NOTICE. 



NOTICE. 



HI -wt ssreral series beginning with 0, to make marks of distinction 

 between A in one series, and that in another. The most useful ease 

 to that in which whole and positive powers of 0, 1, 2, S, Ac., form the 

 cries ia question : thus if we take the series of cubes, 



0>= . 



]> 1 * 8 . A.0=il 



a>. s ,< 12 1 o AO>= 



. 27 18 g AW-e 



4= 64 " 24 " A'0>=0,Ac. 



5>=125 Ol 



The symbol A" 0, whenever is greater than *, (tends for 0; 

 when % is - it stands for 1 x 2 x 3 x . . . . x H. In ail other cases 

 the differences of + ' may be found from those of 0* by the following 

 equation : 



r-i A 1 " 1 0* + A 0' 1 



It U frequently useful to hare the term A r . 0" -M .2.8... (r-l).r 

 arranged in tables. If we wish to make this separately, we have, 

 denoting the preceding fraction by A <r) . 0* 



A (ri o~i = Al'-'l 0" + r A'') 0"-' 



The following table contains both the differences, and the differences 

 divided, as just explained, up to those formed from the series of tenth 

 powen ; arranged so that simple differences must be looked for above 

 or on the dotted lines, and divided differences below the dotted lines ; 

 the first by means of the left hand column and highest row ; the second 

 by the right hand column and lowest row. Thus 



A' s 

 A'0 = 126000 . s-s-i-r- = 1050 





1030 



The only one not in the table is A'' 1 0' which is always unity. 



The uses of these differences mainly consist in the rapidity with 

 which transformations can be made by means of them, whether of a 

 simple algebraical or of 'a transcendental kind : such aa the following, 

 being a whole number : 



3- = *+A ( "0".*(a-l)-rA< 3 > 0". .!<*- !)(*+ 2), 



f Ac. 



* = x + x(x-l), 



x> = x + 8 x(x- 1) + *(*-!)(.<:- 2), 

 x*= r + 7x(x-l) + 6x(*-l)(x-2) 



+ *(*-!) (*-2) (i-3), 



and so on. [See also OPERATION ; SERIES.] 



The following works contain many properties of these numbers : 

 Herschel, ' Examples of the Calculus of Finite Differences.' pumim ; 

 and ' Lib. Useful KnowL : Differential and Integral Calculus,' pp. 253- 

 261, and 307-311. 



NOTICE is a term used in English law with reference to various 

 kinds of transactions. That use of it which is most important, and 

 which it is here proposed to explain, has reference to contracts of buying 

 and selling, and mainly so far as such contracts come under the cogni- 

 sance of courts of equity. In this sense notice signifies the knowledge 

 of a party to the contract of any fact which is connected with the 

 contract, and may become a matter of dispute either between the 

 parties to the contract, or between them or any of them and any other 

 person not a party to that contract. The term notice ig.inoot commonly 

 applied to buying and selling of land, or some interest in land, and the 

 matter generally in dispute is, whether the interest of a person who in 

 not a party to the contract is in any way to be affected by it 



Notice, in English law, is an ambiguous term, and has different 

 meanings according aa we contemplate the giver or the receiver of what 

 U called notice. To give notice U to communicate something to 

 another person : the person who receives the communication is said to 

 fare notice, and when it is proved that he has had such notice, he is 

 presumed to have knowledge of the thing communicated. Thus notice 

 comes to have the meaning of Inouiedyc when applied to him who is 

 the receiver of the notice ; and it is not always easy to avoid the 

 ambiguity resulting from thin double meaning of the word. 



Notice of a fact (notice being here considered with reference to the 

 receiver) may mean either knowledge of the fact itself, or knowledge 

 of some other fact from which arises a legal presumption of knowledge 

 of the fact itself. In both cases the knowledge must be proved by 

 evidence, and the only difference in the evidence U this ; in the former 

 case a fact is to be proved, which fact, when proved, shall be considered 

 knowledge ; and in the second case a fact is to be proved, which cannot 

 be considered as knowledge, but is a fact the establishment of which 

 leads to a legal presumption, that is, to an inference of some fact which 

 is considered as knowledge. If a man receive a written communication 

 from another person of a certain demand upon him by such person, all 

 that can be proved by evidence is that be did receive such communi- 

 cation ; but that fact being established, all the world imputes to the 

 receiver of such communication knowledge of the demand contained in 

 it. The fact, in order to have any relation to the contract, must of 

 course be such a fact as would affect the contract if it were expressly 

 made part of it. A fact of this kind then being established, which is 



either knowledge or legal presumption of knowledge, the legal i 

 sion ia, that the person who hod such knowledge at the time of making 

 the contract must be considered as having acquiesced in such fact ; in 

 other words, such fact must be considered to have the same effect as if 

 it were expressed in and incorporated with the contract. 



Notice has been divided by writers on English law into " actual " 

 and " constructive." Of " actual notice," it is said that " to constitute 

 a binding notice, it must be given by a person interested in the pro- 

 perty, and in the course of the treaty for the purchase. Vague reports 

 from persons not interested in the property, will not all. 

 chaser's conscience ; nor will he be bound by notice in a previous trans- 

 action which he may have forgotten. (Lord St. Leonards, ' V. 

 and Purchasers,' 13th edit. p. (J'Jl ) The some author says of 

 structive notice," that " in its nature it is no more th.-ui evidence of 

 notice, the presumptions of which ore so violent, that the court will 

 not allow even of its being controverted ; but courts of equity will not, 

 extend the doctrine to coses to which it has not hitherto been lu-ld 

 applicable." The difference between the two kinds of notice seems to 

 be rather in degree than in kind. In addition to what has been said 

 on the general subject of knowledge, we may take an instance of what 

 would be called actual notice in Knglish law. We will suppose this 

 actual notice to be a statement in writing mode by a person interested 

 in a certain piece of land and in Uie course of the trr.iiy for the pur- 

 chase of it, and by him handed to the purchaser. Now it is obvious 

 that all this, when proved, does not make the knowledge of the pur- 

 chaser ; but these foots, when proved, arc evidence, of knowledge, " die 

 presumptions of which are so violent " that the universal consent of 

 mankind " will not allow even of its being controverted.'' 'II 

 then no further distinction between actual and constructive notice, 

 considered as a matter belonging to the general subject of evidence, 

 than what has been already stated ; and the only question which con 

 arise in any system of law is, what facts, not capable of I'm 

 sidered as knowledge, shall be considered, when proved, as leading to 

 a legal presumption of such facts as may be considered knowledge. 



These general principles will be better understood by their applies 

 tion to (articular coses, in English law, of buying and selling land. 

 But it should be premised that there are cases of what is often called 

 notice, in English law, where no knowledge of anything is proved, but 

 the existence of a certain thing is proved, and then notice is legally 

 imputed to the person to be affected by it Thus, when there is a 

 public act of parliament, everybody is legally supposed to h -m- 

 of it But this is notice which arises from positive law, anil 

 presumed from the proved knowledge of another fact ; it would there- 

 fore be more appropriate to give it some other name, and not to con- 

 I found it, as some text writers do, with that which they call constructive 

 notice. Another example of such notice made by positive law is, 

 where there is a suit pending* which may nlli'ct the subject of sal* ; 

 in this oase the purchaser is also said to have notice of it, and he buys 

 subject to what may be decreed in the suit. All conveyances by any 

 bankrupt bond fide made and executed before the date of the filing a 

 1 of adjudication are valid, notwithstanding any prior act of 

 bankruptcy committed by the bankrupt, provided the person to whom 



* By the Act 2 Vkt. e. 1 1, parchucrt snd mortjoe arc not to be bound by 

 Hi prndfiti, of which they hare Dot express notice, unltM the namci, &o., of the 

 partki to be affected thereby arc registered, as the Act prescribes. 



