793 



PROJECTION OF THE SPHERE, &c. 



PROOF. 



r.u 



The lines between the degrees are to be understood as represent, 

 half degrees : thus opposite to 991 should come 129 J 140i. Th. 

 use of this table is as follows : suppose the angles xoz, zox, XOY 

 to be severally 123, 104i, and 1324" : thus : 



I 956 

 zox=104i 696 

 993 



Opposite to the angles put down the numbers belonging to them in 

 the table, and opposite to each number the co-ordinate whose capita 

 letter does not appear in the angle. Then opposite to x, y, and z, we 

 have 956, 696, and 993. These numbers show the proportions which 

 the projections of equal lines bear to one another on the three axes. 

 Thus a foot parallel to a; is to a foot parallel to y, as 956 to 696 in the 

 projection. If then a card be taken, and the angle z o x be cut out ; 

 and if a slit be made in the direction of o T, just wide enough to permit 

 a pencil to travel, scales of equal parts may be laid down on o x, o T, 

 and o z, which shall represent the projections of equal lines in the 

 three directions ; and this may be done once for all. It would be easy 

 enough to make a general scale by which the equal parts proper for any 

 angle should be taken out at once. 



The isometrical perspective of Professor Farish [PERSPECTIVE, col. 

 416] is the simplest case of this, namely, that in which the angles are each 

 120*. The only difference between this particular case and any other 

 is, that the former requires only one scale of equal parts, whereas the 

 latter requires either two or three. In other respects this method of 

 using them is precisely the same. 



PROJECTION OF THE SPHERE, SHADOWS, &c. [PER- 

 SPECTIVE.] 



PROLOCUTOR. [CONVOCATION.] 

 PROLOGUE (*p6\oyos, from irpb, before, and \Ayos, peeeJi), is 

 usually applied in English to the short poem or verses, which are 

 sometimes prefixed to new plays to recommend them to the favour of 

 the reader or spectators. In the comedies of Plautus an$ Terence we 

 find prologues of this kind. Aristotle (' Poetik.' c. 12), gives the name 

 of prologue to that part of the Greek tragedy which precedes the 

 parodos, or first speech of the chorus. 



PROMETHEUS (OMfMt). The story of Prometheus takes dif- 

 ferent forms in the Greek legends, but they agree generally in repre- 

 senting the close connection between him and the human race. He is 

 represented by ^Eschylus as one of the Titans, who incurred the 

 resentment of Zeus for taking the part of mortals when Zeus intended 

 to crush them and to send them to the abode of Hades, and also for 

 giving them fire and teaching them all the arts. As a punishment, 

 Zeus binds him to a rock in Scythia, and appoints a vulture to prey on 

 his liver. This is the subject of the ' Prometheus Desmotes,' or ' Pro- 

 metheus Bound,' of ^Eschylus. 



Another old form of the legend, which closely resembles that which 

 JEschylus followed, is given in the ' Theogony ' of Hesiod. Heaiod 

 says that when the gods and men were engaged in a controversy with 

 one another at Mecone (an ancient name of Sicyon), Prometheus, 

 wishing to deceive Zeus, took an ox, and dividing it, placed the flesh 

 and the viscera in the hide, and the bones of the ox in the inside fat, 

 and then asked Zeus to make his choice. Zeus, though aware of the 

 deception, chose the bones and the fat, ".designing evil in his mind 

 against mortal man," and in revenge withheld fire from man. Pro- 

 metheus however secretly stole fire from heaven and gave it to man, 

 and Zeus in return bound Prometheus with chains to a pillar, and sent 

 an eagle to prey upon his liver. Zeus also, in order to injure man, 

 created Pandora, and, after bestowing upon her numerous gifts, sent 

 her to man a " beautiful mischief, for from her is sprung the race of 

 women, of whom the race is thoroughly destructive." Hesiod, in his 

 poem entitled ' Works and Days,' gives at greater length the legend of 

 Pandora, and says that Zeus sent her to Epimetheus ; and that he, not 

 following the advice of Prometheus, who had told him never to receive 

 a gift from Zeus, but to send it back again, took her into his house. 

 These stories .ire supposed to have a meaning : Prometheus is the per- 

 sonification of f'irc-lli'iiiijlil, and Epimetheus of after-thought. 



There is another form of the legend respecting Prometheus, in which 

 he in represented not merely as the friend and protector of the human 

 race, but as their creator. This form is an old one, though neither 

 Hesiod nor ^Eschylus has followed it. There is a fragment of 

 Callimachus, in which he says, " If Prometheus formed thee, and thou 

 art not sprung from some other clay." Plato has adopted this form of 

 the legend in the ' Protagoras,' but with the variation that Prometheus 

 is not the creator, but only the person who endowed man with his 

 senses. He says that the gods formed all mortal animals within the 

 earth, out of the mixture of earth anil fire, and of as many things as 

 are mingled with earth and fire, and that they entrusted to Prometheus 

 and Epimethens the business of providing them with all the faculties 

 necessary for their preservation. He then proceeds to say that 

 Epimethcus begged of Prometheus that he might have the business 

 himself in the first place, and that Prometheus should overlook his 

 work when he had done it. Epimetheus accordingly proceeds to his 

 work, and bestows upon the different animals the means of preserving 

 themselves ; but when man came to be provided for, who was to be 

 Superior to all other animals, Epimetheus had been so prodigal of all 



his resources, that he had nothing left to bestow upon man. Pro- 

 metheus, being at a loss how to remedy the omission of Epimetheus, 

 trom Hephsestus and Athena fire and the intelligence which is 

 displayed in works of art, and gave them to man ; so that by means 

 of this wisdom, and fire as its instrument, men were endowed with the 

 power of providing for themselves. 



Some modern writers suppose that, in the earliest form of the 

 legend, Prometheus was not considered as a deity, but simply as the 

 representative of the human race, and that afterwards he was made a 

 god, the friend and protector of man, and at last their creator. 



Representations of Prometheus are frequent in the latter ages of 

 ancient art, especially in allegorical representations of human life on 

 sarcophagi, and in connection with the Fates, Eros and Psyche, and 

 other legends. (Miiller, ' Archjiologie der Kunst,' 396.) 



PROMISSORY NOTE. [BILL OP EXCHANGE.] 



PROMULGATION. Promulgation is from the Latin Promulgo, 

 which is equivalent to Provulgo, and means " to make public." Black- 

 stone observes of the promulgation of a law, " It may be notified by 

 universal tradition and long practice, which supposes a previous publi- 

 cation, and is the case of the common law of England. It may be 

 notified rivd voce by officers appointed for that purpose, as is done with 

 regard to proclamations, and such acts of parliament as are appointed to 

 be publicly read in churches and other assemblies. It may lastly be 

 notified by writing, printing, or the like, which is the general course 

 taken with all our acts of parliament." A law being a command from 

 a political superior to a political inferior to do or not to do something, 

 with a penalty attached to the violation of the command, it is assumed 

 that the command is made known in some way to all who are bound to 

 obey it ; or that it is known to all. But as to " a universal tradition 

 and long usage," it is a mistake to say that it supposes a previous 

 publication. A long usage does not of itself make law : the usage 

 must be pronounced to be law by some competent authority, and 

 that is the only promulgation which it has. Promulgation by pro- 

 clamation only reaches those who hear it, and everybody cannot 

 hear an act of parliament which is read in churches, for the churches 

 would not hold one-fourth of the people if they all went to hear it 

 read; and if they heard it read, very few would understand it. 

 Printing is at present the most efficient means of promulgating a new 

 statute ; but to all those who cannot read it is ineffectual ; and so it is 

 indeed to those who cannot understand it, which sometimes the judges 

 themselves say they cannot do. 



No remedy can be provided for these difficulties, and it is simply a 

 positive rule of law that a new statute is binding on all persons who 

 are under the authority of the power which makes the statute, from 

 the moment that the statute is made and completed in due form. A 

 person is presumed to know the law, because if ho were allowed to 

 urge ignorance of it as an excuse, it might be urged in so many 

 cases aa to give unbounded room for fraud. The positive rule that all 

 the members of a state are bound by its laws, causes less evil than the 

 admission of the excuse would. 



Promulgation of a law among the Romans meant the placing of the 

 bill (rogatio) in some public place where it could be read before it was 

 voted upon in the Comitia. The Roman rule, which we also adopt, 

 was that ignorance of law (ignorantia juris) was no excuse. (Paulus, 

 Dig. 22, tit. 6. s. 9.) 



PRONOUNS, the name given by grammarians to certain words 

 which are used as substitutes for the names of persons and things. 

 Pronouns properly so called are commonly divided into personal, 

 demonstrative, relative, and interrogative pronouns ; but it appears 

 probable that all pronouns, at least with the exception of the first and 

 second personal pronouns, were originally demonstrative. William 

 Humboldt remarks that the first and second personal pronouns " are 

 not mere substitutes for the names of the persons for whom they 

 stand, but involve the personality of the speaker and of the person 

 spoken to, and the relation between them ; " and in writing and con- 

 versation there is frequently hardly any name which can so clearly 

 designate the person intended as the appropriate personal pronoun. 

 The third personal pronoun in English appears to have been originally 

 a demonstrative, and to contain the same root, la, sa, or ha, which 

 occurs in the demonstrative pronoun in the Latin, Greek, and other 

 cognate languages. 



The relative pronoun may also be regarded as a demonstrative ; for 

 whether the pronoun is used to denote an object pointed out at the 

 lime by the speaker, or an object mentioned just before, or one which 

 is to be immediately brought before the hearer's mind, it is equally 

 demonstrative. In the last of these cases the pronoun is called a 

 relative, as " I saw the man whom you mentioned." In English we 

 lave two forms for the relative, that and who or which. The former 

 s the same word as the demonstrative ; the latter contains the same 

 root as we find in the Latin qui, the Sanscrit, Zend, and Lithuanian ka, 

 and the Gothic hrer and leva. The interrogative pronoun is thu 

 same as the relative in English and many of the cognate languages, 

 and only differs from the relative in referring to something subsequent 

 in<l unknown ; whereas the latter refers to an antecedent and definite 

 subject. 



PRONUNCIATION. [ORATORY.] 



PROOF. [DEMONSTRATION; EVIDENCE; MIRACLE; OATH; PRO- 

 BABILITY] 



