THE POPULAR EDUCATOE. 



vaulted roofs or domes at the extreme or lower end above the 

 chancel, and sometimes also above the aisles. They had com- 

 monly in front the accessory buildings, including the baptistery 

 and the rooms for the catechumens, or those who were preparing 

 for admission into the church. These adjoining erections were 

 then separated from the church by an atrium or hall, surrounded 

 by columns which led from outside to tho door of the church, 

 which always had a porch, or narthex, as it was called. In the 

 Interior, two rows of columns divided the edifice into the nave 

 and the aisles. The nave alone in the ba- 

 silicas or churches of the primitive Chris- 

 tians, terminated in a semicircular arch or 

 choir. At a later period the aisles had 

 also their choirs ; it was then that the first 



L6 ' [^ story or gallery which was erected upon 



__i the aisles disappeared, and the women, for 



whom it was reserved, began to occupy 

 the left side of the building. The different 

 parts of the Basilica of Parenzo will con- 

 vey to the mind of the reader the arrange- 

 ment of the principal parts of the churches 

 now described. 



The exterior of the basilicas was very 

 simple; but the interior was richly deco- 

 rated with mosaics, with paintings, and 

 particularly with splendid marbles, which 

 were used in great profusion; also with 

 monoliths, or columns, made of a single 

 stone, usually stolen from antique edifices, 

 all of the most magnificent description ; 

 and the pedestals, capitals, and cornices 

 were of equally splendid and rich mate- 

 rials. A good example of the old basilica 

 PLAN OP THE BASILICA fg the church of St. Agnes at Rome. 



OF PARENZO. rj n - e R omanes que stylo was formed from 



a. The principal nave. b. the combination of the two former, the 

 The chancel, c. The Latin and the Byzantine; and in these, 

 hall, or atrium, d. ^he arcade played the most prominent part. 

 The baptistry, e. Arche9) indeed, were multiplied in endless 

 The steeple, or bel- variety from the choirs which rose on a 

 fry. /.The sacristy. 



or vestry, h The Clrcu l ar plane, to domes and arched but- 

 choir. fc'fe. Small tresses, those appendages to buildings 

 choirs. I. The tri- which were first employed in this style of 

 cliiiiuin, or supper- architecture. The Romanesque period, 

 room. however, produced edifices different from 



the basilicas, by characters well defined. 



Orientation, or building churches east and west, became the 

 decided rule ; a transverse nave, or transept, changed the ar- 

 rangement of the interior of churches, and gave them the form 

 of a cross. The choir or recess, of a semicircular form, was 

 commonly unique, and spanned the whole width of the edifice, 

 including the nave and the aisles. Some Romanesque churches, 

 however, have preserved the three recesses or choirs ; and these 

 are generally the oldest. The columns were replaced by square 

 piers, ornamented on each side by a column carrying groined 

 arches ; and when stone mouldings were introduced at the edges 

 of the domes, the number of the columns was increased to eight. 

 The shafts of the four intermediate columns were then dispro- 

 portionally lengthened, and departing from the proportions 

 established by antiquity, lost their rational proportion to their 

 diameter ; the choir alone preserved the isolated columns. In- 

 dependently of the principal altar, secondary ones were erected, 

 of which the number was afterwards augmented by those of tho 

 chapels built round the choir. The exterior of the Romanesque 

 churches also presented a very different aspect from that of the 

 basilicas. The belfries, which were at first small, became then 

 of great importance, and were raised above the porch, or above 

 the cross aisle. These constructions were very solid, and had 

 several storeys, partially open, except at top ; and were sur- 

 mounted by lofty stone spires. At a later period, the abut- 

 ments, or spur- walls, became insufficient to sustain the thrust of 

 the great domes, and were then detached from the walls and 

 transformed into buttresses. Specimens of this kind of edifice 

 may be seen in the church of Rosheim, in the Department of 

 the Lower Rhine ; St. Germain-des-Pres, at Paris ; of L'Abbaye- 

 aux-Hommes, at Caen ; of Bocherville, near Rouen ; and others 

 in France. In the most of these churches, there is a small gal- 

 lery over the aisle, like that of St. Gcrmain-des-Prc's at Paris, 



which represents the gallery of the early basilicas. The columns 

 or pillars are united by circular arches, ornamented by archi- 

 volts in simple profile, and the whole of the edifice is covered 

 with groined vaulting, and with stone mouldings of the same 

 description. 



At the commencement of the Romanesque period in the West, 

 the Eastern style of art, the parent of so many architectural 

 novelties, was developed anew in Asia and Africa, and the Arabs, 

 who played so prominent a part in the history of this epoch, 



covered Arabia and Egypt, and 



penetrated the interior of Persia, 

 with their edifices. The Moorish 

 branch extended along the northern 

 side of Africa to the ocean, and 

 there all that an Eastern imagina- 

 tion could produce that was fan- 

 tastical and marvellous, was repro- 

 duced in their architectural works. 

 During the most ancient period of 

 this art the semicircular arch pre- 

 dominated ; but it soon overstepped 

 its central point, and the arch be- 

 coming more than a semicircle, 

 took the shape nearly of a horse- 

 shoe. At a later period, the in- 

 trados, or inner ring of the an;h,was 

 carved in the manner exhibited in 

 tho celebrated Mosque of Cordova. 

 The second period was that of the 

 pointed arch very ancient speci- 

 mens of which are found at Cairo. 

 These monuments or erections are 

 purely Arabic, such as the Mokias 



or Nilometer, and various mosques of that city. In Persia and 

 in India the same stylo is exhibited, and is always found in con- 

 nection with the pointed arch, and the same principles are fol- 

 lowed in the architecture of that country at the present day. 

 Wo give in the annexed engraving a specimen of tho Arabic 

 arch. An important question has never yet been answered 

 respecting the origin of the pointed arch, which was first, as 

 we have seen, used by the Pelasgians, but which, abandoned 

 until the Middle Ages, was again taken up by the Arabian and 

 the Western architects, at an epoch when it is difficult to ascer- 

 tain whether the East preceded the West in its application, or 

 whether the reverse was tho case. Whichever was the oase was 

 of little moment, until it was extended as a complete system of 

 construction, and became the foundation of the Gothic or ogival 

 stylo of architecture. It appeared in the West, in the twelfth 

 century, in several rare edifices, in which it usually occupied the 

 lower part of the building, as presenting more resistance in 

 supporting its elevated portions. From this use, first origi- 

 nating in the demand for solidity, it was extended to all parts 

 of the building. Thus applied, this new system of architecture 

 was developed, took its flight, and the thirteenth, fourteenth, and 

 fifteenth centuries saw its rise, its full vigour, and its decay. 

 The Gothic churches are in general larger than those of the 

 Romanesque period, they are disposed in the same way, but their 

 architecture becomes softer, and the forms more graceful. 



SPECIMEN OP THE ARABIC OU 

 MOORISH ARCH. 



LESSONS IN ARITHMETIC. XXXVIII. 



EQUATION OP PAYMENTS. 



18. THIS is a method by which to find the time at which two 

 or more debts, due at different times, may be equitably paid by 

 one payment, equal to the sum of the amounts of the debts. 

 This time is called the equated time of payment. We will first 

 take the case of two sums. 



The principle upon which the time is calculated is this that 

 the sum of the present values of the two debts is equal to the 

 present value of the sum of the amounts of the debts supposed 

 due at the equated time. 



Thus, if 100 were duo nine months hence, and .50 twelve 

 months hence, at 4 per cent., we must find the present value of 

 each, and add them together. We must then find the time 

 in which, at the given rate of interest, the sum so formed 

 would amount to .150. 



EXAMPLE. Find the equated time of payment of 309, due 



