I i K It ]: A T I V K S (' I K \ < ' K . 



J17 



position in true with a universal Habjout ; bat this never results 



aa a consequence from tho truth of the old proposition, bat 



<>thor grounds. " All equilateral triangles are 



(<[iiiiui K 'uhir " is true, and BO in "all equiangular triangles are 

 i-.|ini.it.-:- 1! ; " but tho truth of tho latter proposition ou 

 inferred from tho truth of the former. Henoe it is that 

 has given a separate and iudepondunt proof of each. It folluwx, 

 thoroforo, that in converting A we mart, in addition to tram*- 

 tho terms, change tho quantity from universal to par- 

 tioular, leaving the quality unchanged. This epooioa of oonver- 

 mon hod been termed by logicians Conversion per Accident. 

 Tii.- ii.nuo has been chosen because this is not really a conversion 

 of tho universal per $e, but by reason of the accident of its con- 

 taining the particular. In other words, tho particular to which 

 A is thus said to bo converted is not, strictly speaking, the con- 

 verso of tho universal A at all, but of the particular I which it 

 contains, i.e., whose truth in implied in its own. 



ler >!' tho so methods, however, will enable us to convert 

 (). Whichever of them be adopted, tho subject of the oonvertend, 

 which in it is undistributed, would in tho converse, being there 

 the predicate of a negative, bo distributed ; and this wonl<l. for 

 Hiiuihir reasons to those above given against the simple conver- 

 sion of A, be useless for the purposes of inference. O, however, 

 may be converted simply by regarding it as I. This is done by 

 considering the negative as attached to the predicate instead of 

 to tho copula. Thus, in " some who possess wealth are not 

 happy," if wo consider the predicate as " not-happy " instead of 

 " happy," the proposition may practically be regarded as I, and 

 then converted simply. This is called Conversion by Contra- 

 position. 



It should be noticed that Singular Propositions are, for the 

 purposes of conversion, regarded as Universals, inasmuch as their 

 subjects may be said to be distributed, being used to stand for 

 the whole of what they can be used to signify. 



The result then is this : E and I are converted simply, A per 

 accidens, and by contraposition. 



We have next to consider, somewhat at length, the nature 

 and theory of Syllogism, the complete understanding of which, 

 and its practical application, may bo said to bo the chief aim and 

 end of Logic. 



We have already seen that tho third operation of the mind 

 is Reasoning, and that this, when expressed in words, is called 

 an Argument, or when put into a certain form laid down by 

 logicians, a Syllogism. We may accept Archbishop Whately's 

 definition of an Argument, which is " an expression in which 

 from something laid down and granted as true (i.e., the Pre- 

 mises), something else (i.e., the Conclusion) beyond this must 

 be admitted to be true, as following necessarily [resulting] 

 from tho other." The same writer defines a Syllogism, which is 

 an argument stated in a regular logical form, as " an argument 

 BO expressed that the oonclusiveness of it is manifest from 

 the mere force of the expression," i.e., without considering tho 

 meaning of the terms : e.g., in this syllogism, " Every Y is 

 X, Z is Y, therefore Z is X," tho conclusion follows from 

 the premises, whatever terms X, Y, and Z respectively are 

 understood to stand for. 



Reserving, however, for our next lesson an explanation of 

 the analysis and rules of tho Syllogism, we will now briefly 

 mention, to show their groundlessness, a few of tho common 

 erroneous impressions abroad upon the subject. 



Some persons have considered it a conclusive argument 

 against the utility of Logic in improving tho reasoning powers 

 and enabling us to reason better, to say that numbers reasoned 

 very well before ever Logic was heard of, and that still greater 

 numbers are in the habit of reasoning correctly now who are 

 ignorant of oven its fundamental principles. This is an objec- 

 tion to tho study of Logic which, when reflected on, must appear 

 absurd. It might just as reasonably bo said that a science of 

 music was useless, because many persons are proficient in music 

 who have never been scientifically taught, and who are wholly 

 unacquainted with its principles ; or that grammar may safely 

 be neglected on tho ground that all persons can speak, and 

 many even grammatically, without ever having been taught it. 

 Indeed, as Archbishop Whately remarks, the practice in any 

 process respecting which any system has been formed, not only 

 may exist independently of the theory, but must have preceded 

 the theory. 



There are others who consider that the method of reasoning 



by means of the syDogUa U a peodkr method, and that than 

 are othar method* difierinff from it which may often b more 

 conveniently employed in referenoo to partioalar bieeto. This 

 U a muUk,,. Hyllogirtio reasoning is not a peenliar fora of 

 reasoning, hot is (with tho possible exception of Induction, 

 which wo shall afterward, consider) tho <NU fora to which all 

 con-oct reasoning may bo reduced, or in whieb it may bo 

 exhibited. The reasoning process is, in every case, no matter 

 what may be the abjeot-mattM- on which it U employed, snb- 

 tantially the tame. Quite M reasonably might oae My that 

 grammar was a peculiar language, and thai men might speak 

 correctly without peaking grammatically. Logic, fat fact, m 

 reference to the syllogistic proceM, U not on art or sdsnoe of 

 reasoning, but the art or science of doing to. 



Other persons have strangely rappoeed that, when the 

 logician teaches that all correct ma toning wf be capable 

 of being reduced to tho syllogistic form, he mean* to convey 

 that no one can two correct arguments, qnlssi he ttnUt them 

 severally at full length in this particular form. A* well, to 

 borrow Archbishop Whately's illustration, might it be supposed 

 that when a chemist teaches us to analyse and reaolvo a com- 

 pound substance into its simple element*, be mnans that we 

 should never use it for any purpose without roposfinn. the actaal 

 process of analysis, or that " to speak grammatically " meane 

 to parse every sentence that we otter. 



BECREATIVE SCIENCE. XIII. 



BEFBACTINO IN8TBUMENTS. 



IK our hut paper a very simple refracting instrument, a aort of 

 " philosophical toy," called the dissolving-view apparatus, wme 



referred to ; and, aa a contract to this, it may be ""*; to 

 know the remarkable care taken in the construction of the leases 

 and general arrangements of a first-claw telescope, each aa an 

 equatorial, and costing 3,000. 



All telescopes have various lenses, bat the glass placed ba4u 

 the object and the eye is called the olject-ylats, and u nraally 

 double convex. This glass projects a spectral image or ghost 

 in the tube, which may be examined by another doable convex 

 lens, denominated an eye-glass ; such an arrangement would be 

 the most ancient form of tho astronomical teleeoope, bat not 

 the most agreeable to use, because by what is called chromatic 

 aberration the images looked at are falsely coloured. 



In an achromatic telescope a double-convex lens of crown glass 

 is combined with a double-concave lent of /tint glass, the first- 

 named being placed outside and nearest the real image obeerred, 

 as shown by tho direction of the arrow in Fig. 1. This beautiful 

 contrivance, made in various ways by Hall and the DoUonds, 

 would, however, avail little if connected with a single ooaru 

 lens. The construction of the eye-piece becomes, therefore, of 

 tho utmost importance, and hence it is not surprising to find 

 the names of distinguished opticians attached to eye-pieces, aa 

 shown at Figs. 2 and 3, the former being the invention of 

 Huygens, the latter of Ramaden. Fig. 2 is termed a uefmUft 

 eye-piece, because the spectral image is formed behind rr, 

 called the Jield-glau, being the lens which lies nearest to the 

 object-glass. Fig. 3 ia usually called the ponlit* eye-piece, in 

 which the spectral image ia formed before the field-glass r r. 

 Both of these eye-pieces are used for special IJUUOBSS ia 

 astronomical observation. 



Thus far the most simple arrangement has been spoken of hi 

 connection with the construction of an astronomical teleeoope; 

 and therefore, by way of contrast, we may now pass to the 

 description of tho great equatorial at Stonyhnrst College, kindly 

 furnished by tho Professor of Astronomy, the ROT. 8. J. Perry. 



This instrument was constructed by Napier for Mr. Peters, of 

 London, and waa purchased by the authorities of Sfcmyhurst 

 College in 1867, to replace the 4-inch equatorial of Jones, which 

 was mounted in the obaervatory attached to the college ia 1889. 



The new teleeoope ia anpported at the centre by an iron pier, 

 .vhich is cast in two pieces, the pillar weighing 17 ewt., and 

 the pedestal 13 cwt. The two are fastened together by iron 

 bolts, which allow of a small play in aximnth. The eleven 

 levelling acrewa upon which the foot rests afford the means of 

 making any small adjustments in leveL 



The aolid concrete foundation on which the instrument vesta 

 ia 10 feet square and 2 thick, and upon it are placed fov 



