鐃術計誌申鐃緒申鐃緒申鐃叔はなわ申鐃緒申法則鐃緒申与鐃緒申鐃銃わ申鐃出わ申鐃緒申鐃緒申鐃緒申呂鐃緒申鐃緒申鐃渋行でわ申鐃暑機鐃緒申鐃緒申鐃循わ申鐃処う鐃夙随申鐃祝件申瓩随申鐃緒申能鐃熟￥申鐃緒申鐃塾よう鐃淑仕誌申鐃緒申廚鐃緒申弔鐃緒申鐃緒申箸剖辰鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃遵い鐃緒申鐃宿わ申鐃粛わ申鐃銃みわ申函鐃緒申垈鐃叔緒申箸鐃緒申鐃緒申曚匹里鐃緒申箸任呂覆鐃緒申鐃緒申發件申鐃緒申鐃緒申鐃重�鐃術わ申鐃緒申里任鐃緒申鐃出￥申鐃緒申鐃緒申曚桧鐃緒申鐃重�鐃叔はなわ申鐃緒申鐃緒申鐃緒申鐃緒申鐃初く鐃緒申鐃緒申鐃塾醐申鐃緒申鐃薯見つわ申鐃緒申鐃暑か鐃宿わ申鐃緒申鐃祝わ申鐃緒申鐃獣てわ申鐃緒申茲�鐃祝思わ申鐃暑。鐃緒申鐃曙が鐃叔わ申鐃緒申弌鐃緒申鐃緒申表鐃緒申鐃祝わ申辰鐃宿緒申鐃緒申鐃緒申鐃緒申任鐃緒申鐃緒申鐃緒申彁鐃緒申魑ヽ鐃重�鐃祝駕申瓩刻申襪鰹申箸鐃緒申任鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申名鐃淑考案者は￥申鐃夙ワ申里鐃緒申攤澆鐃緒申討鐃緒申鐃瞬￥申鐃緒申鐃塾わ申鐃夙に関わ申鐃緒申鐃緒申旅佑鐃緒申鐃緒申鐃准に駈申鐃緒申鐃銃わ申鐃曙た鐃緒申鐃殉わ申鐃緒申鐃緒申鐃緒申鐃塾居申鐃緒申鐃緒申鐃緒申鐃銃￥申鐃緒申鐃塾考わ申鐃祝わ申辰道鐃塾随申鐃祝もた鐃初さ鐃曙た鐃緒申鐃循わ申劼戮鐃緒申鐃�
鐃夙はわ申鐃緒申鐃緒申鐃宿者はバベッワ申鐃緒申竜鐃緒申悗砲弔鐃緒申討鐃緒申鐃緒申鐃緒申鐃緒申鐃峻わ申鐃銃はわ申鐃緒申鐃淑わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鬚垢鐃祝は￥申鐃緒申辰鐃渋随申鐃緒申粒惱鐃緒申鐃宿�鐃竣となる。鐃緒申鐃緒申鐃叔は￥申鐃緒申鐃曙が鐃緒申標鐃夙わ申鐃緒申箸鐃緒申鐃緒申亡悗鐃緒申鐃粛誌申鐃緒申与鐃緒申鐃緒申鐃緒申鐃緒申鐃獣ｏ申鐃緒申鐃緒申襪随申鐃緒申必鐃竣な醐申鐃緒申鐃緒申鐃緒申鐃緒申个鐃緒申茲�鐃舜わ申鐃緒申鐃緒申鐃緒申鐃緒申
I must first premise that this engine is entirely different from that of which there is a notice in the 鐃緒申Treatise on the Economy of Machinery,鐃緒申 by the same author. But as the latter gave rise to the idea of the engine in question, I consider it will be a useful preliminary briefly to recall what were Mr. Babbage's first essays, and also the circumstances in which they originated.
鐃殉わ申鐃叔緒申法鐃銃縁申鐃緒申鐃緒申圓砲鐃獣て書かれた鐃舜居申鐃緒申鐃塾経済に関わ申鐃緒申鐃緒申文鐃緒申Treatise on the Economy of Machinery)鐃駿わ申鐃緒申鐃緒申鐃宿常申鐃緒申譴随申鐃緒申悗箸楼曚覆襪鰹申箸鐃緒申鐃緒申鐃夙わ申鐃淑わ申鐃緒申个鐃緒申鐃緒申覆鐃緒申鐃緒申箸呂鐃緒申鐃緒申鐃緒申鐃緒申狼鐃緒申悗箸浪鐃緒申鐃緒申箸鐃緒申鐃緒申笋わ申鐃緒申鐃塾�鐃緒申鐃緒申鐃出ベッワ申鐃緒申僚鐃緒申鐃塾誌申澆鐃緒申鐃緒申任鐃緒申辰鐃緒申鐃緒申鐃緒申泙鐃緒申鐃緒申鐃緒申慮鐃緒申箸覆辰鐃緒申鐃緒申鐃緒申浪鐃緒申鐃緒申箸鐃緒申鐃緒申鐃緒申箸鐃緒申単鐃祝思わ申鐃瞬わ申鐃塾わ申有鐃術わ申鐃夙考わ申鐃暑。
It is well known that the French government, wishing to promote the extension of the decimal system, had ordered the construction of logarithmical and trigonometrical tables of enormous extent. M. de Prony, who had been entrusted with the direction of this undertaking, divided it into three sections, to each of which was appointed a special class of persons. In the first section the formula were so combined as to render them subservient to the purposes of numerical calculation;in the second, these same formula were calculated for values of the variable, selected at certain successive distances;and under the third section, comprising about eighty individuals, who were most of them only acquainted with the first two rules of arithmetic, the values which were intermediate to those calculated by the second section were interpolated by means of simple additions and subtractions.
鐃緒申鐃淑随申鐃緒申鐃熟囲鰹申張鐃緒申促鐃淑わ申鐃暑こ鐃夙わ申望鐃淳￥申鐃春ワ申鐃緒申鐃緒申椶鐃緒申仗鐃緒申隼鐃緒申儡愎鐃緒申竜鐃緒申鐃緒申表鐃緒申鐃緒申茲μ随申鐃緒申鐃緒申鐃緒申箸呂茲�鐃塾わ申鐃銃わ申鐃暑。鐃緒申鐃塾仕誌申鐃緒申愆鐃緒申鐃緒申鐃処う任命鐃緒申鐃曙た鐃叔プワ申鐃祝は￥申鐃緒申鐃緒申鮖阿弔離鐃緒申鐃緒申鐃緒申鐃緒申鐃淑�鐃緒申鐃緒申鐃緒申鐃曙ぞ鐃緒申鐃緒申鐃緒申未奮鐃緒申悗凌諭鐃緒申乏鐃所振鐃獣わ申鐃緒申鐃叔緒申離鐃緒申鐃緒申鐃緒申鐃緒申任蓮鐃緒申鐃緒申鐃緒申弔鐃緒申慮鐃緒申鐃緒申鐃緒申鐃緒申遊彁鐃緒申鐃重�鐃緒申鐃緒申茲�鐃祝件申腓居申譴随申鐃緒申鐃緒申鐃緒申椶離鐃緒申鐃緒申鐃緒申鐃緒申任蓮鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申僂鐃緒申鐃緒申竸鐃緒申鐃緒申佑鐃緒申彁鐃緒申鐃緒申譴随申鐃緒申鐃緒申鐃祝はわ申鐃緒申鐃緒申鐃緒申鐃熟�続鐃緒申鐃緒申鐃熟囲わ申鐃緒申鐃出れた鐃緒申鐃緒申鐃緒申鐃銃￥申鐃緒申鐃緒申鐃旬のワ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申八鐃緒申鐃粛の個人わ申鐃緒申覆蝓�鐃緒申鐃塾ほとわ申匹鐃緒申鐃縦の誌申鐃術居申則鐃緒申鐃緒申鐃緒申鐃熟わ申鐃銃わ申鐃淑わ申鐃獣わ申鐃緒申鐃緒申鐃緒申鐃旬のワ申鐃緒申鐃緒申鐃緒申鐃叔計誌申鐃緒申鐃曙た鐃粛わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申譟�足鐃緒申鐃緒申鐃夙逸申鐃緒申鐃緒申鐃緒申圓鐃緒申鐃緒申箸砲鐃緒申鐃粛わ申鐃緒申屬鐃緒申譴随申鐃�
An undertaking similar to that just mentioned having been entered upon in England, Mr. Babbage conceived that the operations performed under the third section might be executed by a machine;and this idea he realized by means of mechanism, which has been in part put together, and to which the name Difference Engine is applicable, on account of the principle upon which its construction is founded. To give some notion of this, it will suffice to consider the series of whole square numbers, 1, 4, 9, 16, 25, 36, 49, 64, &c. By subtracting each of these from the succeeding one, we obtain a new series, which we will name the Series of First Differences, consisting of the numbers 3, 5, 7, 9, 11, 13, 15, &c. On subtracting from each of these the preceding one, we obtain the Second Differences, which are all constant and equal to 2. We may represent this succession of operations, and their results, in the following table.
鐃緒申鐃藷グワ申鐃宿で￥申鐃緒申鐃順う鐃宿わ申鐃緒申隼鐃緒申鐃緒申茲�鐃淑削申箸鐃緒申鐃緒申呂鐃緒申鐃銃わ申鐃銃￥申鐃出ベッワ申鐃緒申肋綉�鐃緒申鐃処三鐃緒申鐃緒申鐃緒申鐃緒申鐃塾削申箸狼鐃緒申鐃緒申納孫圓任鐃緒申襪�鐃盾し鐃緒申覆鐃緒申塙佑鐃緒申鐃緒申鐃緒申鐃熟わ申鐃塾ワ申鐃緒申鐃叔ワ申鐃薯あわ申鐃緒申鐃駿まとまっわ申鐃緒申鐃緒申的鐃緒申法鐃祝わ申鐃渋醐申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃銃わ申鐃緒申呂鐃緒申旅鐃渋わ申隆鐃緒申椶箸覆觚駈申鐃緒申鐃緒申慮鐃緒申鐃銃￥申鐃緒申鐃緒申鐃緒申鐃舜￥申Difference Engine鐃祝とわ申鐃緒申名鐃緒申鐃緒申適鐃緒申鐃銃わ申鐃暑。鐃緒申鐃塾考わ申鐃緒申鐃緒申鐃重�鐃祝種申鐃緒申鐃祝は￥申鐃緒申鐃緒申平鐃緒申鐃緒申鐃塾随申鐃緒申 1鐃緒申4鐃緒申9鐃緒申16鐃緒申25鐃緒申36鐃緒申49鐃緒申64鐃緒申鐃縦￥申 鐃緒申佑鐃緒申鐃出よい鐃緒申鐃銃￥申鐃緒申鐃緒申鐃塾随申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申箸砲鐃獣て￥申3鐃緒申5鐃緒申7鐃緒申9鐃緒申11鐃緒申13鐃緒申15鐃緒申鐃縦￥申 鐃夙わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申襦ｏ申鐃緒申鐃緒申能鐃塾鰹申鐃緒申鐃緒申鐃緒申鐃�First Differences Series鐃祝と呼ぶわ申鐃夙にわ申鐃暑。鐃緒申鐃緒申法鐃緒申鐃緒申鐃緒申函鐃緒申鐃緒申鶻�削申鐃緒申Second Differences鐃祝わ申鐃緒申鐃暑。鐃緒申鐃緒申鐃銃￥申鐃緒申鐃緒申呂鐃緒申戮鐃緒申鐃緒申 2 鐃夙なる。鐃緒申鐃緒申鐃叔￥申鐃緒申鐃塾逸申連鐃塾計誌申鐃夙わ申鐃塾件申未鐃宿緒申房鐃緒申鐃緒申鐃緒申鐃� series 鐃熟居申鐃緒申琉鐃縮ｏ申鐃緒申鐃緒申鐃緒申鐃緒申任録鐃緒申鐃緒申鐃緒申鐃緒申鐃暑。
From the mode in which the last two columns B and C have been formed, it is easy to see, that if, for instance, we desire to pass from the number 5 to the succeeding one 7, we must add to the former the constant difference 2;similarly, if from the square number 9 we would pass to the following one 16, we must add to the former the difference 7, which difference is in other words the preceding difference 5, plus the constant difference 2;or again, which comes to the same thing, to obtain 16 we have only to add together the three numbers 2, 5, 9, placed obliquely in the direction ab. Similarly, we obtain the number 25 by summing up the three numbers placed in the oblique direction dc: commencing by the addition 2+7, we have the first difference 9 consecutively to 7;adding 16 to the 9 we have the square 25. We see then that the three numbers 2, 5, 9 being given, the whole series of successive square numbers, and that of their first differences likewise may be obtained by means of simple additions.
B 鐃緒申 C 鐃緒申鐃緒申旅鐃緒申鐃緒申鐃祝￥申鐃緒申蕁�鐃純え鐃緒申 B 鐃緒申砲鐃緒申鐃緒申匿鐃緒申鐃� 5 鐃緒申鐃初次鐃緒申 7 鐃祝誌申鐃祝は￥申鐃緒申鐃緒申鐃緒申 2 鐃緒申辰鐃緒申覆鐃緒申鐃出わ申鐃緒申鐃淑わ申鐃緒申鐃夙わ申鐃銃易わ申分鐃緒申鐃暑。同鐃粛わ申平鐃緒申鐃緒申 9 鐃緒申鐃初次鐃緒申 16 鐃祝誌申鐃夙わ申鐃緒申函鐃�B 鐃緒申虜鐃� 7 鐃緒申辰鐃緒申覆鐃緒申鐃出わ申鐃緒申鐃淑わ申鐃緒申鐃緒申鐃緒申蓮鐃�B 鐃緒申砲鐃緒申鐃緒申觝� 7 鐃塾逸申鐃緒申鐃緒申凌鐃緒申鐃� 5 鐃緒申鐃緒申鐃� 2 鐃緒申辰鐃緒申鐃緒申鐃塾とわ申鐃緒申鐃緒申襦Ｆ縁申鐃緒申鐃緒申箸魴�わ申鐃瞬わ申鐃緒申鐃緒申16 鐃緒申鐃緒申鐃暑た鐃緒申砲蓮鐃宿緒申乃鐃緒申鐃� a 鐃緒申鐃緒申 b 鐃舜斜わ申鐃緒申造鐃緒申鐃緒申鐃縦の随申鐃緒申鐃緒申2鐃緒申5鐃緒申9 鐃緒申足鐃緒申鐃緒申錣誌申鐃緒申鐃緒申鐃叔よい鐃緒申同鐃粛に￥申鐃緒申鐃緒申 d 鐃緒申鐃緒申 c 鐃祝斜わ申鐃緒申造鐃緒申鐃緒申鐃縦の随申鐃緒申鐃緒申鐃竣わ申鐃暑こ鐃夙にわ申辰鐃淑随申鐃緒申鐃� 25 鐃緒申鐃緒申鐃暑。2 + 7 鐃緒申鐃初開鐃熟わ申鐃緒申函鐃緒申能鐃塾削申 9 鐃緒申 7 鐃緒申鐃緒申連続鐃緒申鐃緒申鐃緒申鐃夙わ申鐃緒申鐃緒申鐃暑。鐃緒申鐃緒申鐃銃￥申16 鐃緒申 9 鐃祝加わ申鐃緒申函鐃淑随申鐃緒申鐃� 25 鐃緒申鐃緒申鐃暑。鐃叔緒申了鐃緒申弔凌鐃� 2鐃緒申5鐃緒申9 鐃緒申与鐃緒申鐃緒申鐃緒申弌鐃熟�続鐃緒申鐃緒申鐃緒申鐃銃わ申平鐃緒申鐃緒申鐃夙最緒申虜鐃緒申蓮鐃獣縁申鐃緒申足鐃緒申鐃緒申鐃祝わ申辰鐃銃縁申佑鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申
Now, to conceive how these operations may be reproduced by a machine, suppose the latter to have three dials, designated as A, B, C, on each of which are traced, say a thousand divisions, by way of example, over which a needle shall pass. The two dials, C, B, shall have in addition a registering hammer, which is to give a number of strokes equal to that of the divisions indicated by the needle. For each stroke of the registering hammer of the dial C, the needle B shall advance one division;similarly, the needle A shall advance one division for every stroke of the registering hammer of the dial B. Such is the general disposition of the mechanism.
鐃緒申鐃銃￥申鐃緒申鐃塾よう鐃淑計誌申鐃緒申匹里茲�鐃祝わ申鐃銃居申鐃緒申鐃叔実醐申鐃叔わ申鐃暑か鐃緒申佑鐃緒申襪随申瓠�A鐃緒申B鐃緒申C 鐃夙誌申鐃所さ鐃曙た鐃緒申鐃縦のワ申鐃緒申鐃緒申鐃緒申鐃緒申辰討鐃緒申鐃緒申鐃緒申屬鐃粛わ申鐃暑。鐃緒申鐃曙ぞ鐃緒申鐃緒申鐃淑�鐃塾逸申泙鐃緒申鐃緒申鐃緒申鐃緒申鐃宿むこ鐃夙わ申鐃緒申鐃緒申襦ｏ申磴�鐃出￥申鐃祝わ申鐃縦わ申鐃銃わ申鐃緒申鐃緒申鐃緒申鐃緒申両鐃緒申動鐃緒申鐃処う鐃祝でわ申鐃銃わ申鐃緒申箸鐃緒申襦ｏ申辰鐃緒申董鐃緒申鐃縦のワ申鐃緒申鐃緒申鐃� C鐃緒申B 鐃祝は居申録鐃熟ワ申沺鐃緒申鐃緒申弔鐃緒申討鐃緒申董鐃緒申砲鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申同鐃緒申鐃緒申鐃緒申鐃緒申動鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃� C 鐃塾居申録鐃熟ワ申沺鐃緒申鐃銃逸申鐃緒申戮法鐃緒申鐃緒申鐃緒申鐃緒申 B 鐃塾ワ申鐃緒申楼鐃縦進む。同鐃粛に￥申鐃緒申鐃緒申鐃緒申鐃� B 鐃塾居申録鐃熟ワ申沺鐃緒申鐃銃逸申鐃緒申戮鐃� A 鐃塾針は逸申朕覆燹ｏ申鐃緒申里茲�鐃緒申動鐃庶が鐃緒申鐃所す鐃緒申鐃緒申鐃瞬わ申鐃順雑鐃縦な居申鐃緒申鐃叔わ申鐃暑。
This being understood, let us, at the beginning of the series of operations we wish to execute, place the needle C on the division 2, the needle B on the division 5, and the needle A on the division 9. Let us allow the hammer of the dial C to strike;it will strike twice, and at the same time the needle B will pass over two divisions. The latter will then indicate the number 7, which succeeds the number 5 in the column of first differences. If we now permit the hammer of the dial B to strike in its turn, it will strike seven times, during which the needle A will advance seven divisions;these added to the nine already marked by it will give the number 16, which is the square number consecutive to 9. If we now recommence these operations, beginning with the needle C, which is always to be left on the division 2, we shall perceive that by repeating them indefinitely, we may successively reproduce the series of whole square numbers by means of a very simple mechanism.
鐃緒申鐃塾誌申鐃夙みわ申鐃淑￥申鐃緒申分鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申罅刻申鐃緒申孫圓鐃緒申鐃緒申鐃緒申塙佑鐃緒申討鐃緒申鐃緒申連鐃塾計誌申鐃塾始わ申法鐃緒申泙鐃� C 鐃塾針わ申 2鐃緒申B 鐃塾針わ申 5鐃緒申A 鐃塾針わ申 9 鐃祝刻申錣誌申襦ｏ申鐃緒申鐃緒申鐃緒申 C 鐃塾ハワ申沺鐃緒申鐃銃逸申鐃緒申鐃緒申鐃緒申鐃緒申鐃叔つわ申鐃夙になる。鐃緒申鐃緒申鐃銃￥申鐃緒申 B 鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申覆漾鐃�7 鐃緒申悗鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申表鐃塾最緒申粒鐃緒申鐃緒申鐃緒申鐃� 5 鐃緒申 2 鐃緒申鐃獣わ申鐃緒申譴随申鐃塾わ申鐃緒申鐃緒申鐃緒申鐃銃￥申鐃緒申鐃緒申鐃緒申鐃� B 鐃塾ハワ申沺鐃緒申鐃銃逸申鐃緒申鐃緒申伴鐃緒申鐃緒申任鐃緒申鐃緒申鐃� A 鐃熟種申鐃緒申鐃緒申鐃緒申覆燹ｏ申能鐃祝種申鐃緒申鐃銃わ申鐃緒申 9 鐃祝加わ申鐃緒申鐃緒申里如鐃緒申鐃緒申鐃緒申鐃緒申 16 鐃夙なる。鐃緒申鐃緒申鐃� 9 鐃塾種申鐃緒申平鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃� C 鐃緒申鐃初繰鐃緒申鐃瞬わ申鐃夙わ申鐃暑。C 鐃熟常申鐃� 2 鐃薯示わ申鐃銃わ申鐃緒申里如鐃緒申鐃緒申鐃緒申無鐃渋に件申鐃緒申鐃瞬わ申鐃緒申鐃夙にわ申蝓�鐃緒申単鐃緒申鐃緒申法鐃緒申平鐃緒申鐃緒申鐃緒申連続鐃緒申鐃銃削申鐃出わ申鐃緒申鐃夙わ申鐃叔わ申鐃暑こ鐃夙に居申鐃春わ申鐃緒申鐃緒申鐃緒申鐃緒申
The theorem on which is based the construction of the machine we have just been describing, is a particular case of the following more general theorem: that if in any polynomial whatever, the highest power of whose variable is m, this same variable be increased by equal degrees;the corresponding values of the polynomial then calculated, and the first, second, third, &c. differences of these be taken (as for the preceding series of squares);the mth differences will all be equal to each other. So that, in order to reproduce the series of values of the polynomial by means of a machine analogous to the one above described, it is sufficient that there be (m+1) dials, having the mutual relations we have indicated. As the differences may be either positive or negative, the machine will have a contrivance for either advancing or retrograding each needle, according as the number to be algebraically added may have the sign plus or minus.
鐃緒申鐃塾よう鐃淑わ申鐃塾居申鐃緒申鐃塾器申鐃獣となる原鐃緒申鐃熟￥申鐃緒申鐃緒申鐃緒申的鐃淑醐申鐃緒申鐃塾わ申鐃緒申鐃獣種申幣鐃緒申任鐃緒申襦ｏ申匹里茲�鐃緒申多鐃準式鐃叔も、鐃緒申辰箸鐃盾次鐃緒申鐃術随申鐃塾指随申鐃緒申 m 鐃夙わ申鐃緒申函鐃緒申鐃緒申鐃緒申竸鐃緒申鐃銃縁申鐃緒申鐃緒申鐃緒申鐃緒申辰鐃緒申鐃暑。鐃緒申鐃緒申鐃銃￥申鐃緒申鐃緒申鐃緒申个鐃緒申鐃渋随申犲逸申鐃緒申佑鐃緒申彁鐃緒申鐃緒申鐃暑。鐃緒申鐃緒申鐃銃￥申鐃叔緒申鐃緒申諭鐃緒申鐃緒申鐃緒申棔鐃緒申鐃緒申鐃緒申椶箸鐃緒申辰鐃緒申鐃緒申法鐃緒申鐃緒申鐃緒申粒鐃緒申鐃緒申鐃緒申彁鐃緒申鐃緒申鐃銃わ申鐃緒申鐃緒申鐃緒申鐃淑随申鐃緒申鐃緒申里茲�鐃祝￥申m 鐃緒申鐃旬の鰹申鐃緒申鐃緒申鐃緒申鐃緒申同鐃緒申鐃緒申鐃祝なる。鐃緒申鐃獣て￥申鐃緒申房鐃緒申鐃緒申鐃緒申里鐃銃縁申鐃緒申茲�鐃淑居申鐃緒申鐃祝わ申辰鐃渋随申犲逸申琉鐃熟�鐃緒申鐃粛わ申彁鐃緒申鐃緒申鐃祝は￥申鐃緒申澳愀鐃緒申鐃緒申鐃祝種申鐃緒申鐃緒申鐃塾わ申同鐃緒申 (m+1) 鐃縦のワ申鐃緒申鐃緒申襪�鐃緒申鐃緒申鐃緒申匹鐃緒申鐃緒申箸砲覆襦ｏ申鐃緒申鐃緒申鐃�鐃緒申鐃緒申鐃緒申鐃宿わ申鐃緒申鐃緒申佑任鐃緒申匹鐃緒申鐃緒申鐃緒申的鐃祝加誌申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申里鐃緒申弍鐃緒申鐃緒申董鐃緒申鐃緒申鐃緒申録砲鐃緒申鐃緒申覆發件申鐃緒申聾鐃緒申爐刻申鐃緒申鐃夙みわ申鐃緒申帖鐃�
If from a polynomial we pass to a series having an infinite number of terms, arranged according to the ascending powers of the variable, it would at first appear, that in order to apply the machine to the calculation of the function represented by such a series, the mechanism must include an infinite number of dials, which would in fact render the thing impossible. But in many cases the difficulty will disappear, if we observe that for a great number of functions the series which represent them may be rendered convergent;so that, according to the degree of approximation desired, we may limit ourselves to the calculation of a certain number of terms of the series, neglecting the rest. By this method the question is reduced to the primitive case of a finite polynomial. It is thus that we can calculate the succession of the logarithms of numbers. But since, in this particular instance, the terms which had been originally neglected receive increments in a ratio so continually increasing for equal increments of the variable, that the degree of approximation required would ultimately be affected, it is necessary, at certain intervals, to calculate the value of the function by different methods, and then respectively to use the results thus obtained, as data whence to deduce, by means of the machine, the other intermediate values. We see that the machine here performs the office of the third section of calculators mentioned in describing the tables computed by order of the French government, and that the end originally proposed is thus fulfilled by it.
多鐃準式鐃緒申鐃緒申無鐃緒申鐃緒申鐃緒申鐃緒申鐃縦居申鐃緒申鐃�series鐃祝に移行わ申鐃緒申鐃緒申鐃緒申続鐃緒申鐃緒申鐃術随申鐃塾種申鐃緒申鐃緒申鐃出縁申鐃緒申鐃緒申箸鐃緒申襦ｏ申鐃緒申里茲�鐃淑居申鐃緒申砲鐃獣わ申表鐃緒申鐃緒申鐃緒申鐃舜随申鐃塾計誌申鐃祝居申鐃緒申鐃緒申適鐃術わ申鐃暑た鐃緒申砲蓮鐃縮居申造凌鐃緒申離鐃緒申鐃緒申鐃緒申鐃緒申鐃縦刻申造鐃祝ならざ鐃緒申鐃緒申鐃緒申覆鐃緒申鐃緒申鐃緒申鐃熟￥申物鐃緒申鐃緒申鐃緒申他鐃緒申垈鐃叔緒申砲鐃緒申襪�鐃塾よう鐃祝醐申鐃緒申鐃暑。鐃緒申鐃緒申鐃緒申鐃緒申多鐃緒申鐃塾常申膾わ申鐃熟消わ申鐃暑。鐃緒申鐃塾よう鐃祝わ申鐃緒申表鐃緒申鐃緒申鐃緒申鐃緒申多鐃緒申鐃塾関随申鐃緒申調鐃駿てみわ申函鐃緒申鐃緒申鐃緒申麓鐃渋�鐃緒申鐃緒申鐃塾わ申鐃術わ申鐃暑こ鐃夙わ申鐃叔わ申鐃暑。鐃緒申鐃塾わ申鐃潤、鐃竣求す鐃緒申鐃緒申鐃緒申鐃駿合い鐃祝わ申辰董鐃緒申彁鐃緒申鐃緒申鐃緒申鐃緒申旅鐃緒申鐃緒申鐃緒申鐃渋わ申鐃淳わ申鐃緒申鐃縦わ申旅鐃緒申無鐃暑す鐃暑こ鐃夙わ申鐃叔わ申鐃暑。鐃緒申鐃緒申鐃緒申法鐃祝わ申辰董鐃緒申鐃緒申蠅�有鐃緒申多鐃準式鐃塾器申鐃緒申的鐃淑常申鐃緒申単鐃純化鐃緒申鐃緒申襦ｏ申鐃緒申鐃熟￥申鐃緒申鐃塾よう鐃祝￥申鐃醇々鐃緒申鐃淑￥申鐃夙わ申鐃緒申鐃出随申鐃緒申鐃粛わ申彁鐃緒申鐃緒申襪鰹申箸鐃緒申任鐃緒申鐃夙わ申鐃緒申鐃緒申鐃夙わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃祝わ申鐃緒申鐃銃は￥申鐃緒申鐃緒申無鐃暑さ鐃緒申討鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃順が鐃緒申鐃術随申鐃緒申分鐃緒申同鐃緒申鐃緒申鐃緒申連続鐃緒申鐃緒申鐃緒申鐃緒申続鐃緒申鐃緒申鐃叔緒申的鐃祝わ申鐃竣求す鐃緒申鐃緒申鐃緒申鐃駿合い鐃祝影駈申鐃緒申与鐃緒申鐃暑。鐃緒申鐃緒申岾屬如鐃緒申鐃獣わ申鐃緒申法鐃祝わ申鐃舜随申鐃緒申鐃粛わ申彁鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申砲鐃緒申他鐃緒申鐃緒申鐃緒申佑鐃緒申鐃所す鐃暑こ鐃夙にわ申鐃緒申鐃緒申鐃曙た鐃緒申未函鐃緒申鐃緒申譴常申鐃祝使わ申必鐃竣わ申鐃緒申鐃暑。 鐃春ワ申鐃緒申鐃緒申椶鐃縮随申鐃祝わ申鐃竣誌申鐃緒申鐃曙た表鐃縦わ申鐃銃醐申鐃准わ申鐃緒申鐃楯わ申鐃処三鐃塾ワ申鐃緒申鐃緒申鐃緒申鐃塾計誌申鐃所た鐃緒申鐃緒申鐃緒申鐃薯、わ申鐃緒申鐃祝居申鐃緒申鐃緒申鐃縮わ申鐃緒申鐃緒申鐃夙わ申鐃叔わ申鐃暑こ鐃夙わ申分鐃緒申鐃暑。鐃緒申鐃緒申鐃銃￥申鐃緒申鐃緒申呂鐃緒申發緒申鐃叔わ申鐃銃わ申鐃緒申鐃緒申達鐃緒申鐃緒申鐃緒申足鐃緒申鐃緒申里鐃緒申鐃�
Such is the nature of the first machine which Mr. Babbage conceived. We see that its use is confined to cases where the numbers required are such as can be obtained by means of simple additions or subtractions;that the machine is, so to speak, merely the expression of one particular theorem of analysis;and that, in short, its operations cannot be extended so as to embrace the solution of an infinity of other questions included within the domain of mathematical analysis. It was while contemplating the vast field which yet remained to be traversed, that Mr. Babbage, renouncing his original essays, conceived the plan of another system of mechanism whose operations should themselves possess all the generality of algebraical notation, and which, on this account, he denominates the Analytical Engine.
鐃緒申鐃緒申蓮鐃緒申丱戰奪鐃緒申瓩�鐃叔緒申帽佑鐃緒申鐃緒申鐃緒申竜鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申了鐃緒申僂蓮鐃緒申弋瓩居申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申里茲�鐃緒申単鐃緒申鐃渋�鐃緒申鐃緒申鐃夙逸申鐃緒申鐃緒申鐃祝わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃祝限わ申鐃暑こ鐃夙わ申分鐃緒申鐃暑。鐃縦まりこ鐃塾わ申鐃塾居申鐃緒申鐃熟￥申鐃緒申鐃緒申鐃緒申鐃緒申硫鐃緒申呂慮鐃緒申鐃緒申鐃宿緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申里鐃塾と醐申鐃緒申鐃暑。鐃竣わ申鐃緒申法鐃緒申鐃緒申鐃銃逸申鐃緒申他鐃緒申無鐃渋にわ申鐃緒申鐃緒申鐃重�鐃緒申鐃緒申分鐃緒申亡泙泙鐃緒申鐃緒申鐃緒申硫鐃祝￥申鐃緒申鐃殉わ申鐃緒申箸鐃緒申鐃緒申泙燃鐃縦ワ申鐃緒申襪鰹申箸呂任鐃緒申覆鐃緒申鐃緒申泙鐃緒申鐃緒申任鐃緒申鐃銃わ申鐃淑わ申鐃緒申鐃緒申淵侫鐃緒申鐃緒申鐃宿につわ申鐃銃刻申慮鐃緒申鐃銃わ申鐃緒申鐃緒申鐃緒申鐃出ベッワ申鐃緒申聾鐃緒申隆鐃銃わ申鐃緒申鐃緒申鐃緒申鐃銃￥申鐃緒申鐃銃の逸申鐃緒申的鐃緒申鐃緒申鐃重�鐃緒申表鐃緒申鐃緒申鐃緒申泙鐃緒申鐃熟わ申鐃叔わ申鐃緒申鐃緒申動鐃緒申鐃緒申鐃縦もう鐃緒申弔離鐃緒申鐃緒申謄犢渋わ申侶弉鐃緒申廚鐃緒申弔鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申董鐃緒申鐃熟￥申鐃緒申鐃塾よう鐃緒申鐃緒申鐃緒申鐃緒申鐃初、鐃緒申鐃緒申鐃�鐃緒申鐃熟居申鐃緒申鐃緒申Analytical Engine鐃祝わ申命名鐃緒申鐃緒申鐃緒申
Having now explained the state of the question, it is time for me to develop the principle on which is based the construction of this latter machine. When analysis is employed for the solution of any problem, there are usually two classes of operations to execute:first, the numerical calculation of the various coefficients;and secondly, their distribution in relation to the quantities affected by them. If, for example, we have to obtain the product of two binomials (a+bx) (m+nx), the result will be represented by am + (an + bm) x + bnx2, in which expression we must first calculate am, an, bm, bn;then take the sum of an + bm;and lastly, respectively distribute the coefficients thus obtained amongst the powers of the variable. In order to reproduce these operations by means of a machine, the latter must therefore possess two distinct sets of powers:first, that of executing numerical calculations;secondly, that of rightly distributing the values so obtained.
鐃緒申鐃緒申両鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申譴随申里如鐃緒申鐃緒申里鐃緒申竜鐃緒申鐃緒申了鐃緒申箸澆隆鐃緒申辰箸覆觚駈申鐃緒申鐃粛わ申鐃暑こ鐃夙とわ申鐃暑。鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申硫鐃祝￥申箸鐃緒申道鐃緒申僂鐃緒申譟�鐃縮常申孫圓鐃緒申鐃緒申里鐃緒申鐃緒申鐃緒申留藥誌申任鐃緒申襦ｏ申能鐃緒申鐃粛￥申鐃淑件申鐃緒申鐃塾随申鐃粛計誌申鐃緒申鐃緒申鐃塾種申鐃熟￥申鐃緒申鐃緒申鳳洞鐃緒申鐃緒申鐃緒申鐃縮と器申連鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申分鐃緒申鐃緒申鐃純え鐃出￥申鐃緒申弔鐃緒申鐃準式 (a+bx) (m+nx) 鐃緒申鐃術わ申佑鐃緒申鐃夙￥申鐃緒申鐃塾件申未鐃� am +鐃緒申an + bm)x + bnx2 鐃緒申表鐃緒申鐃緒申鐃緒申襦ｏ申鐃緒申亮鐃緒申任蓮鐃緒申能鐃緒申 am鐃緒申an鐃緒申bm鐃緒申bn 鐃緒申彁鐃緒申鐃緒申覆鐃緒申鐃出わ申鐃緒申鐃淑わ申鐃緒申鐃緒申鐃曙か鐃緒申 an + bm 鐃緒申彁鐃緒申鐃緒申襦ｏ申埜鐃祝￥申鐃緒申鐃塾よう鐃祝わ申鐃緒申鐃緒申鐃緒申譴随申鐃緒申鐃緒申髻△鐃緒申譴常申鐃塾種申鐃緒申鐃緒申鐃術随申鐃緒申鐃緒申分鐃緒申鐃暑。鐃緒申鐃緒申鐃祝わ申蠅鰹申鐃緒申留藥誌申鐃渋醐申鐃緒申鐃緒申砲蓮鐃緒申鐃緒申竜鐃緒申鐃緒申鐃緒申鐃緒申箸琉曚覆鐃叔緒申呂鐃緒申鐃獣てわ申鐃淑わ申鐃緒申个鐃緒申鐃緒申覆鐃緒申鐃緒申泙鐃緒申鐃緒申遊彁鐃緒申鐃渋行わ申鐃緒申能鐃熟￥申鐃緒申鐃緒申鐃銃￥申鐃緒申鐃緒申譴随申佑鐃緒申鐃緒申鐃緒申鐃緒申鐃淑�鐃緒申鐃緒申能鐃熟でわ申鐃暑。
But if human intervention were necessary for directing each of these partial operations, nothing would be gained under the heads of correctness and economy of time;the machine must therefore have the additional requisite of executing by itself all the successive operations required for the solution of a problem proposed to it, when once the primitive numerical data for this same problem have been introduced. Therefore, since, from the moment that the nature of the calculation to be executed or of the problem to be resolved have been indicated to it, the machine is, by its own intrinsic power, of itself to go through all the intermediate operations which lead to the proposed result, it must exclude all methods of trial and guess-work, and can only admit the direct processes of calculation.
鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申分的鐃淑演算鐃緒申鐃駿に人の駕申鐃緒申鐃緒申必鐃竣なのでわ申鐃緒申弌鐃緒申鐃緒申鐃緒申鐃緒申隼鐃緒申屬鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃夙わ申鐃緒申鐃緒申鐃叔わ申鐃緒申鐃緒申物鐃緒申鐃淑わ申鐃緒申鐃緒申鐃獣て￥申鐃緒申鐃駿わ申鐃緒申同鐃緒申鐃緒申鐃緒申里鐃緒申鐃塾器申鐃緒申的鐃淑随申鐃粛デ￥申鐃緒申鐃緒申鐃緒申鐃熟わ申鐃曙た鐃淑ら、鐃緒申鐃塾居申鐃緒申鐃緒申the machine鐃祝わ申与鐃緒申鐃緒申譴随申鐃緒申鐃緒申鬚�わ申鐃緒申法鐃宿�鐃竣となわ申鐃熟�鐃塾演算鐃緒申鐃銃を自身でわ申鐃淑わ申能鐃熟わ申鐃緒申鐃緒申覆鐃緒申鐃出わ申鐃緒申鐃淑わ申鐃緒申鐃縦まり、鐃渋行わ申鐃緒申鐃駿わ申鐃竣誌申鐃緒申鬚�わ申鐃駿わ申鐃緒申鐃所が鐃藷示わ申鐃曙た鐃瞬間わ申鐃初、鐃旬種申的鐃緒申能鐃熟で￥申与鐃緒申鐃緒申譴随申鐃縮に誌申鐃殉でわ申鐃緒申鐃重�鐃淑演算鐃緒申鐃銃わ申圓鐃緒申鐃緒申鐃縦常申鐃緒申雰彁鐃緒申鐃緒申鐃緒申里澆鐃緒申鐃銃わ申鐃緒申里如鐃緒申鐃緒申鐃緒申鐃緒申垪鐃緒申鐃緒申禄鐃緒申鐃緒申鐃緒申鐃淑わ申鐃緒申个鐃緒申鐃緒申覆鐃緒申鐃�
It is necessarily thus;for the machine is not a thinking being, but simply an automaton which acts according to the laws imposed upon it. This being fundamental, one of the earliest researches its author had to undertake, was that of finding means for effecting the division of one number by another without using the method of guessing indicated by the usual rules of arithmetic. The difficulties of effecting this combination were far from being among the least;but upon it depended the success of every other. Under the impossibility of my here explaining the process through which this end is attained, we must limit ourselves to admitting that the first four operations of arithmetic, that is addition, subtraction, multiplication and division, can be performed in a direct manner through the intervention of the machine. This granted, the machine is thence capable of performing every species of numerical calculation, for all such calculations ultimately resolve themselves into the four operations we have just named. To conceive how the machine can now go through its functions according to the laws laid down, we will begin by giving an idea of the manner in which it materially represents numbers.
鐃緒申鐃緒申鐃宿�鐃緒申的鐃淑わ申鐃夙わ申鐃緒申鐃緒申鐃塾居申鐃緒申鐃熟思刻申鐃熟わ申鐃緒申鐃渋醐申澆任呂覆鐃緒申鐃緒申鐃緒申鐃緒申与鐃緒申鐃緒申譴随申鐃渋э申暴鐃緒申辰鐃銃逸申鐃獣縁申鐃淑種申動鐃緒申鐃瞬でわ申鐃暑。鐃緒申鐃緒申牢鐃緒申鐃重�鐃淑醐申鐃緒申鐃叔￥申鐃緒申鐃緒申鐃塾削申圓鐃緒申鐃緒申鐃夙まなわ申鐃緒申个鐃緒申鐃緒申覆鐃緒申鐃緒申鐃塾醐申鐃緒申里鐃緒申鐃緒申里劼箸弔蓮鐃緒申名鐃塾計誌申鐃緒申則鐃祝わ申鐃緒申鷦┐鐃緒申鐃緒申弭鐃緒申鐃祝￥申砲鐃初ず鐃祝￥申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申未凌鐃緒申鐃緒申燃鐃緒申箸鐃緒申鐃緒申鐃緒申箸飽鐃縮ｏ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申法鐃薯見つわ申鐃暑こ鐃夙わ申鐃獣わ申鐃緒申鐃緒申鐃緒申鐃夙み刻申錣誌申飽鐃縮ｏ申鐃緒申鐃緒申鐃緒申鐃暑困鐃緒申老茲件申鴇鐃緒申覆鐃緒申鐃塾ではなわ申鐃緒申鐃緒申鐃緒申鐃銃￥申鐃緒申鐃緒申鐃緒申他鐃緒申鐃緒申鐃緒申鐃祝逸申存鐃緒申鐃緒申鐃塾わ申鐃獣わ申鐃緒申鐃緒申鐃緒申鐃祝私が鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申的鐃緒申達鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申垈鐃叔緒申鐃緒申硫鐃緒申任蓮鐃緒申鐃渋э申藥誌申里澆魄靴鐃緒申箸鐃緒申鐃緒申鐃緒申填鐃緒申鐃緒申覆鐃緒申鐃出わ申鐃緒申鐃淑わ申鐃緒申鐃縦まり、鐃獣誌申鐃緒申鐃緒申鐃緒申鐃緒申鐃処算鐃緒申鐃緒申鐃緒申鐃銃緒申鐃緒申鐃叔わ申鐃暑。鐃緒申鐃緒申鐃塾演算鐃緒申直鐃旬居申鐃緒申鐃緒申鐃緒申鐃叔実行わ申鐃暑こ鐃夙わ申鐃叔わ申鐃暑。鐃緒申鐃緒申砲鐃所、鐃緒申鐃塾居申鐃緒申鐃熟￥申鐃緒申鐃緒申鐃緒申鐃緒申鐃塾随申鐃粛計誌申鐃緒申鐃縦まわ申鐃緒申蠅件申鐃緒申佑弔留藥誌申鐃淑�鐃緒申任鐃緒申鐃竣誌申鐃緒申鐃銃を、実行わ申鐃暑こ鐃夙わ申鐃叔わ申鐃緒申茲�鐃祝なる。鐃緒申鐃塾居申鐃緒申鐃緒申鐃緒申鐃緒申鐃所さ鐃曙た鐃緒申則鐃祝緒申鐃緒申鐃緒申鐃塾居申能鐃緒申孫圓鐃緒申鐃緒申鐃祝￥申鐃粛わ申鐃暑た鐃緒申法鐃緒申鐃緒申鐃書現わ申鐃緒申鐃緒申鐃緒申亡悗鐃緒申襯�鐃緒申鐃叔ワ申鐃緒申鐃緒申呂鐃暑こ鐃夙にわ申鐃暑。
Let us conceive a pile or vertical column consisting of an indefinite number of circular discs, all pierced through their centres by a common axis, around which each of them can take an independent rotatory movement. If round the edge of each of these discs are written the ten figures which constitute our numerical alphabet, we may then, by arranging a series of these figures in the same vertical line, express in this manner any number whatever. It is sufficient for this purpose that the first disc represent units, the second tens, the third hundreds, and so on. When two numbers have been thus written on two distinct columns, we may propose to combine them arithmetically with each other, and to obtain the result on a third column. In general, if we have a series of columns consisting of discs, which columns we will designate as V0V1, V2, V3, V4, &c., we may require, for instance, to divide the number written on the column V1 by that on the column V4, and to obtain the result on the column V7. To effect this operation, we must impart to the machine two distinct arrangements;through the first it is prepared for executing a division, and through the second the columns it is to operate on are indicated to it, and also the column on which the result is to be represented. If this division is to be followed, for example, by the addition of two numbers taken on other columns, the two original arrangements of the machine must be simultaneously altered. If, on the contrary, a series of operations of the same nature is to be gone through, then the first of the original arrangements will remain, and the second alone must be altered Therefore, the arrangements that may be communicated to the various parts of the machine may be distinguished into two principal classes:
鐃緒申鐃緒申鐃塾な随申鐃塾縁申鐃竣わ申鐃術み重ねわ申物鐃緒申鐃縦常申留鐃緒申鐃緒申佑鐃緒申襦ｏ申鐃緒申討留鐃緒申廚鐃緒申羶器申鐃緒申鐃緒申未鐃所が鐃緒申鐃緒申鐃緒申鐃銃わ申鐃所、鐃緒申鐃曙ぞ鐃緒申鐃緒申鐃塾�鐃緒申鐃銃わ申鐃塾種申鐃緒申鐃醇心鐃祝駕申転鐃緒申鐃暑こ鐃夙わ申鐃叔わ申鐃暑。鐃緒申鐃曙ぞ鐃緒申留鐃緒申廚粒鐃緒申鐃緒申法鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申譴随申鐃緒申鐃春ワ申鐃駿ットわ申鐃緒申覆觸緒申凌鐃緒申鐃緒申鐃緒申颪�わ申箸鐃緒申鐃夙￥申鐃緒申鐃塾随申鐃緒申鐃緒申連鐃淑わ申鐃銃縁申鐃緒申鐃縦常申鐃緒申鐃緒申揃鐃緒申鐃暑こ鐃夙にわ申蝓�鐃宿のよう鐃淑随申鐃緒申鐃緒申表鐃緒申鐃叔わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申能鐃塾縁申鐃竣は逸申琉漫鐃緒申鐃緒申鐃緒申椶留鐃緒申廚禄鐃緒申琉漫鐃緒申鐃緒申鐃緒申椶留鐃緒申廚鐃宿器申琉未箸鐃緒申辰鐃緒申鐃緒申砲鐃緒申弌鐃緒申鐃緒申鐃緒申鐃重�鐃緒申達鐃緒申鐃緒申鐃暑。鐃緒申弔凌鐃緒申鐃緒申鐃循なわ申鐃緒申鐃祝書けば￥申鐃緒申鐃塾随申鐃緒申同鐃塾を算緒申的鐃緒申鐃夙み刻申錣誌申鐃緒申發�鐃述とつの縁申鐃緒申坊鐃縮わ申个鐃緒申茲�鐃緒申命鐃緒申鐃暑こ鐃夙わ申鐃叔わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申未法鐃緒申鐃緒申廚鐃緒申鐃淑わ申鐃緒申鐃緒申連鐃粛￥申鐃緒申鐃曙ぞ鐃緒申鐃� V0鐃緒申V1鐃緒申V2鐃緒申V3鐃緒申V4鐃緒申鐃縦￥申 鐃夙呼ぶわ申鐃夙にわ申鐃暑。鐃醇々鐃熟￥申鐃純え鐃出￥申鐃緒申鐃緒申 V1 鐃祝書かれた鐃緒申鐃緒申鐃緒申 V4 鐃叔鰹申蝓�鐃緒申未鐃� V7 鐃祝出わ申鐃夙わ申鐃緒申鐃緒申鐃緒申命鐃緒申鐃暑こ鐃夙わ申鐃叔わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申留藥誌申飽鐃縮ｏ申鐃緒申鐃緒申鐃緒申鐃暑た鐃緒申砲蓮鐃緒申鐃縦の緒申鐃緒申鐃緒申圓鐃淑わ申鐃緒申个鐃緒申鐃緒申覆鐃緒申鐃緒申能鐃熟￥申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申孫圓鐃緒申襪随申鐃塾緒申鐃緒申鐃緒申鐃緒申鐃祝￥申鐃初算鐃緒申鐃峻わ申鐃緒申鐃緒申鐃塾誌申鐃緒申任鐃緒申襦ｏ申鐃縮わ申表鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃所さ鐃緒申襦ｏ申發件申鐃緒申僚鐃緒申鐃緒申鐃渋鰹申鐃緒申董鐃緒申磴�鐃出￥申鐃縮の縁申鐃緒申砲鐃緒申鐃緒申弔凌鐃緒申鐃緒申硫短鐃緒申鐃緒申圓鐃緒申鐃塾でわ申鐃緒申弌鐃緒申能鐃祝述べわ申鐃緒申弔僚鐃緒申鐃緒申楼鐃緒申討鐃緒申儿鐃緒申鐃緒申鐃淑わ申鐃緒申个鐃緒申鐃緒申覆鐃緒申鐃緒申仂鐃重�鐃祝￥申同鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申辰鐃緒申鐃熟�鐃塾演算鐃緒申鐃峻わ申鐃銃わ申鐃緒申里任鐃緒申鐃出￥申鐃叔緒申僚鐃緒申鐃緒申呂鐃緒申里泙泙如鐃緒申鐃緒申鐃緒申椶僚鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申儿鐃緒申鐃緒申鐃淑わ申鐃緒申个鐃緒申鐃緒申覆鐃緒申鐃緒申鐃緒申辰董鐃緒申鐃緒申竜鐃緒申鐃緒申鐃緒申諭鐃緒申鐃緒申鐃淑�鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申任鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申蓮鐃緒申鐃縦の器申鐃緒申的鐃緒申鐃夙わ申分鐃緒申鐃暑こ鐃夙わ申鐃叔わ申鐃暑。
By this latter we mean that which indicates the columns to be operated on. As for the operations themselves, they are executed by a special apparatus, which is designated by the name of mill, and which itself contains a certain number of columns, similar to those of the Variables. When two numbers are to be combined together, the machine commences by effacing them from the columns where they are written, that is, it places zero on every disc of the two vertical lines on which the numbers were represented;and it transfers the numbers to the mill. There, the apparatus having been disposed suitably for the required operation, this latter is effected, and, when completed, the result itself is transferred to the column of Variables which shall have been indicated. Thus the mill is that portion of the machine which works, and the columns of Variables constitute that where the results are represented and arranged. After the preceding explanations, we may perceive that all fractional and irrational results will be represented in decimal fractions. Supposing each column to have forty discs, this extension will be sufficient for all degrees of approximation generally required.
鐃緒申鐃緒申鐃旬の緒申鐃緒申鐃祝わ申辰董鐃緒申罅刻申榔藥誌申鐃緒申圓鐃緒申鐃緒申鐃緒申鐃舜種申鐃緒申鐃暑。鐃初算鐃緒申鐃塾わ申里亡悗鐃緒申討蓮鐃緒申潺鐃緒申mill鐃祝と呼ばわ申鐃緒申鐃緒申未鐃緒申鐃緒申屬砲鐃獣て実行わ申鐃緒申襦ｏ申潺鐃祝は￥申鐃緒申鐃緒申凌鐃緒申鐃緒申竸鐃緒申隼鐃緒申鐃緒申茲�鐃淑縁申鐃曙が鐃緒申鐃暑。鐃緒申弔凌鐃緒申鐃緒申鐃緒申箸濆鐃緒さ鐃緒申鐃夙￥申鐃緒申鐃塾居申鐃緒申鐃熟わ申鐃塾随申鐃緒申辰鐃緒申鐃緒申箸鐃緒申鐃緒申鐃熟わ申襦ｏ申弔泙蝓⇔常申妊鐃緒申鐃緒申鐃緒申凌鐃緒申鐃緒申鐃宿緒申鐃緒申鐃緒申鐃緒申鐃縦常申鐃緒申鐃薯ゼワ申鐃祝わ申鐃暑。鐃緒申鐃緒申砲鐃獣て随申鐃緒申鐃熟ミワ申鐃緒申鐃緒申鐃緒申襦ｏ申鐃緒申鐃緒申任蓮鐃緒申鐃緒申屬鐃緒申弋瓩居申譴随申藥誌申僂里鐃緒申鐃緒申適鐃准わ申鐃緒申鐃瞬わ申鐃緒申討鐃緒申董鐃緒申彁鐃緒申鐃緒申孫圓鐃緒申鐃暑。鐃緒申鐃緒申鐃銃わ申鐃曙が鐃緒申鐃緒申鐃夙￥申鐃緒申未六鐃緒申蠅居申譴随申竸鐃緒申留鐃緒申鐃緒申鐃緒申鐃緒申鐃暑。鐃淳ワ申呂鐃緒申竜鐃緒申鐃緒申琉鐃緒申鐃緒申箸鐃緒申堂鐃銃�鐃緒申鐃緒申鐃塾でわ申鐃所、鐃術随申鐃塾縁申鐃緒申老鐃縮わ申表鐃緒申鐃緒申鐃緒申鐃術意わ申鐃緒申鐃緒申鐃淑�鐃緒申鐃緒申鐃緒申鐃緒申鐃塾わ申鐃緒申鐃淑降わ申鐃緒申鐃緒申鐃祝わ申蝓�鐃緒申鐃銃わ申分鐃緒申鐃緒申無鐃緒申鐃緒申鐃塾件申未禄鐃緒申平鐃緒申両鐃緒申鐃緒申箸鐃緒申鐃宿緒申鐃緒申鐃緒申鐃暑こ鐃夙わ申分鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申譴常申鐃塾縁申鐃曙が鐃粛緒申鐃緒申留鐃緒申廚鐃緒申鐃獣てわ申鐃緒申弌鐃緒申鐃緒申未鐃緒申弋瓩居申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃銃わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申
It will now be inquired how the machine can of itself, and without having recourse to the hand of man, assume the successive dispositions suited to the operations. The solution of this problem has been taken from Jacquard's apparatus, used for the manufacture of brocaded stuffs, in the following manner:—
鐃緒申鐃緒申任蓮鐃緒申鐃緒申竜鐃緒申鐃緒申呂匹里茲�鐃祝わ申鐃銃￥申鐃粛の種申鐃緒申鐃暑こ鐃夙なわ申連続鐃緒申鐃緒申鐃初算鐃緒申適鐃緒申鐃叔わ申鐃緒申里鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃塾駕申法鐃熟ワ申鐃純カ鐃緒申鐃宿わ申鐃緒申鐃瞬わ申鐃緒申鐃緒申鐃緒申譴随申鐃緒申鐃緒申鐃緒申鐃緒申鐃粛随申鐃緒申brocaded stuffs鐃祝わ申鐃緒申鐃緒申鐃祝使わ申鐃緒申鐃緒申鐃瞬で種申鐃塾よう鐃緒申動鐃庶す鐃暑。
Two species of threads are usually distinguished in woven stuffs;one is the warp or longitudinal thread, the other the woof or transverse thread, which is conveyed by the instrument called the shuttle, and which crosses the longitudinal thread or warp. When a brocaded stuff is required, it is necessary in turn to prevent certain threads from crossing the woof, and this according to a succession which is determined by the nature of the design that is to be reproduced. Formerly this process was lengthy and difficult, and it was requisite that the workman, by attending to the design which he was to copy, should himself regulate the movements the threads were to take. Thence arose the high price of this description of stuffs, especially if threads of various colours entered into the fabric. To simplify this manufacture, Jacquard devised the plan of connecting each group of threads that were to act together, with a distinct lever belonging exclusively to that group. All these levers terminate in rods, which are united together in one bundle, having usually the form of a parallelopiped with a rectangular base. The rods are cylindrical, and are separated from each other by small intervals. The process of raising the threads is thus resolved into that of moving these various lever-arms in the requisite order. To effect this, a rectangular sheet of pasteboard is taken, somewhat larger in size than a section of the bundle of lever-arms. If this sheet be applied to the base of the bundle, and an advancing motion be then communicated to the pasteboard, this latter will move with it all the rods of the bundle, and consequently the threads that are connected with each of them. But if the pasteboard, instead of being plain, were pierced with holes corresponding to the extremities of the levers which meet it, then, since each of the levers would pass through the pasteboard during the motion of the latter, they would all remain in their places. We thus see that it is easy so to determine the position of the holes in the pasteboard, that, at any given moment, there shall be a certain number of levers, and consequently of parcels of threads, raised, while the rest remain where they were. Supposing this process is successively repeated according to a law indicated by the pattern to be executed, we perceive that this pattern may be reproduced on the stuff. For this purpose we need merely compose a series of cards according to the law required, and arrange them in suitable order one after the other; then, by causing them to pass over a polygonal beam which is so connected as to turn a new face for every stroke of the shuttle, which face shall then be impelled parallelly to itself against the bundle of lever-arms, the operation of raising the threads will be regularly performed. Thus we see that brocaded tissues may be manufactured with a precision and rapidity formerly difficult to obtain.
鐃縮常、鐃緒申鐃緒申鐃塾糸が鐃緒申物鐃緒申鐃緒申廼鐃緒申未鐃緒申鐃銃わ申鐃暑。鐃述とつは縦誌申任鐃緒申襦ｏ申發�鐃述とつは駕申鐃緒申如鐃緒申鐃緒申鐃�shuttle鐃祝と呼ばわ申鐃緒申鐃祝わ申辰董鐃緒申鳥鐃緒申鐃准っわ申鐃縮わ申鐃緒申襦ｏ申鐃緒申与鐃緒申砲鐃緒申鐃緒申鐃祝は￥申鐃緒申鐃緒申了鐃薯横誌申噺鮑垢鐃緒申鐃緒申覆鐃緒申鐃緒申箸鐃宿�鐃竣わ申鐃緒申鐃緒申鐃緒申録鐃緒申鐃緒申鐃緒申箸鐃緒申討鐃緒申鐃緒申鐃緒申佑砲鐃緒申鐃殉わ申連続鐃緒申鐃緒申鐃緒申鐃祝緒申鐃獣て行わ申鐃暑。鐃緒申鐃縦てはわ申鐃塾駕申鐃緒申鐃熟誌申鐃瞬わ申鐃緒申鐃緒申鐃緒申鐃書しわ申鐃緒申里如鐃緒申鐃緒申佑竜鐃緒申鐃緒申辰鐃緒申鐃緒申童鐃緒申鐃緒申茲�鐃夙わ申鐃緒申鐃緒申鐃粛わ申鐃曙心鐃緒申鐃緒申砲蓮鐃緒申鐃緒申鐃緒申動鐃緒申鐃緒申鐃緒申鐃緒申鐃淑わ申鐃緒申个鐃緒申鐃緒申覆鐃緒申辰鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申蕕鰹申亮鐃緒申鐃緒申鐃淑わ申鐃緒申鐃緒申砲覆辰鐃緒申鐃緒申辰砲鐃緒申鐃緒申鐃緒申鐃緒申平鐃緒申了紊�鐃緒申鐃緒申鐃緒申泙譴随申鐃塾は高い鐃緒申鐃緒申鐃緒申鐃緒申鐃粛随申鐃緒申鐃緒申造鐃緒申単鐃純化鐃緒申鐃暑た鐃緒申法鐃緒申鐃緒申礇�鐃緒申鐃宿はわ申鐃曙ぞ鐃緒申了鐃緒申鐃夙わ申鐃緒申鐃緒申動鐃緒申鐃処う鐃祝￥申鐃夙にのわ申属鐃緒申鐃緒申鐃縮￥申鐃塾ワ申弌鐃緒申亡鐃熟�鐃春わ申鐃緒申鐃緒申法鐃緒申涌討鐃緒申鐃緒申鐃緒申鐃緒申譴常申鐃塾ワ申弌鐃緒申魯鐃緒申奪匹能鐃獣種申鐃緒申討鐃緒申襦ｏ申鐃緒申鐃緒申董鐃緒申鐃緒申鐃熟逸申束鐃祝まとわ申鐃緒申鐃曙、鐃縮常、長鐃緒申鐃緒申鐃緒申戞鐃緒申鐃緒申箸鐃緒申鐃淑随申鐃熟誌申鐃緒申里侶鐃緒申砲覆襦ｏ申鐃緒申奪匹榔鐃緒申鐃緒申鐃緒申如鐃緒申鐃緒申澆鐃緒申鐃緒申鐃緒申粉岾屬鐃緒申鐃緒申鐃緒申離鐃緒申鐃緒申襦ｏ申鐃緒申鐃緒申鐃緒申紊駕申鐃緒申鐃緒申鐃熟￥申鐃緒申鐃緒申鐃緒申鐃旬のワ申弌鐃緒申鐃宿�鐃竣に縁申鐃緒申鐃緒申動鐃緒申鐃緒申鐃緒申鐃夙わ申分鐃薯さわ申襦ｏ申鐃緒申鐃緒申動鐃緒申鐃緒申鐃緒申鐃緒申法鐃緒申鐃出￥申鐃緒申鐃緒申鐃緒申鐃渋�鐃緒申鐃緒申分鐃緒申鐃緒申分鐃順き鐃緒申長鐃緒申鐃緒申鐃塾醐申鐃醇が鐃術わ申鐃緒申鐃暑。鐃緒申鐃塾醐申鐃醇が束鐃緒申鐃緒申鐃緒申屬鐃緒申譴随申鐃緒申鐃緒申鐃緒申董鐃緒申鐃緒申覆鐃緒申鐃銃逸申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申辰鐃緒申蕁�鐃緒申鐃緒申呂鐃緒申鐃祝わ申辰鐃緒申鐃緒申討離鐃緒申奪鐃渋�鐃緒申動鐃緒申鐃緒申鐃緒申鐃緒申鐃塾件申漫鐃緒申鐃緒申鐃緒申抜鐃熟�鐃春わ申鐃緒申譴随申鐃緒申動鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃醇が平坦鐃叔はなわ申鐃緒申鐃緒申弌鐃緒申鐃緒申鐃獣種申帽腓�鐃処う鐃祝穴が鐃緒申鐃緒申鐃緒申鐃緒申討鐃緒申鐃緒申蕁�鐃緒申鐃緒申鐃塾ワ申弌鐃緒申蓮鐃緒申鐃緒申罎�動鐃緒申鐃銃わ申鐃緒申屐鐃緒申鐃緒申鐃緒申鐃緒申瓩器申鐃緒申鐃緒申鐃出￥申鐃熟醐申鐃塾逸申鐃瞬に残わ申鐃曙た鐃殉まになわ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申辰董鐃緒申鐃緒申鐃塾件申琉鐃緒申屬呂鐃緒申里茲�鐃祝器申単鐃祝件申鐃緒申任鐃緒申襪鰹申箸鐃淑�鐃緒申鐃暑。鐃宿の瞬間にわ申鐃緒申鐃銃も、鐃緒申鐃緒申鐃殉っわ申鐃緒申鐃塾ワ申弌鐃緒申鐃緒申鐃緒申鐃緒申伴鐃緒申鐃緒申琉鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃淑鰹申鐃塾誌申鐃緒申屬鐃緒申鐃緒申砲鐃緒申董鐃緒申鐃緒申鐃緒申紊駕申鐃緒申襦ｏ申鐃緒申硫鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申佑砲鐃所示鐃緒申鐃緒申覽�則鐃祝緒申鐃獣て￥申連続鐃緒申鐃銃件申鐃緒申鐃瞬わ申鐃緒申鐃夙￥申鐃緒申鐃粛わ申鐃緒申物鐃塾常申忘童鐃緒申鐃緒申鐃緒申箸鐃緒申鐃緒申里鐃淑�鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃重�鐃塾わ申鐃緒申法鐃緒申弋瓩居申鐃暑規則鐃祝緒申鐃獣て逸申連鐃塾ワ申鐃緒申鐃宿わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申適鐃緒申鐃淑緒申鐃緒申鐃緒申鐃緒申屬鐃緒申鐃緒申鐃緒申鐃緒申鐃宿わ申鐃緒申鐃緒申鐃曙か鐃初、鐃緒申鐃緒申鐃緒申鐃緒申圓鐃緒申茲刻申鐃緒申戮某鐃緒申鐃緒申鐃緒申未鐃緒申僂鐃緒申鐃処う鐃緒申鐃緒申続鐃緒申鐃曙た鐃緒申多鐃術件申鐃緒申鐃渋の常申鐃緒申未蕕誌申襪鰹申箸砲鐃所、鐃縮はわ申鐃曙自鐃夙わ申平鐃峻に￥申鐃緒申弌鐃緒申鐃緒申鐃緒申鐃緒申束鐃緒申鐃出わ申鐃銃駕申鐃緒申鐃淑み￥申鐃緒申鐃緒申鐃緒申鐃遵げ鐃緒申鐃緒申鐃熟居申則鐃緒申鐃緒申鐃緒申鐃峻わ申鐃暑。鐃緒申鐃緒申鐃緒申鐃銃￥申鐃緒申鐃縦ては器申単鐃叔はなわ申鐃獣わ申鐃緒申鐃緒申鐃緒申鐃春わ申鐃緒申鐃曙た鐃緒申物鐃緒申鐃緒申鐃緒申鐃塾わ申鐃縦随申速鐃緒申鐃緒申造鐃緒申鐃緒申鐃塾わ申分鐃緒申鐃暑。
Arrangements analogous to those just described have been introduced into the Analytical Engine. It contains two principal species of cards: first, Operation cards, by means of which the parts of the machine are so disposed as to execute any determinate series of operations, such as additions, subtractions, multiplications, and divisions;secondly, cards of the Variables, which indicate to the machine the columns on which the results are to be represented. The cards, when put in motion, successively arrange the various portions of the machine according to the nature of the processes that are to be effected, and the machine at the same time executes these processes by means of the various pieces of mechanism of which it is constituted.
鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申法鐃緒申鐃緒申鐃熟居申鐃舜わ申導鐃緒申鐃緒申鐃曙た鐃緒申鐃緒申鐃緒申砲鐃緒申鐃緒申鐃緒申隆鐃緒申鐃重�鐃淑ワ申鐃緒申鐃宿わ申鐃夙わ申鐃暑。鐃緒申鐃緒申鐃旬は演算鐃緒申鐃緒申鐃宿で￥申鐃緒申鐃緒申砲鐃所、鐃獣誌申鐃緒申鐃緒申鐃緒申鐃緒申鐃処算鐃緒申鐃緒申鐃緒申鐃夙わ申鐃獣わ申鐃緒申鐃緒申鐃緒申譴随申鐃熟�鐃塾演算鐃緒申孫圓鐃緒申鐃処う鐃緒申鐃塾居申鐃緒申鐃塾逸申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申襦ｏ申鐃緒申鐃緒申椶蓮鐃緒申竸鐃緒申鐃緒申鐃緒申匹如鐃緒申鐃縮わ申表鐃緒申鐃緒申鐃緒申襯�鐃緒申鐃宿わ申鐃緒申蠅刻申鐃緒申痢鐃緒申鐃緒申鐃緒申匹蓮鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申函鐃緒申孫圓鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鳳鐃緒申鐃緒申討鐃緒申竜鐃緒申鐃緒申鐃緒申諭鐃緒申鐃緒申鐃淑�鐃緒申連続鐃緒申鐃銃緒申鐃緒申鐃緒申鐃暑。鐃緒申鐃緒申鐃銃￥申同鐃緒申鐃祝￥申鐃緒申鐃塾居申鐃緒申鐃熟￥申鐃緒申鐃塾逸申鐃緒申鐃緒申覆鐃緒申鐃緒申泙鐃緒申泙糞鐃緒申鐃緒申砲鐃所こ鐃緒申鐃塾緒申鐃緒申鐃緒申孫圓鐃緒申襦�
In order more perfectly to conceive the thing, let us select as an example the resolution of two equations of the first degree with two unknown quantities. Let the following be the two equations, in which x and y are the unknown quantities:—
鐃緒申蟯逸申鐃緒申砲鐃緒申鐃緒申佑鐃緒申襪随申鐃祝￥申鐃緒申弔鐃縮わ申凌鐃緒申鐃緒申鐃緒申連立鐃曙次鐃緒申鐃緒申鐃緒申鐃塾駕申鐃緒申鐃夙わ申鐃暑。鐃緒申鐃緒申 x 鐃緒申 y 鐃緒申未鐃塾随申鐃緒申鐃緒申弔亮鐃緒申鐃粛わ申鐃暑。
We deduce 
, and for y an analogous expression. Let us continue to represent by V0, V1, V2, &c. the different columns which contain the numbers, and let us suppose that the first eight columns have been chosen for expressing on them the numbers represented by m, n, d, m', n', d', n and n', which implies that V0=m, V1=n, V2=d, V3=m', V4=n', V5=d', V6=n, V7=n'.
鐃緒申鐃緒申鐃緒申立鐃縦￥申y 鐃緒申同鐃粛の種申鐃叔わ申鐃暑。鐃緒申鐃緒申続鐃緒申鐃緒申鐃純う鐃瞬刻申鐃緒申納鐃緒申鐃緒申鐃緒申鐃緒申 V0鐃緒申V1鐃緒申V2鐃緒申鐃縦…わ申表鐃緒申鐃緒申鐃暑こ鐃夙とわ申鐃暑。鐃叔緒申鐃夙�鐃縦の縁申鐃緒申鐃� m鐃緒申n鐃緒申d鐃緒申m'鐃緒申n'鐃緒申d'鐃緒申n鐃緒申n 鐃緒申表鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申表鐃緒申鐃緒申鐃暑た鐃緒申忙箸鐃緒申鐃緒申里箸鐃緒申襦ｏ申弔泙蝓�V0=m鐃緒申V1=n鐃緒申V2=d鐃緒申V3=m'鐃緒申V4=n'鐃緒申V5=d'鐃緒申V6=n鐃緒申V7=n' 鐃夙わ申鐃緒申鐃緒申鐃夙になる。
The series of operations commanded by the cards, and the results obtained, may be represented in the following table:—
鐃緒申鐃緒申鐃宿にわ申鐃舜種申鐃緒申鐃緒申鐃緒申連鐃塾計誌申鐃夙件申未麓鐃宿緒申里茲�鐃緒申表鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申
Since the cards do nothing but indicate in what manner and on what columns the machine shall act, it is clear that we must still, in every particular case, introduce the numerical data for the calculation. Thus, in the example we have selected, we must previously inscribe the numerical values of m, n, d, m', n', d', in the order and on the columns indicated, after which the machine when put in action will give the value of the unknown quantity x for this particular case. To obtain the value of y, another series of operations analogous to the preceding must be performed. But we see that they will be only four in number, since the denominator of the expression for y, excepting the sign, is the same as that for x, and equal to n'm-nm'. In the preceding table it will be remarked that the column for operations indicates four successive multiplications, two subtractions, and one division. Therefore, if desired, we need only use three operation-cards;to manage which, it is sufficient to introduce into the machine an apparatus which shall, after the first multiplication, for instance, retain the card which relates to this operation, and not allow it to advance so as to be replaced by another one, until after this same operation shall have been four times repeated. In the preceding example we have seen, that to find the value of x we must begin by writing the coefficients m, n, d, m', n', d', upon eight columns, thus repeating n and n' twice. According to the same method, if it were required to calculate y likewise, these coefficients must be written on twelve different columns. But it is possible to simplify this process, and thus to diminish the chances of errors, which chances are greater, the larger the number of the quantities that have to be inscribed previous to setting the machine in action. To understand this simplification, we must remember that every number written on a column must, in order to be arithmetically combined with another number, be effaced from the column on which it is, and transferred to the mill. Thus, in the example we have discussed, we will take the two coefficients m and n', which are each of them to enter into two different products, that is m into mn' and md', n' into mn' and n'd. These coefficients will be inscribed on the columns V0 and V4. If we commence the series of operations by the product of m into n', these numbers will be effaced from the columns V0 and V4, that they may be transferred to the mill, which will multiply them into each other, and will then command the machine to represent the result, say on the column V6. But as these numbers are each to be used again in another operation, they must again be inscribed somewhere;therefore, while the mill is working out their product, the machine will inscribe them anew on any two columns that may be indicated to it through the cards;and as, in the actual case, there is no reason why they should not resume their former places, we will suppose them again inscribed on V0 and V4, whence in short they would not finally disappear, to be reproduced no more, until they should have gone through all the combinations in which they might have to be used.
鐃緒申鐃緒申鐃宿はどの縁申鐃緒申鐃緒申个鐃緒申討匹里茲�鐃祝随申鐃緒申鐃書うわ申鐃緒申惻鐃緒申鐃緒申鐃緒申鐃緒申鐃淑ので￥申鐃緒申鐃銃の常申鐃祝わ申鐃緒申鐃銃￥申鐃竣誌申鐃塾わ申鐃緒申凌鐃緒申優如鐃緒申鐃緒申鐃粛随申鐃緒申討鐃緒申覆鐃緒申鐃出わ申鐃緒申鐃淑わ申鐃塾わ申鐃緒申鐃初か鐃叔わ申鐃暑。鐃醇々鐃緒申鐃緒申鐃緒申鐃緒申鐃叔は￥申鐃緒申鐃緒申鐃祝随申鐃緒申 m鐃緒申n鐃緒申d鐃緒申m'鐃緒申n'鐃緒申d' 鐃緒申鐃緒申蠅居申譴随申鐃緒申鐃祝緒申鐃緒申鐃縮わ申颪�なわ申鐃緒申个鐃緒申鐃緒申覆鐃緒申辰鐃緒申鐃緒申鐃緒申両鐃緒申屬任鐃緒申竜鐃緒申鐃緒申鐃緒申鐃銃�鐃緒申鐃緒申函鐃緒申鐃緒申両鐃緒申鐃縮わ申凌鐃� x 鐃緒申与鐃緒申鐃緒申譴随申鐃�y 鐃緒申鐃粛わ申鐃緒申鐃祝は￥申鐃緒申連鐃塾演算鐃緒申鐃緒申両鐃緒申鐃銃縁申佑房孫圓鐃緒申覆鐃緒申鐃出わ申鐃緒申鐃淑わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申六佑弔凌鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申匹鐃緒申里鐃淑�鐃緒申鐃暑。分鐃緒申亮鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃銃￥申x 鐃塾わ申里鐃銃縁申鐃緒申任鐃緒申襦ｏ申弔泙鐃� n'm-nm' 鐃夙なる。鐃緒申鐃宿緒申任蓮鐃緒申鐃緒申鐃塾計誌申鐃熟四つわ申連続鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申弔慮鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申討劼箸弔僚鐃緒申鐃緒申隼鐃緒申蠅居申鐃銃わ申鐃暑こ鐃夙に居申鐃春わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃獣て￥申鐃緒申鐃緒申離鐃緒申鐃緒申匹鐃緒申鐃緒申鐃夙わ申鐃夙わ申鐃緒申鐃緒申鐃夙わ申任鐃緒申襦ｏ申鐃緒申鐃緒申存鐃緒申鐃緒申鐃祝は￥申鐃純え鐃出￥申鐃叔緒申僚鐃緒申鐃緒申慮紂�鐃緒申鐃塾演算鐃祝関わ申鐃暑カ鐃緒申鐃宿わ申鐃楯誌申鐃緒申鐃緒申鐃緒申鐃曙が鐃粛回繰わ申鐃瞬わ申鐃緒申鐃殉で￥申鐃緒申鐃緒申鐃宿わ申鐃緒申鐃祝進み削申鐃緒申鐃術わ申鐃塾わ申澆鐃緒申鐃緒申鐃瞬わ申導鐃緒申鐃緒申鐃緒申鐃緒申匹鐃緒申鐃緒申鐃緒申鐃緒申鐃叔は￥申未鐃塾随申 x 鐃薯算出わ申鐃暑た鐃緒申法鐃緒申鐃緒申鐃� m鐃緒申n鐃緒申d鐃緒申m'鐃緒申n'鐃緒申d'鐃緒申n鐃緒申n 鐃緒申颪�刻申鐃準こ鐃夙わ申鐃緒申呂瓩随申鐃�n 鐃緒申 n' 鐃緒申鐃緒申鐃駿書かわ申討鐃緒申襦Ｆ縁申鐃緒申鐃祝￥申任鐃緒申函鐃�y 鐃緒申鐃緒申鐃塾に￥申鐃緒申鐃塾よう鐃淑件申鐃緒申鐃緒申鐃緒申留鐃緒申鐃祝書き刻申鐃殉なわ申鐃緒申个鐃緒申鐃緒申覆鐃緒申鐃緒申箸砲覆襦ｏ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申僚鐃緒申鐃緒申鐃緒申略鐃緒申鐃緒申鐃銃￥申鐃緒申鐃所が鐃緒申鐃緒申鐃緒申鐃叔緒申鐃緒申鮓困蕕刻申鐃緒申箸鐃緒申任鐃緒申襦ｏ申鐃銃�鐃緒申鐃祝わ申鐃塾居申鐃緒申鐃祝ワ申鐃獣トわ申鐃緒申鐃緒申鐃粛わ申多鐃緒申鐃循ど￥申鐃緒申鐃緒申硫鐃叔緒申鐃緒申鐃緒申腓�鐃緒申鐃淑る。鐃緒申鐃塾器申略鐃緒申鐃緒申鐃緒申鐃薯するた鐃緒申砲蓮鐃緒申鐃緒申鐃緒申凌鐃緒申佑蓮鐃緒申鐃緒申鐃重�鐃祝もう鐃緒申鐃緒申鐃塾随申鐃粛わ申鐃夙み刻申錣誌申襪随申鐃祝￥申鐃緒申鐃曙か鐃緒申探遒件申潺鐃緒申鐃緒申鐃緒申覆鐃緒申鐃出わ申鐃緒申鐃淑わ申鐃緒申鐃夙わ申廚鐃緒申鐃緒申鐃緒申鐃宿�鐃竣わ申鐃緒申鐃暑。鐃緒申曚匹鐃緒申鐃叔は￥申鐃緒申弔侶鐃緒申鐃� m 鐃緒申 n' 鐃緒申鐃緒申紊駕申鐃緒申鐃緒申鐃緒申鐃緒申蓮鐃�m 鐃緒申 mn' 鐃緒申 md' 鐃祝￥申n' 鐃緒申 mn' 鐃緒申 n'd 鐃夙わ申鐃獣わ申鐃緒申鐃祝￥申鐃緒申鐃曙ぞ鐃緒申飽鐃獣わ申鐃術わ申鐃緒申鐃熟わ申鐃緒申襦ｏ申鐃緒申鐃緒申侶鐃緒申鐃緒申榔鐃緒申鐃� V0 鐃緒申 V4 鐃祝書き刻申鐃殉わ申襦ｏ申鐃熟�鐃塾演算鐃緒申 m 鐃緒申 n' 鐃緒申鐃術わ申鐃緒申呂鐃緒申箸鐃緒申鐃夙￥申鐃緒申鐃緒申鐃塾随申鐃粛わ申 V0 鐃緒申 V4 鐃緒申鐃緒申探遒居申鐃淳ワ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃銃￥申鐃緒申鐃淳わ申鐃祝掛わ申鐃緒申錣居申鐃銃わ申鐃塾居申鐃緒申鐃祝件申未鐃宿緒申鐃緒申鐃緒申鐃処う鐃緒申命鐃緒申鐃暑こ鐃夙になる。V6 鐃塾縁申鐃緒申暴颪�刻申鐃殉わ申襪鰹申箸砲鐃緒申茲�鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃瞬刻申呂鐃緒申譴常申鐃祝￥申鐃縮の演算鐃叔削申鐃緒申鐃術わ申鐃緒申襦ｏ申匹鐃緒申鐃緒申暴颪い討鐃緒申鐃宿�鐃竣わ申鐃緒申鐃暑。鐃緒申鐃獣て￥申鐃淳ルが鐃術わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃叔￥申鐃緒申鐃緒申砲鐃緒申竜鐃緒申鐃緒申呂鐃緒申鐃緒申凌鐃緒申佑髻▲鐃緒申鐃緒申匹砲鐃獣て指種申鐃緒申鐃緒申鐃叔わ申鐃緒申鐃緒申鐃緒申鐃緒申暴颪�わ申鐃夙になわ申里鐃緒申鐃緒申鐃緒申鐃緒申董鐃緒申尊櫃離鐃緒申鐃緒申鐃緒申任蓮鐃緒申鐃緒申鐃緒申凌鐃緒申佑聾鐃緒申砲鐃緒申辰鐃緒申鐃緒申暴颪�わ申鐃緒申鐃粛鰹申呂覆鐃緒申鐃緒申罅刻申蓮鐃緒申討鐃� V0 鐃緒申 V4 鐃祝書かわ申鐃夙思わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃処う鐃緒申鐃緒申法鐃緒申鐃宿は消わ申鐃緒申覆鐃緒申辰鐃緒申鐃緒申箸砲覆鐃塾わ申鐃緒申鐃緒申鐃緒申幣鐃淑ｏ申未鐃緒申覆鐃緒申鐃緒申鐃祝￥申鐃緒申鐃緒申鐃塾随申鐃緒申鐃緒申鐃夙わ申鐃緒申任鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申討留藥誌申鐃緒申箸濆鐃緒せ鐃祝駈申鐃緒申鐃緒申鐃殉では￥申
We see, then, that the whole assemblage of operations requisite for resolving the two above equations of the first degree may be definitely represented in the following table:—
鐃遵記鐃緒申弔琉貅￥申鐃緒申鐃緒申鐃緒申鐃薯くわ申鐃緒申鐃宿�鐃竣わ申鐃緒申鐃銃の演算鐃緒申鵑蚕鐃緒申鐃緒申鐃緒申鐃緒申蕕�鐃祝種申鐃緒申表鐃塾よう鐃緒申表鐃緒申鐃緒申鐃緒申鐃熟わ申鐃緒申鐃緒申鐃順き鐃緒申鐃緒申鐃緒申鐃緒申
In order to diminish to the utmost the chances of error in inscribing the numerical data of the problem, they are successively placed on one of the columns of the mill;then, by means of cards arranged for this purpose, these same numbers are caused to arrange themselves on the requisite columns, without the operator having to give his attention to it; so that his undivided mind may be applied to the simple inscription of these same numbers.
鐃叔わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃塾随申鐃粛デ￥申鐃緒申鐃緒申颪�刻申鐃準こ鐃夙にわ申鐃緒申鐃緒申硫鐃叔緒申鐃緒申鮓困蕕刻申鐃緒申瓠�鐃緒申鐃緒申鐃熟ミワ申留鐃緒申鐃塾ひとつわ申連続鐃緒申鐃緒申鐃瞬わ申鐃緒申襦ｏ申鐃緒申鐃緒申董鐃緒申鐃緒申撻譟種申鐃緒申鐃緒申鐃緒申佞鐃淑э申鐃宿�鐃竣なわ申鐃緒申鐃緒申鐃緒申鐃緒申的鐃塾わ申鐃緒申鐃緒申儖佞鐃緒申譴随申鐃緒申鐃緒申匹砲鐃所、鐃緒申鐃緒申鐃塾随申鐃粛は種申鐃緒申必鐃竣な縁申鐃緒申鐃緒申儖佞鐃緒申鐃暑。鐃緒申鐃緒申痢鐃緒申鐃緒申撻譟種申鐃緒申呂鐃緒申鐃緒申凌鐃緒申佑鐃緒申鐃緒申呂鐃緒申襪鰹申箸鐃緒申貎器申任鐃緒申襦�
According to what has now been explained, we see that the collection of columns of Variables may be regarded as a store of numbers, accumulated there by the mill, and which, obeying the orders transmitted to the machine by means of the cards, pass alternately from the mill to the store and from the store to the mill, that they may undergo the transformations demanded by the nature of the calculation to be performed.
鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申討鐃緒申鐃塾わ申鐃祝わ申辰董鐃緒申竸鐃緒申鐃淑わ申鐃緒申鐃緒申僚鐃緒申泙鐃熟￥申鐃緒申鐃粛わ申鐃叔種申鐃緒申鐃夙みなわ申鐃緒申鐃叔わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃塾随申鐃粛はミワ申鐃緒申鐃緒申鐃緒申譟�鐃緒申鐃緒申鐃宿にわ申蠅鰹申竜鐃緒申鐃緒申鐃緒申鐃緒申鐃曙た命鐃緒申鳳鐃緒申鐃緒申董鐃緒申潺襪�鐃初ス鐃夙ワ申鐃緒申store鐃祝￥申鐃緒申鐃夙ワ申鐃緒申鐃緒申潺鐃舜行わ申鐃処し鐃緒申鐃渋行わ申鐃緒申鐃竣誌申鐃緒申鐃緒申鐃緒申鐃祝わ申辰鐃緒申弋瓩居申鐃緒申鐃術駕申鐃緒申个襦�
Hitherto no mention has been made of the signs in the results, and the machine would be far from perfect were it incapable of expressing and combining amongst each other positive and negative quantities. To accomplish this end, there is, above every column, both of the mill and of the store, a disc, similar to the discs of which the columns themselves consist. According as the digit on this disc is even or uneven, the number inscribed on the corresponding column below it will be considered as positive or negative. This granted, we may, in the following manner, conceive how the signs can be algebraically combined in the machine. When a number is to be transferred from the store to the mill, and vice versa, it will always be transferred with its sign, which will effected by means of the cards, as has been explained in what precedes. Let any two numbers then, on which we are to operate arithmetically, be placed in the mill with their respective signs. Suppose that we are first to add them together;the operation-cards will command the addition:if the two numbers be of the same sign, one of the two will be entirely effaced from where it was inscribed, and will go to add itself on the column which contains the other number;the machine will, during this operation, be able, by means of a certain apparatus, to prevent any movement in the disc of signs which belongs to the column on which the addition is made, and thus the result will remain with the sign which the two given numbers originally had. When two numbers have two different signs, the addition commanded by the card will be changed into a subtraction through the intervention of mechanisms which are brought into play by this very difference of sign. Since the subtraction can only be effected on the larger of the two numbers, it must be arranged that the disc of signs of the larger number shall not move while the smaller of the two numbers is being effaced from its column and subtracted from the other, whence the result will have the sign of this latter, just as in fact it ought to be. The combinations to which algebraical subtraction give rise, are analogous to the preceding. Let us pass on to multiplication. When two numbers to be multiplied are of the same sign, the result is positive;if the signs are different, the product must be negative. In order that the machine may act conformably to this law, we have but to conceive that on the column containing the product of the two given numbers, the digit which indicates the sign of that product has been formed by the mutual addition of the two digits that respectively indicated the signs of the two given numbers;it is then obvious that if the digits of the signs are both even, or both odd, their sum will be an even number, and consequently will express a positive number;but that if, on the contrary, the two digits of the signs are one even and the other odd, their sum will be an odd number, and will consequently express a negative number. In the case of division. instead of adding the digits of the discs, they must be subtracted one from the other, which will produce results analogous to the preceding;that is to say, that if these figures are both even or both uneven, the remainder of this subtraction will be even;and it will be uneven in the contrary case. When I speak of mutually adding or subtracting the numbers expressed by the digits of the signs, I merely mean that one of the sign-discs is made to advance or retrograde a number of divisions equal to that which is expressed by the digit on the other sign-disc. We see, then, from the preceding explanation, that it is possible mechanically to combine the signs of quantities so as to obtain results conformable to those indicated by algebra.
鐃緒申鐃殉では件申未鐃緒申鐃緒申砲弔鐃緒申童鐃緒申擇鐃緒申覆鐃緒申辰鐃緒申鐃緒申鐃緒申竜鐃緒申鐃緒申蓮鐃緒申鐃緒申鐃緒申鐃縮わ申鐃順し表鐃緒申鐃緒申鐃緒申能鐃熟わ申鐃淑わ申鐃緒申鐃緒申鐃緒申任老茲件申憧鐃緒申鐃緒申任呂覆鐃緒申鐃緒申鐃緒申鐃緒申達鐃緒申鐃緒申鐃暑た鐃緒申法鐃緒申鐃緒申肇鐃緒申肇潺鐃塾常申鐃緒申鐃緒申鐃緒申討留鐃緒申鐃塾常申法鐃緒申鐃緒申貅�鐃夙わ申鐃緒申鐃緒申鐃緒申鐃塾わ申同鐃粛の縁申鐃竣わ申鐃瞬わ申鐃緒申鐃緒申鐃塾デワ申鐃緒申鐃緒申鐃塾桁が鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申砲鐃獣て￥申鐃緒申鐃塾縁申鐃緒申暴颪�れた鐃緒申鐃粛はわ申鐃曙ぞ鐃緒申鐃緒申鐃盾し鐃緒申鐃緒申鐃緒申箸澆覆鐃緒申鐃緒申鐃緒申鐃祝わ申蝓�鐃緒申鐃塾わ申鐃緒申鐃緒申如鐃緒申鐃緒申竜鐃緒申鐃緒申鐃緒申鐃醇が鐃宿のよう鐃祝誌申鐃術演算鐃緒申鐃緒申襪�鐃緒申佑鐃緒申襪鰹申箸鐃緒申任鐃緒申襦ｏ申鐃緒申肇鐃緒申鐃緒申鐃淳ワ申愎鐃緒申佑鐃緒申鐃緒申鐃曙た鐃緒申鐃緒申鐃盾し鐃緒申鐃熟わ申鐃塾逆の誌申鐃緒申必鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申襦ｏ申鐃緒申鐃熟ワ申鐃緒申鐃宿にわ申鐃渋行わ申鐃緒申襦ｏ申鐃緒申鐃緒申鐃緒申立鐃縦わ申鐃夙わ申鐃緒申鐃緒申鐃緒申鐃曙た鐃緒申鐃醇々鐃緒申鐃竣誌申鐃緒申圓鐃緒申匹鐃緒申鐃緒申弔凌鐃緒申佑癲�鐃緒申鐃曙ぞ鐃緒申鐃緒申鐃緒申醗鐃緒申縫潺鐃緒申鐃緒申鐃緒申屬鐃緒申箸鐃緒申襦ｏ申能鐃祝わ申鐃緒申鐃渋�鐃緒申鐃淑わ申弌鐃緒申藥誌申鐃緒申鐃緒申匹浪短鐃緒申鐃縮随申瓩刻申襦ｏ申鐃縦の随申鐃粛わ申鐃緒申罎�同鐃緒申鐃叔わ申鐃緒申弌鐃緒申鐃緒申里鐃緒申鐃緒申里劼箸弔牢鐃緒申鐃緒申暴颪�わ申討鐃緒申鐃緒申鐃曙か鐃緒申探遒居申鐃暑。鐃緒申鐃緒申鐃銃￥申鐃盾う鐃緒申鐃緒申鐃緒申鐃瞬号が鐃書かわ申討鐃緒申鐃緒申鐃緒申鵬短鐃緒申鐃緒申鐃暑。鐃緒申鐃塾緒申鐃緒申鐃塾間￥申鐃緒申鐃塾居申鐃緒申鐃熟￥申鐃淑わ申蕕�鐃緒申鐃緒申鐃瞬にわ申蝓�鐃獣誌申鐃緒申鐃渋行わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃醇が動鐃緒申鐃塾わ申鐃緒申鐃緒申鐃暑こ鐃夙わ申鐃叔わ申鐃暑。鐃緒申弔凌鐃緒申佑鐃緒申磴�鐃緒申鐃緒申鐃緒申辰討鐃緒申鐃緒申鐃緒申蓮鐃緒申泙鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申琉磴わ申砲鐃緒申導鐃緒申鐃緒申鐃緒申覽￥申鐃緒申硫鐃緒申鐃緒申砲鐃獣て￥申鐃緒申鐃緒申鐃宿にわ申辰道惻鐃緒申鐃緒申譴随申短鐃縮随申鐃熟醐申鐃緒申命鐃緒申鐃緒申儿鐃緒申鐃緒申鐃暑。鐃緒申鐃緒申鐃緒申鐃緒申弔里鐃緒申鐃緒申鐃緒申腓�鐃緒申鐃緒申鐃塾随申鐃粛にのわ申有鐃緒申鐃淑ので￥申鐃緒申鐃緒申鐃緒申鐃緒申鐃粛わ申鐃緒申鐃塾縁申鐃曙か鐃緒申探遒居申譟�鐃盾う鐃緒申鐃緒申鐃塾随申鐃粛わ申鐃初減鐃緒申鐃緒申鐃緒申屬蓮鐃緒申腓�鐃緒申鐃緒申鐃粛わ申鐃緒申鐃薯示わ申鐃緒申鐃竣わ申動鐃緒申鐃淑わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃初、鐃緒申鐃順う鐃宿実際にわ申鐃緒申鐃緒申鐃緒申戮鐃緒申未蝓�鐃緒申未鐃緒申腓�鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申弔鐃緒申箸砲覆襦ｏ申鐃緒申鐃緒申両鐃緒申發鰹申鐃緒申同鐃粛となる。鐃処算鐃祝つわ申鐃銃考わ申鐃暑。鐃楯わ申鐃緒申錣居申鐃緒申鐃緒申弔凌鐃緒申佑鐃緒申鐃醇が同鐃緒申鐃緒申鐃熟件申未鐃緒申鐃緒申砲覆襦ｏ申鐃醇が鐃純う鐃緒申鐃緒申鐃術わ申鐃緒申砲覆襦ｏ申鐃緒申竜鐃緒申鐃緒申鐃緒申鐃緒申竜鐃渋э申暴鐃緒申辰鐃銃逸申遒刻申襪随申鐃祝￥申与鐃緒申鐃緒申譴随申鐃縦の随申鐃粛わ申鐃術わ申鐃叔種申鐃緒申鐃緒申鐃緒申任蓮鐃緒申僂鐃緒申鐃緒申鮗┐鐃緒申鐃熟￥申鐃緒申弔凌鐃緒申鐃緒申鐃緒申鐃緒申鮗┐鐃緒申鐃緒申鐃緒申鐃重�鐃淑加誌申鐃祝わ申辰萄鐃緒申鐃緒申箸澆覆鐃緒申覆鐃緒申鐃出なわ申覆鐃緒申鐃緒申鐃緒申侶紊�両鐃緒申鐃夙わ申鐃緒申鐃緒申鐃緒申發件申鐃緒申牢鐃緒申鐃緒申鐃獣わ申鐃緒申鐃熟￥申鐃緒申鐃塾刻申弯鐃緒申篭鐃緒申鐃緒申砲覆蝓�鐃緒申鐃緒申鐃緒申鐃緒申表鐃緒申鐃緒申鐃暑。鐃緒申鐃緒申鐃緒申鐃緒申鐃出常申的鐃祝￥申鐃緒申弔鐃緒申鐃緒申侶紊�鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃叔もう鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申両鐃順、鐃緒申鐃塾刻申弯鐃緒申牢鐃緒申鐃祝なり、鐃緒申鐃緒申鐃緒申鐃宿緒申鐃緒申鐃緒申襦ｏ申鐃緒申鐃緒申両鐃順、鐃緒申鐃塾件申留鐃緒申廚旅鐃竣わ申鐃緒申鐃緒申法鐃緒申鐃緒申鐃緒申鐃緒申鐃盾う鐃緒申鐃緒申鐃薯減誌申鐃緒申鐃淑わ申鐃緒申个鐃緒申鐃緒申覆鐃緒申鐃緒申鐃緒申鐃熟乗算鐃塾常申鐃緒申同鐃粛の件申未砲覆襦ｏ申鐃緒申鐃緒申侶紊�両鐃緒申鐃夙わ申鐃緒申鐃緒申鐃緒申發件申鐃緒申牢鐃緒申鐃塾常申隋�鐃緒申鐃塾削申鐃塾随申鐃緒申鐃熟駈申鐃緒申鐃祝なる。鐃春の常申鐃熟￥申鐃緒申鐃塾削申鐃熟器申鐃緒申砲覆襦ｏ申鐃緒申鐃宿緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申澆鵬短鐃緒申發件申鐃緒申聾鐃緒申鐃緒申箸鐃緒申鐃緒申里蓮鐃緒申鐃緒申鐃緒申廚里劼箸弔蝋鐃殉れた鐃緒申鐃緒申鐃緒申鐃緒申鐃淑￥申鐃緒申鐃準さ鐃緒申鐃緒申茲�鐃祝緒申鐃緒申討鐃緒申襦ｏ申鐃緒申鐃緒申討鐃緒申譴�鐃緒申他鐃緒申鐃緒申鐃緒申鐃竣にわ申鐃宿緒申鐃緒申鐃緒申鐃緒申鐃塾わ申同鐃緒申鐃緒申鐃緒申箸鐃緒申鐃緒申鐃緒申鐃緒申里鐃緒申箸鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申蕁�鐃緒申鐃緒申納鐃緒申鐃緒申譴随申鐃塾に緒申鐃獣わ申鐃緒申未鐃緒申鐃緒申鐃処う鐃祝￥申鐃緒申鐃緒申的鐃緒申鐃緒申鐃塾随申鐃緒申鐃順す鐃暑こ鐃夙わ申鐃緒申能鐃叔わ申鐃緒申箸鐃緒申鐃緒申里鐃淑�鐃緒申鐃暑。
The machine is not only capable of executing those numerical calculations which depend on a given algebraical formula, but it is also fitted for analytical calculations in which there are one or several variables to be considered. It must be assumed that the analytical expression to be operated on can be developed according to powers of the variable, or according to determinate functions of this same variable, such as circular functions, for instance;and similarly for the result that is to be attained. If we then suppose that above the columns of the store, we have inscribed the powers or the functions of the variable, arranged according to whatever is the prescribed law of development, the coefficients of these several terms may be respectively placed on the corresponding column below each. In this manner we shall have a representation of an analytical development;and, supposing the position of the several terms composing it to be invariable, the problem will be reduced to that of calculating their coefficients according to the laws demanded by the nature of the question. In order to make this more clear, we shall take the following very simple example, in which we are to multiply (a + bx1) by (A + B cos1x). We shall begin by writing x0 , x1, cos0x, cos1x, above the columns V0, V1, V2, V3; then since, from the form of the two functions to be combined, the terms which are to compose the products will be of the following nature, x0鐃緒申cos0x, x0鐃緒申cos1x, x1鐃緒申cos0x, x1鐃緒申cos1x, these will be inscribed above the columns V4, V5, V6, V7. The coefficients of x0, x1, cos0x, cos1x being given, they will, by means of the mill, be passed to the columns V0, V1, V2 and V3. Such are the primitive data of the problem. It is now the business of the machine to work out its solution, that is, to find the coefficients which are to be inscribed on V4, V5, V6, V7. To attain this object, the law of formation of these same coefficients being known, the machine will act through the intervention of the cards, in the manner indicated by the following table:—
鐃緒申鐃塾居申鐃緒申鐃熟￥申鐃緒申鐃緒申鐃緒申与鐃緒申鐃緒申譴随申鐃緒申鐃塾醐申鐃緒申鐃祝緒申鐃獣わ申鐃緒申鐃粛計誌申鐃緒申孫圓鐃緒申鐃叔緒申呂鐃緒申鐃緒申任呂覆鐃緒申鐃緒申劼箸弔發件申鐃緒申呂鐃緒申鐃緒申弔鐃緒申鐃緒申竸鐃緒申鐃緒申慮鐃緒申鐃緒申鐃緒申鐃緒申的鐃淑計誌申鐃祝わ申適鐃順し鐃銃わ申鐃暑。鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃熟種申鐃熟￥申鐃術随申鐃巡三鐃術関随申鐃塾よう鐃緒申有鐃渋関随申鐃緒申determinate functions鐃祝の種申鐃緒申鐃祝縁申鐃緒申鐃緒申展鐃緒申鐃緒申鐃暑こ鐃夙わ申鐃叔わ申鐃暑。鐃緒申鐃緒申鐃緒申鐃緒申茲�鐃夙わ申鐃銃わ申鐃緒申鐃縮につわ申鐃銃わ申同鐃粛でわ申鐃暑。鐃緒申鐃夙ワ申鐃塾縁申鐃緒申両鐃祝￥申鐃緒申鐃緒申鐃盾し鐃緒申鐃熟￥申鐃宿のよう鐃淑わ申里任癲�鐃緒申鐃所さ鐃曙た展鐃緒申鐃緒申則鐃祝緒申鐃獣わ申鐃術意わ申鐃曙た鐃舜随申鐃緒申鐃術随申鐃薯記わ申鐃夙わ申鐃処う鐃緒申鐃緒申鐃緒申鐃塾刻申侶鐃緒申鐃緒申蓮鐃緒申弍鐃緒申鐃緒申鐃緒申鐃緒申暴颪�わ申襦ｏ申鐃緒申鐃緒申鐃祝￥申砲鐃緒申鐃緒申鐃重醐申鐃緒申鐃宿緒申鐃祝￥申鐃緒申鐃緒申襪鰹申箸砲覆襦ｏ申鐃緒申鐃緒申董鐃緒申鐃緒申鐃緒申旅鐃塾逸申鐃瞬わ申鐃緒申鐃術になわ申茲�鐃祝刻申鐃緒申鐃緒申鐃緒申弌鐃緒申鐃緒申鐃熟￥申鐃緒申鐃緒申鐃緒申鐃緒申鐃祝わ申鐃緒申弋瓩居申鐃暑規則鐃祝緒申鐃獣わ申鐃緒申鐃緒申鐃緒申彁鐃緒申鐃緒申襪鰹申箸亡憤弉鐃緒申鐃緒申鐃暑。鐃盾う鐃緒申鐃緒申分鐃緒申鐃緒申笋刻申鐃緒申鐃緒申襪随申鐃祝￥申鐃緒申鐃緒申鐃緒申鐃祝器申単鐃緒申鐃純、(a + bx1) 鐃緒申 (A + B cos1x) 鐃緒申櫃鐃緒申襪鰹申箸鐃緒申鐃遵げ鐃暑。鐃緒申鐃緒申 V0鐃緒申V1鐃緒申V2鐃緒申V3 鐃塾常申法鐃�x0鐃緒申x1鐃緒申cos0x鐃緒申cos1x 鐃緒申颪�わ申鐃夙わ申鐃緒申呂鐃暑。鐃緒申腓居申鐃緒申鐃緒申弔隆愎鐃緒申侶鐃緒申鐃緒申鐃緒申蕁�鐃術の刻申麓鐃緒申亮鐃緒申鐃夙なる。x0鐃緒申cos0x鐃緒申x0鐃緒申cos1x鐃緒申x1鐃緒申cos0x鐃緒申x1鐃緒申cos1x 鐃緒申鐃緒申鐃熟縁申鐃緒申 V4鐃緒申V5鐃緒申V6鐃緒申V7 鐃塾常申傍鐃緒申鐃緒申鐃暑。鐃緒申鐃緒申鐃夙わ申鐃緒申 x0鐃緒申x1鐃緒申cos0x鐃緒申 cos1x 鐃緒申与鐃緒申鐃緒申譟�鐃緒申鐃緒申鐃熟ミワ申砲鐃所、V0鐃緒申V1鐃緒申V2鐃緒申V3 鐃緒申鐃熟わ申鐃緒申襦ｏ申鐃緒申鐃緒申鐃緒申鐃緒申鐃塾器申鐃緒申的鐃淑デ￥申鐃緒申鐃夙なる。鐃緒申鐃緒申鐃緒申鐃初が鐃緒申鐃塾居申鐃緒申鐃塾仕誌申鐃叔わ申鐃緒申鐃塾計誌申鐃叔わ申鐃暑。鐃緒申鐃緒申鐃� V4鐃緒申V5鐃緒申V6鐃緒申V7 鐃祝居申鐃緒申鐃曙た鐃緒申鐃緒申鐃薯見つわ申鐃暑こ鐃夙わ申鐃緒申鐃緒申鐃塾￥申鐃緒申鐃緒申鐃緒申里鐃緒申討鐃緒申鐃銃縁申鐃緒申鐃緒申鐃緒申旅鐃緒申鐃緒申鐃渋э申箸鐃緒申鐃緒申鐃重�鐃緒申鐃緒申達鐃緒申鐃暑た鐃緒申法鐃緒申鐃緒申竜鐃緒申鐃緒申蓮鐃緒申鐃緒申鐃宿緒申房鐃緒申鐃緒申鐃祝￥申如鐃緒申鐃緒申鐃緒申匹鐃緒申鐃緒申砲鐃緒申動鐃庶す鐃緒申鐃�鐃順き鐃緒申鐃緒申鐃緒申)
It will now be perceived that a general application may be made of the principle developed in the preceding example, to every species of process which it may be proposed to effect on series submitted to calculation. It is sufficient that the law of formation of the coefficients be known, and that this law be inscribed on the cards of the machine, which will then of itself execute all the calculations requisite for arriving at the proposed result. If, for instance, a recurring series were proposed, the law of formation of the coefficients being here uniform, the same operations which must be performed for one of them will be repeated for all the others;there will merely be a change in the locality of the operation, that is, it will be performed with different columns. Generally, since every analytical expression is susceptible of being expressed in a series ordered according to certain functions of the variable, we perceive that the machine will include all analytical calculations which can be definitively reduced to the formation of coefficients according to certain laws, and to the distribution of these with respect to the variables.
鐃緒申鐃殉までわ申鐃緒申鐃緒申鐃緒申展鐃緒申鐃緒申鐃曙た鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃重�鐃淑ワ申鐃竣リケ鐃緒申鐃緒申鐃緒申鐃舜考誌申鐃緒申覆鐃暑。鐃緒申鐃緒申鐃塾刻申鐃緒申鐃緒申則鐃緒申分鐃緒申鐃緒申鐃緒申匹鐃緒申箸鐃緒申鐃緒申鐃緒申箸砲覆襦ｏ申鐃緒申鐃緒申董鐃緒申鐃緒申竜鐃渋э申呂鐃緒申竜鐃緒申鐃緒申離鐃緒申鐃緒申匹傍鐃緒申鐃緒申鐃暑。鐃緒申鐃塾居申鐃緒申鐃熟￥申鐃緒申鐃曙か鐃初、鐃緒申鐃夙で出わ申鐃緒申鐃緒申未忙鐃暑た鐃緒申鐃宿�鐃竣わ申鐃緒申鐃銃の計誌申鐃緒申孫圓鐃緒申襦ｏ申磴�鐃出￥申鐃循環わ申鐃緒申鐃熟�鐃塾計誌申鐃緒申鐃藷示わ申鐃曙た鐃夙わ申鐃緒申函鐃緒申鐃緒申鐃緒申旅鐃緒申鐃緒申鐃渋э申楼鐃緒申鐃叔￥申鐃緒申鐃緒申鐃緒申里劼箸弔里鐃緒申鐃緒申孫圓鐃緒申覆鐃緒申鐃出わ申鐃緒申鐃淑わ申鐃緒申鐃緒申鐃塾なわ申鐃塾ひとつでわ申鐃暑、同鐃緒申鐃初算鐃緒申鐃緒申他鐃塾わ申鐃駿てのわ申鐃緒申坊鐃緒申鐃緒申屬鐃緒申鐃暑こ鐃夙になる。鐃初算鐃塾常申蠅�鐃術わ申鐃緒申鐃緒申鐃叔￥申鐃純う鐃緒申鐃緒申砲鐃緒申鐃緒申胴圓鐃緒申鐃夙わ申鐃緒申鐃緒申鐃夙わ申鐃緒申鐃縮常、鐃緒申鐃緒申鐃緒申鐃緒申呂凌鐃緒申鐃緒申蓮鐃緒申鐃緒申鐃緒申鐃緒申鐃塾関随申鐃緒申鐃術随申鐃祝緒申鐃獣わ申鐃初算鐃塾緒申鐃緒申砲鐃獣わ申表鐃緒申鐃緒申鐃緒申襪鰹申箸鐃緒申鐃銃わ申鐃緒申里如鐃緒申鐃緒申竜鐃緒申鐃緒申蓮鐃緒申鐃緒申蕕�鐃祝￥申鐃緒申鐃暑規則鐃祝緒申鐃獣わ申鐃緒申鐃緒申鐃塾刻申鐃緒申鐃祝器申略鐃緒申鐃叔わ申鐃緒申鐃緒申鐃銃の駕申鐃熟計誌申鐃薯、わ申鐃緒申鐃緒申鐃銃に含む。
We may deduce the following important consequence from these explanations, viz. that since the cards only indicate the nature of the operations to be performed, and the columns of Variables with which they are to be executed, these cards will themselves possess all the generality of analysis, of which they are in fact merely a translation. We shall now further examine some of the difficulties which the machine must surmount, if its assimilation to analysis is to be complete. There are certain functions which necessarily change in nature when they pass through zero or infinity, or whose values cannot be admitted when they pass these limits. When such cases present themselves, the machine is able, by means of a bell, to give notice that the passage through zero or infinity is taking place, and it then stops until the attendant has again set it in action for whatever process it may next be desired that it shall perform. If this process has been foreseen, then the machine, instead of ringing, will so dispose itself as to present the new cards which have relation to the operation that is to succeed the passage through zero and infinity. These new cards may follow the first, but may only come into play contingently upon one or other of the two circumstances just mentioned taking place.
鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃初次鐃塾緒申鐃竣な件申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申襪鰹申箸鐃緒申任鐃緒申襪�鐃盾し鐃緒申覆鐃緒申鐃緒申鐃緒申覆鐃緒申鐃緒申鐃緒申鐃緒申鐃宿は実行わ申鐃緒申鐃初算鐃緒申鐃緒申鐃緒申鐃夙￥申鐃緒申鐃曙が鐃渋行わ申鐃緒申鐃緒申竸鐃緒申留鐃緒申鐃緒申鐃緒申蠅刻申鐃緒申鐃緒申鐃淑ので￥申鐃緒申鐃緒申鐃塾ワ申鐃緒申鐃宿はわ申鐃曙自鐃夙￥申鐃緒申鐃熟わ申鐃緒申鐃緒申分鐃緒申鐃粛�鐃緒申鐃暑こ鐃夙になる。鐃緒申鐃緒申鐃熟実際のとわ申鐃緒申単鐃淑わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃塾居申鐃緒申鐃舜の駕申鐃熟の吸種申鐃緒申鐃淑わ申鐃緒申鐃緒申鐃塾でわ申鐃緒申弌鐃緒申鐃緒申譴�鐃緒申鐃緒申鐃緒申鐃緒申鐃淑わ申鐃緒申个鐃緒申鐃緒申覆鐃緒申鐃緒申鐃緒申鐃緒申弔鐃緒申虜鐃緒申鐃祝つわ申鐃銃考わ申鐃銃みる。鐃緒申鐃盾し鐃緒申鐃緒申無鐃緒申鐃緒申鐃緒申未鐃緒申鐃緒申鐃盾し鐃緒申鐃熟極限わ申鐃縮わ申鐃緒申傍鐃緒申討鐃緒申襪鰹申箸鐃緒申任鐃緒申覆鐃緒申佑鐃緒申未鐃緒申鐃祝は￥申鐃旬種申的鐃緒申鐃術刻申鐃緒申必鐃竣となる、鐃緒申鐃暑い鐃緒申鐃縦わ申鐃塾関随申鐃緒申鐃緒申鐃暑。鐃緒申鐃塾よう鐃淑ワ申鐃緒申鐃緒申鐃緒申与鐃緒申鐃緒申譴随申鐃緒申蓮鐃緒申鐃緒申竜鐃緒申鐃緒申鐃緒申鐃緒申鐃縮居申鐃緒申鐃緒申鐃縮過が鐃緒申鐃獣わ申鐃緒申鐃夙わ申戰鐃祝わ申鐃駿告し￥申鐃緒申鐃緒申鐃銃￥申鐃縦わ申鐃祝実行わ申鐃緒申必鐃竣のわ申鐃暑何鐃緒申鐃緒申鐃緒申僚鐃緒申鐃緒申鐃緒申討咼鐃緒申奪箸鐃緒申鐃緒申泙任鐃緒申鐃淳わ申鐃暑こ鐃夙わ申鐃叔わ申鐃暑。鐃緒申鐃塾ワ申鐃初ー鐃緒申予鐃塾わ申鐃緒申鐃緒申里覆鐃出￥申鐃緒申鐃塾居申鐃緒申鐃熟￥申鐃駿常申鐃緒申弔蕕刻申鐃緒申鐃祝￥申鐃緒申鐃緒申無鐃緒申鐃緒申鐃緒申眠瓩件申鐃緒申鐃塾緒申鐃緒申鐃祝器申連鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃宿わ申与鐃緒申鐃緒申茲�鐃祝￥申鐃緒申鐃緒申鐃緒申鐃緒申屬鐃緒申襪鰹申箸砲覆襦ｏ申鐃緒申鐃緒申凌鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申匹郎能鐃塾わ申里鐃渋鰹申鐃緒申鐃緒申發件申鐃淑わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃祝￥申鐃緒申曚表劼戮鐃緒申鐃縦の常申鐃瞬のどわ申鐃初か鐃祝なっわ申鐃緒申鐃緒申鐃夙わ申鐃緒申鐃緒申鐃夙もあ鐃緒申鐃緒申鐃暑。
Let us consider a term of the form abn; since the cards are but a translation of the analytical formula, their number in this particular case must be the same, whatever be the value of n;that is to say, whatever be the number of multiplications required for elevating b to the nth power (we are supposing for the moment that n is a whole number). Now, since the exponent n indicates that b is to be multiplied n times by itself, and all these operations are of the same nature, it will be sufficient to employ one single operation-card, viz. that which orders the multiplication.
abn 鐃夙わ申鐃緒申鐃緒申鐃塾刻申鐃粛わ申鐃暑。鐃緒申鐃緒申鐃宿は駕申鐃熟の醐申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申里任發�鐃暑か鐃初、鐃緒申鐃緒申鐃緒申鐃緒申離鐃緒申鐃緒申鐃緒申砲鐃緒申鐃緒申討鐃緒申凌鐃緒申佑鐃銃縁申鐃緒申任覆鐃緒申鐃出わ申鐃緒申鐃淑わ申鐃緒申鐃緒申鐃緒申鐃�n鐃夙わ申鐃暑。鐃緒申鐃淑わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃�b 鐃緒申 n 鐃緒申鐃塾指随申鐃祝上げ鐃暑た鐃緒申鐃宿�鐃竣となわ申荵誌申硫鐃緒申鐃叔わ申鐃緒申丙鐃緒申鐃� n 鐃緒申鐃緒申鐃緒申鐃夙みなわ申鐃祝わ申鐃緒申鐃叔￥申鐃舜随申 n 鐃熟￥申b 鐃緒申 n 鐃藷、種申鐃夙で乗算鐃緒申鐃暑こ鐃夙を示わ申鐃銃わ申鐃暑。鐃緒申鐃緒申鐃緒申留藥誌申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃銃縁申鐃緒申任覆里如鐃緒申鐃緒申鐃塾演算鐃緒申鐃緒申鐃宿わ申鐃術意わ申鐃緒申鐃緒申鐃緒申鐃緒申匹鐃緒申鐃緒申鐃緒申覆鐃緒申鐃緒申鐃処算鐃塾ワ申鐃緒申鐃宿でわ申鐃暑。
But when n is given for the particular case to be calculated, it will be further requisite that the machine limit the number of its multiplications according to the given values. The process may be thus arranged. The three numbers a, b and n will be written on as many distinct columns of the store;we shall designate them V0, V1, V2;the result abn will place itself on the column V3. When the number n has been introduced into the machine, a card will order a certain registering-apparatus to mark (n-1), and will at the same time execute the multiplication of b by b. When this is completed, it will be found that the registering-apparatus has effaced a unit, and that it only marks (n-2);while the machine will now again order the number b written on the column V1 to multiply itself with the product b2 written on the column V3, which will give b3. Another unit is then effaced from the registering-apparatus, and the same processes are continually repeated until it only marks zero. Thus the number bn will be found inscribed on V3, when the machine, pursuing its course of operations, will order the product of bn by a;and the required calculation will have been completed without there being any necessity that the number of operation-cards used should vary with the value of n. If n were negative, the cards, instead of ordering the multiplication of a by bn, would order its division;this we can easily conceive, since every number, being inscribed with its respective sign, is consequently capable of reacting on the nature of the operations to be executed. Finally, if n were fractional, of the form p/q, an additional column would be used for the inscription of q, and the machine would bring into action two sets of processes, one for raising b to the power p, the other for extracting the qth root of the number so obtained.
鐃盾し n 鐃緒申鐃緒申鐃緒申鐃塾随申鐃塾常申鐃緒申彁鐃緒申鐃緒申鐃処う鐃緒申鐃緒申鐃熟わ申鐃緒申鐃塾なわ申弌鐃緒申鐃緒申呂鐃緒申鐃緒申荵誌申硫鐃緒申鐃緒申鐃緒申鐃渋わ申鐃緒申鐃宿加居申能鐃緒申必鐃竣とわ申鐃暑。鐃緒申鐃塾緒申鐃緒申鐃熟種申鐃塾よう鐃祝緒申鐃緒申鐃緒申鐃緒申襪�鐃盾し鐃緒申覆鐃緒申鐃緒申鐃緒申弔凌鐃緒申鐃� a鐃緒申b鐃緒申n 鐃熟￥申鐃緒申鐃緒申鐃銃縁申鐃緒申琉曚覆襯刻申肇鐃緒申留鐃緒申鐃祝書かわ申襦ｏ申罅刻申蓮鐃緒申鐃緒申鐃緒申鐃�V0鐃緒申V1鐃緒申V2鐃夙称わ申鐃暑。鐃緒申未鐃� abn 鐃緒申 V3 鐃祝書かわ申襦ｏ申鐃緒申竜鐃緒申鐃緒申某鐃緒申鐃� n 鐃緒申鐃緒申鐃熟わ申鐃曙た鐃緒申鐃緒申鐃緒申鐃緒申離鐃緒申鐃緒申匹鐃緒申鐃緒申覽�録鐃緒申鐃瞬￥申registering-apparatus鐃祝わ申 (n-1) 鐃緒申録鐃緒申鐃緒申茲μ随申瓩刻申襦ｏ申鐃緒申鐃緒申董鐃緒申鐃緒申離鐃緒申鐃緒申匹鐃銃縁申鐃緒申鐃� b 鐃緒申 b 鐃塾乗算鐃緒申孫圓鐃緒申襦ｏ申鐃緒申譴�鐃緒申了鐃緒申鐃緒申函鐃緒申鐃熟随申鐃緒申屬鐃緒申鐃祝ットわ申探遒件申鐃緒申里鐃淑�鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申董鐃緒申鐃緒申鐃緒申鐃� (n-2) 鐃緒申録鐃緒申鐃緒申鐃緒申鐃緒申任鐃緒申襦Ｆ縁申鐃緒申法鐃緒申鐃緒申竜鐃緒申鐃緒申郎討鐃� V1 鐃塾縁申鐃緒申暴颪�れた鐃緒申鐃緒申 b 鐃祝￥申V3 鐃祝書かれた鐃緒申 b2 鐃緒申茲醐申鐃処う命鐃潤す鐃暑。鐃緒申鐃緒申鐃銃￥申鐃緒申鐃緒申鐃� b3 鐃緒申与鐃緒申鐃暑。鐃緒申鐃曙か鐃初、鐃盾う鐃述とつのワ申縫奪箸鐃緒申鐃熟随申鐃緒申屬鐃緒申鐃獣去さ鐃緒申襦ｏ申鐃緒申鐃緒申鐃銃縁申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃熟随申鐃緒申屬離鐃祝ットわ申鐃緒申鐃祝なわ申泙之鐃緒申鐃緒申屬鐃緒申鐃暑。鐃緒申鐃塾よう鐃祝わ申鐃銃￥申鐃緒申鐃緒申 bn 鐃緒申 V3 鐃祝書かわ申襦ｏ申鐃緒申竜鐃緒申鐃緒申禄鐃緒申鐃緒申鐃渋鰹申鐃� bn 鐃緒申 a 鐃緒申茲醐申鐃処う命鐃潤す鐃暑。鐃緒申鐃緒申鐃銃￥申鐃緒申鐃緒申 n 鐃緒申同鐃緒申鐃緒申鐃緒申鐃塾ワ申鐃緒申鐃緒申鐃緒申鐃緒申鐃宿�鐃竣とわ申鐃暑こ鐃夙なわ申鐃緒申必鐃竣な計誌申鐃熟器申了鐃緒申鐃暑こ鐃夙になる。鐃盾し鐃緒申n 鐃緒申鐃緒申任鐃緒申鐃出￥申鐃緒申鐃緒申鐃宿わ申 a 鐃緒申 bn 鐃緒申茲醐申鐃緒申鐃緒申鐃祝￥申鐃緒申鐃処う鐃緒申命鐃緒申鐃暑こ鐃夙になる。鐃緒申鐃緒申牢鐃獣縁申鐃淑�鐃緒申鐃暑こ鐃夙わ申鐃緒申鐃淑わ申鐃淑わ申弌鐃緒申弍鐃緒申鐃緒申鐃緒申鐃緒申鐃春わ申鐃緒申鐃曙た鐃緒申鐃熟どわ申鐃淳な￥申鐃渋行わ申鐃緒申藥誌申鐃緒申鐃緒申鐃緒申忘鐃緒申僂鐃緒申襪鰹申箸鐃緒申任鐃緒申襪�鐃緒申鐃緒申鐃緒申埜鐃祝￥申n 鐃緒申 p/q 鐃夙わ申鐃緒申鐃緒申鐃塾常申鐃緒申鐃塾常申鐃熟￥申鐃述とわ申余分鐃淑縁申鐃緒申鐃夙っわ申 q 鐃緒申颪�刻申鐃準、鐃緒申鐃緒申鐃銃￥申鐃緒申鐃緒申鐃緒申鐃緒申鐃夙の緒申鐃緒申鐃緒申圓鐃緒申鐃緒申箸砲覆襦ｏ申劼箸弔鐃� b 鐃緒申 p 鐃処、鐃盾う鐃述とつはわ申鐃緒申鐃緒申鐃緒申鐃曙た鐃緒申鐃緒申 q 鐃処根鐃叔わ申鐃暑。
Again, it may be required, for example, to multiply an expression of the form axm+bxn by another Axp+Bxq, and then to reduce the product to the least number of terms, if any of the indices are equal. The two factors being ordered with respect to x, the general result of the multiplication would be Aaxm+p+Abxn+p+Baxm+q+Bbxn+q. Up to this point the process presents no difficulties;but suppose that we have m=p and n=q, and that we wish to reduce the two middle terms to a single one (Ab+Ba)xm+q. For this purpose, the cards may order m+q and n+p to be transferred into the mill, and there subtracted one from the other;if the remainder is nothing, as would be the case on the present hypothesis, the mill will order other cards to bring to it the coefficients Ab and Ba, that it may add them together and give them in this state as a coefficient for the single term xn+p=xm+q.
鐃銃び￥申axm+bxn 鐃緒申 Axp+Bxq 鐃緒申茲醐申董鐃緒申發件申鐃緒申討了愎鐃緒申鐃銃縁申鐃緒申覆鐃出￥申鐃術わ申脳鐃緒申旅鐃緒申鐃祝醐申鐃緒申鐃暑こ鐃夙わ申鐃緒申鮗┐鐃宿�鐃竣わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃縦わ申鐃緒申鐃叔わ申 x 鐃祝わ申鐃緒申鐃緒申鐃春わ申鐃緒申函鐃緒申鐃緒申両荵誌申琉鐃緒申鐃重�鐃淑件申未鐃� Aaxm+p+Abxn+p+Baxm+q+Bbxn+q 鐃夙なる。鐃緒申鐃緒申鐃殉での緒申鐃緒申鐃緒申鐃書しわ申鐃夙わ申鐃緒申鐃緒申無鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申m=p 鐃緒申 n=q 鐃夙わ申鐃緒申鐃緒申錣�鐃緒申鐃緒申箸鐃緒申襦ｏ申鐃緒申了鐃緒申鐃緒申羶器申鐃緒申鐃緒申鐃緒申弔砲泙箸瓩随申鐃緒申鐃� (Ab+Ba)xm+q 鐃竣わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申的鐃塾わ申鐃緒申法鐃緒申鐃緒申鐃緒申匹鐃� m+q 鐃緒申 n+p 鐃緒申潺鐃緒申鐃緒申鐃所、鐃緒申鐃緒申鐃叔逸申鐃緒申鐃緒申鐃緒申發�鐃緒申鐃緒申鐃薯減わ申鐃緒申茲μ随申瓩刻申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃淳の駕申鐃緒申里茲�鐃祝￥申鐃緒申鐃緒申鐃塾件申未鐃緒申鐃緒申覆鐃出￥申鐃淳ワ申鐃緒申未離鐃緒申鐃緒申匹坊鐃緒申鐃� Ab 鐃緒申 Ba 鐃緒申鐃緒申辰討鐃緒申鐃処う鐃舜種申鐃緒申鐃暑。鐃緒申鐃緒申鐃緒申足鐃緒申鐃緒申錣誌申董鐃獣縁申鐃塾刻申 xn+p=xm+q 鐃塾件申鐃緒申鐃祝わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃�
This example illustrates how the cards are able to reproduce all the operations which intellect performs in order to attain a determinate result, if these operations are themselves capable of being precisely defined.
鐃緒申鐃緒申鐃緒申蓮鐃緒申鐃緒申里飽鐃縮ｏ申鐃緒申鐃夙わ申鐃緒申鐃緒申分鐃緒申鐃緒申藥誌申任鐃緒申鐃出￥申鐃緒申鐃緒申鐃宿わ申鐃宿のよう鐃祝わ申鐃銃￥申鐃緒申鐃所さ鐃曙た鐃緒申未暴个鐃緒申鐃緒申鐃祝￥申鐃緒申鐃銃の演算鐃緒申鐃緒申鐃緒申鐃緒申発鐃緒申鐃緒申鐃暑か鐃薯示わ申鐃緒申里鐃緒申鐃�
Let us now examine the following expression:—
which we know becomes equal to the ratio of the circumference to the diameter, when n is infinite. We may require the machine not only to perform the calculation of this fractional expression, but further to give indication as soon as the value becomes identical with that of the ratio of the circumference to the diameter when n is infinite, a case in which the computation would be impossible. Observe that we should thus require of the machine to interpret a result not of itself evident, and that this is not amongst its attributes, since it is no thinking being. Nevertheless, when the cos of n鐃緒申=1/0 has been foreseen, a card may immediately order the substitution of the value of 鐃緒申 (鐃緒申 being the ratio of the circumference to the diameter), without going through the series of calculations indicated. This would merely require that the machine contain a special card, whose office it should be to place the number 鐃緒申 in a direct and independent manner on the column indicated to it. And here we should introduce the mention of a third species of cards, which may be called cards of numbers. There are certain numbers, such as those expressing the ratio of the circumference to the diameter, the Numbers of Bernoulli, &c., which frequently present themselves in calculations. To avoid the necessity for computing them every time they have to be used, certain cards may be combined specially in order to give these numbers ready made into the mill, whence they afterwards go and place themselves on those columns of the store that are destined for them. Through this means the machine will be susceptible of those simplifications afforded by the use of numerical tables. It would be equally possible to introduce, by means of these cards, the logarithms of numbers;
but perhaps it might not be in this case either the shortest or the most appropriate method;
for the machine might be able to perform the same calculations by other more expeditious combinations, founded on the rapidity with which it executes the first four operations of arithmetic.
To give an idea of this rapidity, we need only mention that Mr. Babbage believes he can, by his engine, form the product of two numbers, each containing twenty figures, in three minutes.
鐃緒申鐃緒申鐃叔種申鐃塾種申鐃祝つわ申鐃銃考わ申鐃暑。
n 鐃緒申無鐃緒申鐃緒申砲覆鐃夙￥申鐃緒申鐃塾種申鐃緒申鐃淳種申率鐃緒申鐃緒申鐃緒申鐃緒申鐃淑るこ鐃夙は種申鐃緒申鐃緒申鐃緒申
鐃緒申鐃緒申鐃叔我々鐃熟わ申鐃塾居申鐃緒申鐃祝￥申鐃緒申鐃緒申分鐃緒申鐃緒申鐃緒申彁鐃緒申鐃緒申鐃緒申鐃緒申鐃叔はなわ申鐃緒申鐃緒申鐃緒申某覆鐃叔円種申率鐃緒申同鐃緒申箸澆覆鐃緒申鐃祝なっわ申鐃緒申同鐃緒申鐃緒申鐃塾らせ鐃暑こ鐃夙わ申鐃竣求す鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申尊櫃鐃� n 鐃緒申無鐃緒申鐃緒申離鐃緒申鐃緒申鐃緒申箸鐃緒申鐃緒申里老彁鐃緒申任鐃緒申覆鐃緒申里鐃緒申鐃緒申鐃緒申鐃緒申調鐃駿わ申砲蓮鐃緒申鐃緒申竜鐃緒申鐃緒申鐃緒申鐃緒申蕕�鐃祝種申鐃夙わ申鐃緒申个鐃緒申鐃塾ではなわ申鐃緒申未砲弔鐃緒申堂鐃潤す鐃緒申茲�鐃竣求し鐃淑わ申鐃緒申个鐃緒申鐃緒申覆鐃緒申鐃緒申鐃緒申竜鐃緒申鐃緒申六弭佑鐃緒申鐃渋醐申澆任呂覆鐃緒申里如鐃緒申鐃緒申鐃緒申鐃緒申鐃春とわ申鐃緒申箸鐃緒申鐃緒申任呂覆鐃緒申鐃緒申鐃緒申鐃叔も、n = 1/0 鐃塾誌申鐃緒申 cos 鐃熟醐申鐃縮わ申鐃緒申鐃夙わ申鐃叔わ申鐃緒申 (?)鐃緒申鐃舜種申鐃緒申鐃曙た鐃緒申連鐃塾計誌申鐃緒申圓鐃緒申鐃緒申箸覆鐃緒申鐃緒申鐃緒申鐃緒申匹呂鐃緒申鐃緒申弌弗个榔濕鐃塾�鐃祝わ申鐃瞬わ申鐃緒申鐃緒申鐃緒申茲μ随申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申呂鐃緒申竜鐃緒申鐃緒申鐃緒申鐃緒申未淵鐃緒申鐃緒申匹鐃緒申屬鐃緒申鐃緒申鐃緒申鐃緒申匹鐃緒申鐃緒申鐃緒申鐃緒申任蓮鐃緒申个鐃縦常申椶鐃緒申鐃緒申鐃塾�鐃緒申鐃緒申鐃緒申法鐃叔縁申鐃緒申暴颪�わ申討鐃緒申襦ｏ申鐃緒申鐃緒申如鐃緒申罅刻申六鐃緒申鐃緒申鐃緒申椶離鐃緒申鐃緒申匹砲弔鐃緒申童鐃緒申擇鐃緒申覆鐃緒申鐃出わ申鐃緒申鐃淑わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃塾ワ申鐃緒申鐃宿と呼ばわ申鐃駿わ申鐃緒申里任鐃緒申襦ｏ申戰鐃縮ワ申鐃緒申鐃緒申濕鐃塾�鐃塾よう鐃緒申鐃駿￥申鐃竣誌申鐃緒申鐃術わ申鐃緒申鐃緒申鐃殉っわ申鐃緒申鐃緒申鐃緒申鐃緒申襦ｏ申鐃緒申鐃緒申箸鐃緒申戮鐃緒申鐃緒申彁鐃緒申鐃緒申鐃宿�鐃竣わ申無鐃緒申鐃処う鐃祝￥申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申凌鐃緒申佑箸鐃緒申襪随申鐃祝￥申鐃緒申鐃暑い鐃緒申鐃縦わ申鐃塾ワ申鐃緒申鐃宿わ申潺鐃緒申鐃緒申鐃縮わ申鐃夙み刻申鐃緒申任鐃緒申鐃緒申鐃緒申箸鐃緒申任鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申砲鐃所、鐃緒申鐃緒申鐃宿はわ申鐃塾わ申鐃緒申離鐃緒申肇鐃緒申留鐃緒申鐃祝￥申鐃緒申鐃曙自鐃夙に居申鐃緒申鐃曙た鐃緒申鐃緒申箸鐃緒申峠颪�刻申鐃殉わ申襦ｏ申鐃緒申亮鐃緒申覆砲鐃獣て￥申鐃緒申鐃塾居申鐃緒申鐃緒申鐃緒申鐃宿緒申鐃緒申鐃術わ申鐃暑こ鐃夙にわ申鐃緒申鐃緒申鐃緒申鐃緒申略鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申箸砲覆襦ｏ申鐃緒申鐃熟￥申鐃緒申鐃緒申鐃塾ワ申鐃緒申鐃宿にわ申辰鐃緒申仗鐃宿緒申鐃夙わ申鐃緒申鐃夙わ申鐃叔わ申鐃暑こ鐃夙わ申鐃縮ｏ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃盾し鐃緒申鐃緒申鐃緒申箸鐃緒申鐃熟￥申鐃緒申鐃塾常申鐃緒申辰箸鐃緒申短鐃緒申鐃盾し鐃緒申鐃熟削申適鐃緒申鐃緒申法鐃叔はなわ申鐃緒申鐃盾し鐃緒申覆鐃緒申鐃緒申鐃緒申竜鐃緒申鐃緒申蓮鐃緒申鐃渋э申藥誌申鐃渋行わ申鐃緒申箸鐃緒申鐃緒申鐃渋�鐃緒申鐃祝逸申存鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申速鐃緒申鐃夙み刻申錣誌申砲鐃所、同鐃緒申鐃竣誌申鐃緒申孫圓任鐃緒申襪�鐃盾し鐃緒申覆鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申速鐃緒申鐃祝つわ申鐃銃は￥申鐃出ベッワ申鐃潤が鐃緒申竜鐃緒申悗砲鐃獣て￥申鐃緒申分鐃緒申鐃緒申暴鐃緒申鐃緒申凌鐃緒申佑両荵誌申鐃緒申任鐃緒申鐃夙随申鐃緒申鐃銃わ申鐃暑、鐃夙わ申鐃緒申鐃緒申鐃緒申鐃淑わ申鐃緒申
鐃緒申 鐃緒申鐃緒申無鐃渋常申鐃術にわ申鐃淳種申率鐃塾計誌申鐃熟ワ申鐃緒申鐃所ス鐃塾ワ申鐃緒申鐃所ス鐃緒申発鐃緒申鐃緒申鐃緒申鐃緒申痢鐃�
Perhaps the immense number of cards required for the solution of any rather complicated problem may appear to be an obstacle;but this does not seem to be the case. There is no limit to the number of cards that can he used. Certain stuffs require for their fabrication not less than twenty thousand cards, and we may unquestionably far exceed even this quantity.
鐃緒申鐃緒申鐃初く鐃緒申鐃緒申鐃緒申鐃叔わ申複鐃緒申鐃緒申鐃緒申鐃緒申硫鐃緒申里鐃緒申鐃祝は￥申必鐃竣なワ申鐃緒申鐃宿わ申鐃緒申鐃緒申平鐃緒申鐃緒申祿駕申任鐃緒申鐃処う鐃祝醐申鐃緒申鐃暑か鐃盾し鐃緒申覆鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃熟わ申鐃緒申鐃叔はなわ申鐃緒申鐃緒申鐃術でわ申鐃暑カ鐃緒申鐃宿わ申鐃緒申鐃緒申砲鐃緒申鐃緒申造呂覆鐃緒申鐃緒申鐃緒申鐃竣誌申鐃熟わ申鐃緒申鐃緒申鐃緒申鐃緒申里鐃緒申鐃緒申鐃緒申鐃薯くわ申鐃緒申覆鐃緒申鐃緒申鐃緒申匹鐃宿�鐃竣とわ申鐃緒申鐃順が鐃緒申鐃暑。鐃緒申鐃緒申鐃銃￥申鐃緒申鐃緒申鐃淑わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃熟るか鐃祝常申鐃暑こ鐃夙もあ鐃緒申鐃緒申鐃暑。
Resuming what we have explained concerning the Analytical Engine, we may conclude that it is based on two principles: the first consisting in the fact that every arithmetical calculation ultimately depends on four principal operations&addition, subtraction, multiplication, and division; the second, in the possibility of reducing every analytical calculation to that of the coefficients for the several terms of a series. If this last principle be true, all the operations of analysis come within the domain of the engine. To take another point of view: the use of the cards offers a generality equal to that of algebraical formula, since such a formula simply indicates the nature and order of the operations requisite for arriving at a certain definite result, and similarly the cards merely command the engine to perform these same operations; but in order that the mechanisms may be able to act to any purpose, the numerical data of the problem must in every particular case be introduced. Thus the same series of cards will serve for all questions whose sameness of nature is such as to require nothing altered excepting the numerical data. In this light the cards are merely a translation of algebraical formula, or, to express it better, another form of analytical notation.
鐃緒申鐃殉で駕申鐃熟居申鐃舜につわ申鐃緒申鐃緒申鐃緒申鐃緒申鐃銃わ申鐃緒申鐃緒申里忘討鐃緒申鐃緒申函鐃緒申鐃緒申鐃緒申鐃緒申弔慮鐃渋э申亡鐃重わ申鐃夙件申鐃緒申鐃重わ申鐃暑こ鐃夙わ申鐃叔わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申能鐃塾醐申則鐃熟￥申鐃緒申鐃緒申鐃緒申鐃緒申遊彁鐃緒申鐃緒申能鐃重�鐃祝は￥申鐃獣誌申鐃緒申鐃緒申鐃緒申鐃緒申鐃処算鐃緒申鐃緒申鐃緒申鐃夙わ申鐃緒申鐃粛つの演算鐃祝わ申鐃淑わ申鐃緒申鐃夙わ申鐃緒申鐃緒申鐃渋でわ申鐃暑。鐃緒申鐃緒申鐃旬の醐申則鐃熟￥申鐃緒申鐃緒申鐃緒申鐃緒申老彁鐃緒申蓮鐃緒申鐃緒申鐃塾わ申鐃曙ぞ鐃緒申旅鐃塾件申鐃緒申鐃塾計誌申鐃祝器申略鐃緒申鐃叔わ申鐃緒申鐃叔緒申鐃緒申鐃緒申鐃緒申鐃夙わ申鐃緒申鐃緒申鐃夙でわ申鐃暑。鐃叔醐申慮鐃渋э申鐃緒申鐃緒申造覆鐃出￥申鐃緒申鐃銃の駕申鐃熟緒申鐃緒申鐃熟わ申鐃塾居申鐃舜にわ申辰討任鐃緒申鐃夙わ申鐃緒申鐃緒申鐃夙になる。鐃縮の醐申鐃緒申鐃薯すわ申函鐃緒申鐃緒申鐃緒申匹了鐃緒申僂鐃緒申鐃緒申鐃塾醐申鐃緒申鐃緒申箸鐃緒申鐃緒申箸任鐃緒申襦ｏ申覆鐃緒申覆鐃出￥申鐃緒申鐃塾よう鐃淑醐申鐃緒申鐃熟確実な件申未忙鐃暑た鐃緒申鐃宿�鐃竣な演算鐃緒申命鐃緒申鐃緒申鐃緒申鐃緒申鐃獣縁申房鐃緒申鐃緒申鐃塾わ申鐃緒申鐃緒申任鐃緒申襦ｏ申鐃緒申鐃緒申匹呂鐃緒申鐃緒申同鐃緒申鐃処う鐃祝居申鐃舜に演算鐃緒申命鐃潤す鐃緒申砲鐃緒申鐃緒申覆鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鬚い鐃緒申覆鐃緒申鐃重�鐃祝も供鐃緒申鐃暑こ鐃夙わ申鐃叔わ申鐃緒申茲�鐃祝わ申鐃暑た鐃緒申法鐃緒申匹里茲�鐃淑常申鐃叔わ申鐃獣ても、鐃緒申鐃緒申凌鐃緒申優如鐃緒申鐃緒申鐃緒申鐃緒申呂鐃緒申鐃淑わ申鐃緒申个鐃緒申鐃緒申覆鐃緒申鐃緒申鐃緒申優如鐃緒申鐃緒申鐃緒申儿鐃緒申鐃緒申鐃淑鰹申鐃緒申鐃竣求し鐃淑わ申鐃処う鐃緒申単調鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃熟￥申鐃緒申鐃緒申同鐃緒申鐃緒申連鐃塾ワ申鐃緒申鐃宿にわ申鐃緒申鐃緒申鐃緒申鐃緒申襪鰹申箸砲覆襦ｏ申鐃緒申里茲�鐃淑器申鐃緒申鐃緒申鐃緒申癲�鐃緒申鐃緒申鐃宿わ申単鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃塾￥申鐃盾し鐃緒申鐃熟わ申鐃緒申鐃緒申鐃緒申匹鐃緒申鐃緒申鐃緒申鐃重�鐃緒申表鐃緒申鐃塾件申鐃緒申表鐃緒申鐃緒申鐃緒申鐃緒申里覆里鐃緒申鐃�
Since the engine has a mode of acting peculiar to itself, it will in every particular case be necessary to arrange the series of calculations conformably to the means which the machine possesses; for such or such a process which might be very easy for a calculator may be long and complicated for the engine, and vice versa.
鐃緒申鐃塾居申鐃舜はわ申鐃緒申鐃緒申有鐃緒申動鐃緒申癲種申匹鐃緒申鐃縦ので￥申鐃宿のよう鐃淑常申鐃叔も、鐃緒申鐃塾居申鐃緒申鐃塾わ申鐃緒申鐃緒申鳳鐃緒申鐃緒申鐃緒申鐃熟�鐃塾計誌申鐃緒申鐃術意わ申鐃緒申必鐃竣わ申鐃緒申鐃暑。鐃竣誌申鐃緒申砲箸辰討呂箸討鐃緒申単鐃淑わ申里鐃緒申鐃緒申鐃緒申竜鐃緒申悗砲鐃縦刻申鐃淑ｏ申鐃緒申覆鐃塾になるこ鐃夙もあ鐃暑、鐃緒申鐃緒申鐃銃わ申鐃塾逆の常申鐃盾あ鐃緒申鐃緒申鐃暑。
Considered under the most general point of view, the essential object of the machine being to calculate, according to the laws dictated to it, the values of numerical coefficients which it is then to distribute appropriately on the columns which represent the variables, it follows that the interpretation of formula and of results is beyond its province, unless indeed this very interpretation be itself susceptible of expression by means of the symbols which the machine employs. Thus, although it is not itself the being that reflects, it may yet be considered as the being which executes the conceptions of intelligence. The cards receive the impress of these conceptions, and transmit to the various trains of mechanism composing the engine the orders necessary for their action. When once the engine shall have been constructed, the difficulty will be reduced to the making out of the cards; but as these are merely the translation of algebraical formula, it will, by means of some simple notations, be easy to consign the execution of them to a workman. Thus the whole intellectual labour will be limited to the preparation of the formula, which must be adapted for calculation by the engine.
鐃緒申鐃緒申鐃緒申鐃緒申的鐃淑誌申鐃緒申鐃緒申鐃緒申佑鐃緒申鐃夙￥申鐃緒申鐃塾居申鐃緒申鐃塾最わ申鐃緒申廚鐃緒申鐃重�鐃熟￥申鐃舜種申鐃緒申鐃曙た鐃緒申則鐃祝緒申鐃緒申鐃術随申鐃緒申表鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申適鐃准わ申分鐃循わ申鐃曙た鐃緒申鐃緒申鐃緒申鐃粛わ申彁鐃緒申鐃緒申襪鰹申箸任鐃緒申鐃緒申鐃緒申鐃緒申尊檗鐃緒申泙鐃緒申砲鐃緒申硫鐃潤そ鐃曙自鐃夙わ申鐃緒申鐃塾居申鐃緒申鐃緒申鐃緒申鐃術わ申鐃暑記鐃緒申砲鐃緒申表鐃緒申鐃緒申鐃緒申討鐃緒申鐃処う鐃祝なわ申覆鐃緒申造鐃熟￥申鐃緒申鐃塾居申鐃緒申鐃熟醐申鐃緒申鐃夙件申未硫鐃潤が鐃緒申鐃曙自鐃夙わ申鐃塾逸申鐃縦駈申鐃緒申鐃緒申箸鐃緒申鐃緒申鐃緒申箸鐃緒申表鐃緒申鐃緒申襦ｏ申鐃緒申竜鐃緒申鐃緒申蓮鐃緒申鐃緒申貅�鐃夙考わ申鐃緒申存鐃淳ではなわ申鐃緒申鐃緒申鐃緒申鐃緒申任癲�鐃竣考にわ申鐃緒申鐃緒申砲暴鐃緒申鐃緒申鐃銃逸申鐃緒申鐃渋醐申澆里茲�鐃祝みなわ申鐃緒申鐃夙わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申匹呂鐃緒申里茲�鐃緒申鐃緒申鐃祝わ申鐃緒申鐃緒申鐃緒申鐃暑た鐃緒申里鐃塾で￥申鐃緒申鐃塾居申鐃舜わ申鐃緒申鐃緒申鐃暑機鐃緒申鐃祝￥申鐃緒申鐃緒申鐃緒申鐃銃�鐃緒申鐃緒申鐃緒申里鐃宿�鐃竣わ申命鐃緒申鐃緒申鐃緒申鐃緒申襦ｏ申鐃緒申戮鐃緒申里茲�鐃淑居申鐃舜わ申鐃緒申鐃循わ申鐃緒申鐃夙￥申鐃緒申鐃緒申魯鐃緒申鐃緒申匹鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申箸鐃緒申鐃緒申鐃緒申箸砲覆襦ｏ申箸聾鐃緒申辰討癲�鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃塾わ申鐃夙なので￥申鐃緒申鐃緒申鐃縦わ申鐃緒申単鐃緒申鐃宿緒申鐃緒申砲鐃獣て￥申鐃緒申鐃術者にわ申鐃緒申亮孫圓鐃緒申鐃緒申鐃緒申鐃緒申里牢鐃獣縁申覆鐃緒申箸鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申辰董鐃緒申鐃緒申鐃緒申鐃宿�鐃竣とわ申鐃緒申鐃夙わ申鐃緒申鐃塾は￥申鐃緒申鐃塾居申鐃舜で計誌申鐃緒申鐃緒申里鐃重�鐃緒申鐃緒申鐃緒申鐃叔￥申鐃緒申鐃緒申鐃緒申表鐃緒申鐃緒申鐃暑こ鐃夙に限わ申鐃暑。
Now, admitting that such an engine can be constructed, it may be inquired: what will be its utility? To recapitulate; it will afford the following advantages:‐First, rigid accuracy. We know that numerical calculations are generally the stumbling-block to the solution of problems, since errors easily creep into them, and it is by no means always easy to detect these errors. Now the engine, by the very nature of its mode of acting, which requires no human intervention during the course of its operations, presents every species of security under the head of correctness: besides, it carries with it its own check; for at the end of every operation it prints off, not only the results, but likewise the numerical data of the question; so that it is easy to verify whether the question has been correctly proposed. Secondly, economy of time: to convince ourselves of this, we need only recollect that the multiplication of two numbers, consisting each of twenty figures, requires at the very utmost three minutes. Likewise, when a long series of identical computations is to be performed, such as those required for the formation of numerical tables, the machine can be brought into play so as to give several results at the same time, which will greatly abridge the whole amount of the processes. Thirdly, economy of intelligence: a simple arithmetical computation requires to be performed by a person possessing some capacity; and when we pass to more complicated calculations, and wish to use algebraical formula in particular cases, knowledge must be possessed which presupposes preliminary mathematical studies of some extent. Now the engine, from its capability of performing by itself all these purely material operations, spares intellectual labour, which may be more profitably employed. Thus the engine may be considered as a real manufactory of figures, which will lend its aid to those many useful sciences and arts that depend on numbers. Again, who can foresee the consequences of such an invention? In truth, how many precious observations remain practically barren for the progress of the sciences, because there are not powers sufficient for computing the results! And what discouragement does the perspective of a long and arid computation cast into the mind of a man of genius, who demands time exclusively for meditation, and who beholds it snatched from him by the material routine of operations! Yet it is by the laborious route of analysis that he must reach truth; but he cannot pursue this unless guided by numbers; for without numbers it is not given us to raise the veil which envelopes the mysteries of nature. Thus the idea of constructing an apparatus capable of aiding human weakness in such researches, is a conception which, being realized, would mark a glorious epoch in the history of the sciences. The plans have been arranged for all the various parts, and for all the wheel-work, which compose this immense apparatus, and their action studied; but these have not yet been fully combined together in the drawings and mechanical notation. The confidence which the genius of Mr. Babbage must inspire, affords legitimate ground for hope that this enterprise will be crowned with success; and while we render homage to the intelligence which directs it, let us breathe aspirations for the accomplishment of such an undertaking.
鐃緒申鐃銃￥申鐃緒申鐃塾よう鐃淑居申鐃舜わ申鐃緒申鐃循でわ申鐃緒申箸鐃緒申董鐃緒申鐃緒申里茲�鐃緒申鐃巡い鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃粛�鐃緒申鐃緒申鐃熟駕申鐃緒申鐃緒申鐃緒申鐃藷すわ申醗焚鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申襦ｏ申泙鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申里鐃緒申鐃緒申鐃緒申遊彁鐃緒申鐃緒申鐃緒申鐃緒申鐃処す鐃緒申鐃叔の障害鐃叔わ申鐃暑こ鐃夙わ申分鐃緒申鐃暑。鐃緒申単鐃祝醐申鐃所が鐃緒申鐃緒申鐃緒申爐件申鐃緒申鐃緒申鐃緒申鐃塾わ申鐃緒申里老茲件申憧鐃獣縁申任呂覆鐃緒申鐃緒申鐃緒申竜鐃緒申悗任鐃緒申鐃出￥申鐃緒申鐃緒申動鐃緒申鐃緒申屬鐃緒申鐃緒申鐃緒申鐃緒申蕁�鐃初算鐃塾駕申鐃緒申鐃叔人の駕申鐃緒申鐃緒申必鐃竣とわ申鐃淑わ申鐃緒申鐃緒申鐃緒申鐃旬でわ申鐃緒申鐃緒申鐃緒申鐃緒申鐃祝わ申蠅�鐃緒申鐃緒申鐃緒申鐃塾逸申鐃緒申鐃緒申鐃藷供わ申鐃暑。鐃緒申鐃緒申鵬辰鐃緒申董鐃緒申鐃緒申悗房鐃緒申箸離鐃緒申鐃緒申奪鐃緒申鐃叔緒申發�鐃暑。鐃緒申鐃舜は￥申鐃初算鐃緒申鐃緒申鐃緒申鐃緒申戮法鐃緒申鐃縮わ申鐃緒申鐃叔はなわ申鐃緒申鐃緒申凌鐃緒申優如鐃緒申鐃緒申鐃緒申鐃熟わ申鐃暑。鐃緒申鐃獣て￥申鐃緒申鐃所が鐃緒申鐃緒申鐃緒申与鐃緒申鐃緒申譴随申鐃緒申鐃叔э申鐃緒申鐃塾わ申鐃緒申単鐃叔わ申鐃暑。鐃緒申鐃緒申鐃緒申鐃旬は￥申鐃緒申鐃瞬わ申鐃緒申鐃緒申任鐃緒申襦ｏ申鐃緒申鐃緒申里鐃緒申鐃暑た鐃緒申法鐃緒申罅刻申六鐃淑�鐃緒申鐃緒申暴鐃緒申鐃緒申凌鐃緒申佑両荵誌申鐃緒申任鐃緒申襪鰹申箸鐃竣わ申鐃出わ申鐃淑わ申鐃銃はわ申鐃緒申鐃淑わ申鐃緒申同鐃緒申鐃処う鐃祝￥申鐃緒申鐃緒申表鐃塾刻申鐃緒申長鐃緒申鐃緒申連鐃緒申同鐃緒申鐃竣誌申鐃緒申鐃渋行わ申鐃緒申鐃緒申隋�鐃緒申鐃塾居申鐃緒申鐃熟￥申同鐃緒申鐃祝わ申鐃緒申鐃縦わ申鐃塾件申未鐃粛随申鐃緒申鐃処う鐃緒申動鐃緒申鐃緒申鐃夙わ申鐃叔わ申鐃暑。鐃緒申鐃緒申蓮鐃緒申鐃緒申未僚鐃緒申鐃緒申鐃緒申里鬚�なわ申短鐃緒申鐃緒申鐃瞬で緒申鐃緒申鐃暑こ鐃夙につなわ申鐃暑。鐃処三鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申任鐃緒申襦Ｃ縁申鐃竣誌申鐃熟若干鐃緒申能鐃熟わ申鐃緒申鐃緒申鐃銃わ申鐃緒申佑砲鐃獣てわ申鐃緒申襪鰹申箸鐃緒申弋瓩刻申襦ｏ申鐃緒申複鐃緒申鐃淑計誌申鐃塾常申鐃熟￥申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申箸鐃緒申鐃緒申箸鐃祝常申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃塾よう鐃淑常申鐃熟￥申鐃純干鐃緒申鐃熟囲わ申予鐃緒申鐃緒申鐃緒申的鐃淑醐申鐃緒申鐃緒申鐃緒申鐃夙わ申鐃緒申鐃塾種申鐃緒申鐃緒申鐃緒申鐃緒申鐃銃わ申鐃淑わ申鐃緒申个鐃緒申鐃緒申覆鐃緒申鐃緒申鐃緒申董鐃緒申鐃緒申竜鐃緒申悗両鐃緒申蓮鐃緒申鐃緒申扮藥誌申鐃緒申里鐃塾はわ申鐃曙自鐃夙でわ申鐃淑わ申能鐃熟わ申鐃緒申鐃緒申里如鐃緒申佑鐃緒申圓鐃緒申鐃緒申鐃緒申鐃緒申有鐃術なわ申里箸鐃緒申董鐃緒申鐃緒申鐃重�鐃淑削申箸鐃縦わ申鐃緒申鐃緒申鐃獣て￥申鐃緒申鐃舜は随申鐃祝随申鐃緒申鐃塾刻申鐃緒申噺鐃緒申覆鐃緒申襦ｏ申鐃緒申鐃熟￥申多鐃緒申鐃塾随申鐃緒申鐃祝逸申存鐃緒申鐃緒申奮悗箋誌申僂鐃緒申鐃緒申立鐃縦わ申鐃緒申鐃緒申鐃緒申鐃銃わ申鐃巡い鐃緒申鐃緒申襦Ｃ�鐃緒申鐃緒申鐃塾よう鐃緒申発鐃緒申鐃塾件申未鐃粛緒申里鐃緒申襪鰹申箸鐃緒申任鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃渋際￥申鐃緒申鐃緒申鐃縦の居申鐃重な醐申鐃醇が鐃緒申鐃緒申未鐃竣誌申鐃緒申鐃緒申鐃熟わ申鐃緒申足鐃祝わ申蝓�鐃渋種申的鐃祝科学の随申鐃緒申砲箸辰鐃緒申鐃緒申咾幣鐃緒申屬濃弔鐃緒申鐃銃わ申鐃暑こ鐃夙わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃熟随申鐃緒申鐃竣考にわ申鐃緒申鐃緒申鐃瞬わ申箸鐃緒申鐃緒申鐃緒申隼廚辰討鐃緒申鐃重件申佑凌鐃緒申鐃緒申蠅駕申鐃緒申鐃緒申鐃曙た長鐃緒申鐃縦まわ申覆鐃緒申彁鐃緒申亡悗鐃緒申鐃緒申鐃緒申腓わ申里箸譴随申鐃緒申鐃緒申魏，鐃緒申砲鐃叔わ申鐃緒申里鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申董鐃獣�鐃緒申鐃緒申鐃緒申鐃渋際に件申泙鐃緒申擇辰鐃緒申鐃緒申砲鐃緒申彁鐃緒申鐃緒申鐃緒申爐�鐃初そ鐃緒申鐃獣ワ申辰討鐃緒申襪鰹申箸傍鐃緒申佞鐃緒申討鐃緒申鐃塾わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃夙はわ申鐃緒申鐃緒申鐃緒申鐃渋わ申鐃緒申達鐃緒申鐃暑こ鐃夙は￥申鐃緒申鐃楯な駕申鐃熟わ申鐃術み重ねなのわ申鐃緒申鐃緒申鐃祝わ申辰鐃銃鰹申鐃緒申鐃淑わ申鐃渋り、鐃緒申呂鐃緒申鐃緒申鐃宿わ申続鐃緒申鐃暑こ鐃夙わ申鐃叔わ申鐃淑わ申鐃緒申鐃緒申鐃緒申鐃淑わ申鐃祝￥申鐃緒申鐃緒申鐃緒申鐃緒申鐃淑わ申鐃緒申戞鐃緒申鐃緒申紊駕申襪鰹申箸呂任鐃緒申覆鐃緒申鐃緒申鐃緒申辰董鐃緒申鐃緒申里茲�鐃淑醐申鐃緒申砲鐃緒申鐃緒申鐃粛間の種申鐃緒申鐃緒申鐃巡う能鐃熟わ申鐃緒申鐃緒申鐃緒申屬鐃緒申箸鐃塾�鐃銃わ申箸鐃緒申鐃緒申佑鐃緒申蓮鐃緒申鐃緒申鐃重�鐃祝なわ申弔弔鐃緒申襪件申鐃緒申奮悗鐃緒申鐃祝わ申鐃緒申鐃緒申鐃緒申鐃緒申蕕件申鐃緒申鐃緒申鐃緒申鐃緒申曚鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申侶弉鐃緒申鐃粛￥申鐃緒申分鐃緒申砲錣随申辰討鐃緒申襦ｏ申鐃緒申鐃緒申討鐃緒申譴�鐃緒申鐃緒申鐃塾居申鐃緒申鐃緒申鐃緒申屬箸鐃緒申慮鐃緒申罎居申譴親逸申鐃緒申鐃緒申个鐃緒申里鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申呂泙鐃緒申鐃緒申鐃緒申糞鐃緒申鐃重�鐃緒申表鐃緒申鐃祝わ申鐃緒申澤廚鐃緒申鐃夙わ申鐃緒申鐃殉わ申討鐃緒申覆鐃緒申鐃緒申丱戰奪鐃緒申鐃塾削申能鐃祝随申発鐃緒申鐃曙た鐃緒申鐃緒申鐃熟￥申鐃緒申鐃塾誌申鐃夙わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃夙わ申鐃緒申望鐃淳わ申鐃緒申鐃緒申鐃淑削申鐃緒申了鐃緒申辰討鐃緒申襦ｏ申鐃緒申里茲�鐃淑わ申鐃夙わ申愆鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申坊桧佞鐃淑э申鐃緒申鐃銃縁申鐃緒申法鐃緒申鐃緒申里茲�鐃淑考わ申鐃緒申存鐃緒申鐃緒申鐃夙わ申鐃緒申鐃順き鐃緒申望鐃淳わ申鐃夙わ申鐃叔はなわ申鐃緒申鐃緒申