PRO 



PRO 



being called lateral planes. The edges 

 at which these meet are lateral edges ; 

 and the edges at which they meet the 

 terminal planes are iermirial edges. 



PRISMATIC SPECTRUM. Solar 

 Spectrum. The variously-coloured ap- 

 pearance presented by a ray of light, 

 when separated into its constituent parts 

 by refraction through a glass prism. 

 The appearance consists of an oblong 

 image, containing seven colours, which 

 are simple or homogeneous, as distin- 

 guished from the white ray, which is 

 compound or heterogeneous. 



PRISME'NCHYMA {npiafxa, a prism, 

 '^yxvfjia, infusion). The name given by 

 Morren to the prismatical variety of the 

 parenchyma of plants. 



PRIVATIVE TERMS. In Logic, 

 terms which denote that a certain view 

 might be taken of an object, though it is 

 not so taken, are called privative. Thus, 

 in the expression, "the moon is some- 

 times invisible," the word invisible is 

 used privatively, for the moon is capable 

 of being seen. See Negative Term. 



PROBABILITIES or CHANCES. The 

 popular use of these terms has no very 

 distinct meaning. The mathematical 

 meaning points out a real value existing 

 in the circumstances. A question of 

 probability is termed direct, when, cer- 

 tain causes being given as existent, from 

 which a certain event may proceed, the 

 probability of that event happening is 

 required. A question of probability is 

 termed inverse, when, an event being 

 given as existent, and proceeding from 

 one of several causes, the probability of 

 one proposed cause being the true one 

 is required. 



PROBLEM (7rp6/3\»])ua, any thing pro- 

 posed as a task). A proposition in which 

 something is proposed to be done ; as a 

 line to be drawn under some given con- 

 ditions, some figure to be constructed, 

 &c. The solution of the problem con- 

 sists in showing how the thing required 

 may be done by the aid of the rule and 

 the compass. The demonstration con- 

 sists in proving that the proceos indi- 

 cated in the solution really attains the 

 required end. A postulate is a problem, 

 the solution of which is assumed. 



PROBOSCI'DEA. A group of pachy- 

 dermatous animals, containing only the 

 elephant and its extinct congeners, the 

 mammoth and the mastodon, character- 

 ized by their elongated nose, or pro- 

 boscis. 



PROCYON, or a CANIS MINOR. A 

 272 



star of the first magnitude in the con- 

 stellation Canis Minor. 



PRODUCT. In arithmetic, a product 

 is the result of the multiplication of two 

 or more quantities. The result of the 

 addition of two or more quantities is 

 called the sum. 



PRODUCTA. An extinct genus of 

 fossil bivalve shells, occurring only in 

 the older secondary rocks. It is closely 

 allied to the living genus Terebratula. 



PROGRESSION (progredior, to ad- 

 vance). This term, in its general sense, 

 means going forward ; but its use in 

 algebra and arithmetic denotes that the 

 progress takes place in a determinate 

 order — that it is motion measured by 

 some scale. 



1. Progression, Arithmetical. Quan- 

 tities are said to be in arithmetical pro- 

 gression, when they increase or decrease 

 by a common difference. Thus, 1, 3, 5, 

 7, &c., 8, 4, 0, —4, &c. ; a,a + d, a -it 2d, 

 a + id, &c., are in arithmetical progres- 

 sion, the common differences being 2, 

 — 4, and d, respectively. 



2. Progression, Geometrical. Quantities 

 are said to be in geometrical progression, 

 when they increase or decrease by a 

 common factor; in other words, when 

 the ratio of any two successive terms is 

 the same. Thus, 1, 3, 9, 27, &c., 16, 4, 

 1, h &c., h — fe, — 4fi —5% &c., a, ar, 

 ar^, ar^, &c., are in geometrical progres- 

 sion, the common factors, or ratios (as 

 they are called), being 3, J, — f, and r, 

 respectively. 



3. Progression, Harm onical. Quantities 

 are said to be in harmonical progression, 

 when their reciprocals are in arithmetical 

 progression ; in other words, when any 

 three successive terms are so related, 

 that the first is to the third as the dif- 

 ference between the first and the second 

 is to the difference between the second 

 and the third. Thus, since, 1, 3, 5, 7, 

 &c., \, — \, — I, — I, are in arithmetical 

 progression, their reciprocals, 1, J, |, 

 \, &c., 4, —4, — §, — |, &c., are in har- 

 monical progression. Again, if a, b, c, 

 are in harmonical progression, 



a '. c W a — b '. b — c. 



PROJE'CTILE {projicio, to cast for- 

 ward). A heavy body which has been 

 projected in a direction not vertical. The 

 theory of projectiles investigates the rela- 

 tions between the space described, the 

 time of motion, and the velocity acquired 

 by a body when impelled by some motive 

 force. 



PROJE'CTION. The representation 



