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TEE POPULAR SCIENCE MONTHLY.— SUPPLEMENT. 



been fictitious, and has been attained at the cost J 

 of spiritual meaning. 1 And, coming to recent 

 times, although we may admire the ingenuity 

 displayed in the logical machines of Earl Stan- 

 hope and of Stanley Jevons, in the formal logic 

 of De Morgan, and in the calculus of Boole ; al- 

 though as mathematicians we may feel satisfac- 

 tion that these feats (the possibility of which was 

 clear a priori) have been actually accomplished : 

 yet we must bear in mind that their application 

 is really confined to cases where the subject-mat- 

 ter is perfectly uniform in character, and that be- 

 yond this range they are liable to encumber rather 

 than to assist thought. 



Not unconnected with this intimate associa- 

 tion of ideas and their expression is the fact that, 

 whichever may have been cause, whichever effect, 

 or whether both may not in turn have acted as 

 cause and effect, the culminating age of classic 

 art was contemporaneous with the first great de- 

 velopment of mathematical science. 2 In an ear- 

 lier part of this discourse I have alluded to the 

 importance of mathematical precision recognized 

 in the technique of art during the Cinque-cento ; 

 and I have now time only to add that, on looking 

 still further back, it would seem that sculpture 

 and painting, architecture and music, nay, even 

 poetry itself, received a new, if not their first 

 true, impulse at the period when geometric form 



1 A specimen will he found in the " Moralia " of 

 Gregory the Great, lib. i , c. xiv., of which I quote 

 only the arithmetical part : 



" Quid in septenario numero, nisi summa perfec- 

 tionis accipitur? Ut enim liumana? rationis causas 

 de septenario numero taceamus, quce afferunt, qudd 

 idcirco perfectus sit, quia exprimo pari constat, et 

 primo impari ; ex primo, qui dividi potest, et primo, 

 qui dividi non potest ; certissime scimus, quod sep- 

 tcnarium nnmerum Scriptura Sacra pro perfectione 

 ponere consuevit. ... A septenario quippe numero 

 in duodenarium surgitur. Nam septenarius suis in 

 se partihus multiplicatus, ad duodenarium tenditur. 

 Sive enim quatuor per tria, sive per quatuor tria du- 

 cantur, septem in duodecim vertuntur. . . . Jam su- 

 pcrius dictum est, quod in quinquaseriario numero, 

 qui septem hebdomadibus ac monadeadditaimpletur, 

 requies desiirnatur ; denario autem numero summa 

 perfection^ exprimetur." 



2 Approximate dates b. c. of— 



Sculptors, Painters, and Poets. Mathematicians. 



Stesichorns 600. Thales 600. 



Pindar 523-442. Pythagoras 550. 



yEschylus 500-450. Anaxagoras 500-450. 



Sophocles 495-400. Hippocrates 460. 



Euripides 480-400. 



Phidias 488-432. 



Praxiteles 450-400. Theoetetus 440. 



Zeuxis 400. Archytas 400. 



Apellcs 350. 



Scopas 350. Euclid 323-2S3. 



appeared fresh chiseled by the hand of the math- 

 ematician, and when the first ideas of harmony 

 and proportion rang joyously together in the 

 morning tide of art. 



Whether the views on which I have here in- 

 sisted be in any way novel, or whether they be 

 merely such as from habit or from inclination are 

 usually kept out of sight, matters little. But 

 whichever be the case, they may still furnish a 

 solvent of that rigid aversion which both litera- 

 ture and art are too often inclined to maintain 

 toward science of all kind?. It is a very old story 

 that, to know one another better, to dwell upon 

 similarities rather than upon diversities, are the 

 first stages toward a better understanding be- 

 tween two parties ; but in few cases has it a truer 

 application than in that here discussed. To rec- 

 ognize the common growth of scientific and other 

 instincts until the time of harvest is not only con- 

 ducive to a rich crop, but it is also a matter of 

 prudence, lest, in trying to root up weeds from 

 among the wheat, we should at the same time 

 root up that which is as valuable as wheat. 

 When Pascal's father had shut the door of his 

 son's study to mathematics, and closeted him 

 with Latin and Greek, he found on his return 

 that the walls were teeming with formula? and 

 figures, the more congenial product of the boy's 

 mind. Fortunately for the boy, and fortunately 

 also for science, the mathematics were not torn 

 up, but were suffered to grow together with other 

 subjects. And all said and done, the lad was not 

 the worse scholar or man of letters in the end. 

 But, truth to tell, considering the severance which 

 still subsists in education and during our early 

 years between literature and science, we can 

 hardly wonder if, when thrown together in the 

 after-work of life, they should meet as strangers ; 

 or if the severe garb, the curious implements, and 

 the strange wares of the latter, should seem little 

 attractive when contrasted with the light com- 

 panionship of the former. The day is yet young, 

 and in the early dawn many things look weird 

 and fantastic which in fuller light prove to be 

 familiar and useful. The outcomings of science, 

 which at one time have been deemed to be but 

 stumbling-blocks scattered in the way, may ulti- 

 mately prove stepping-stones which have been 

 carefully laid to form a pathway over difficult 

 places for the children of " sweetness and of 

 light." 



The instances on which we have dwelt are 

 only a few out of many in which mathematics 

 may be found ruling and governing a variety of 

 subjects. It is as the supreme result of all expe- 



