SKKTCII1NG FIIOM NATURE. 



167 





Slba. of currant* 1 Ib. of hope, 5 lbn. of hops 2 Ibs. of tobacco 

 lit 4a. per Ib, what in tho value of 1 Ib. of rioo P 

 1 Ib. rioo. 



2 Ib*. currants. 



105 16 



shillings = ild. - Hfd. Answer. 



EXAMPLE 3. A certain book is to contain 5 sheets of paper, 

 md 4000 copies are to be printed. Supposing a ream of paper 

 to weigh 24 Ibs., what would be the saving upon the expense of 

 publishing tho work, owing to a reduction of the price of the 

 paper Id. per pound f 



4000 copies. 



5 sheets. 



24 x 20 



24 Ibs. 



Id. reduction. 



4000x 5 x 24 

 4 d. = lOOOd. = 4 3s. 40. 



EXAMPLE 4. Find the course of exchange between London 

 and Paris i.e., the number of francs equivalent to 1 from 

 the following data : 



Tho market price of standard gold in London is 78s. per oz., 

 and the premium on gold in Paris is 8 francs per thousand. 



The Mint price of a kilogramme -(32'154 oz.) of pure gold in 

 Paris is 3434'44 francs. 



1 



20s. 



I oz. standard gold. 



II oz. flue gold. 



2'154 



1000< 



3431 '44 francs, mint price. 



1008 francs (with premium) . 



06s. Fixed Number. In the above operation, the only 

 variable quantities are the 78s. expressing the price of gold in 

 London at the time, and tho 1008 francs indicating the amount 

 of premium upon gold in Paris at the time. 



If we omit these two terms, we get an invariable ratio 

 3434-44 x 11 x 20 



Thu being determined, we need only multiply it by the ratio 

 of tho two variable quantities, to determine the course of ex- 

 change in any given case. 



Thu invariable ratio is called the Fixed Number, and it of 

 important practical two in the regulation of < 



KEY TO EXERCISES IN ARITHMETIC. -XJj. 



1. 5. 

 8. 15}. 



3. 25{. 



4. 11 J hilling*. 



5. 4/u per cent. 



ElEBCISE 61. 



7. 3 lt. of the first 



two to 4 of the 



iMt. 



8. Equal quantities 



of each. 



9. 21s. 2M. 



10. (1) 1 K*U. of each 

 of the spirit* to 3 

 galls, of water. 

 (2) 6 galls, of the 

 hut to 1 galL of 

 each of tho othm 

 and of tho water 



SKETCHING FROM NATURE. II. 



RETIRING LINES-POINT OP SIGHT, ETC. 



IF our pupils win carefully follow tho advice we gave them in 

 the last lesson, and at first strictly confine their attention to 

 very simple subjects, they will soon find themselves in a position 

 to attempt with confidence something more advanced, which 

 will include much that will make a demand upon their know- 

 ledge and experience in perspective. When we consider the 

 infinite variety of the positions of lines, and the relations they 

 bear to each other, so many difficulties arise, that we must 

 naturally look about us for assistance altogether independent of 

 mere manual practice, of which no amount of experience, how- 

 ever large it may be, can satisfactorily help us, and therefor* 

 wo must have recourse to perspective. In our very first attempts 

 tlie one great difficulty presents itself, viz., how to draw the lines 

 which retire ; here is the starting point from which every rule 

 proceeds, and this difficulty every one will discover immediately 

 he sits down to draw from nature. Objects parallel with our 

 position, or with the picture plane, like the posts in Fig. 1, have 

 no retiring lines the lines which represent them are either hori- 

 zontal or perpendicular ; if horizontal, they are drawn across 

 the picture, and those which are perpendicular in the object are 

 drawn so. Therefore, with proper attention to the positions and 

 proportions of these lines, exercises of this kind will be found 

 very easy ; but when we come to lines in other positions with 

 regard to the picture plane, those which retire that is, go away 

 from us, like the lines cf a railway when viewed from the top of 

 a bridge other considerations present themselves ; lines of this 

 class may retire either horizontally, or at an inclination. Those 

 of our pupils who are accompanying us through the course of 

 " Geometrical Perspective" given in these pages, will not have 

 to be told that there are established rules to aid us in drawing 

 these lines according to the position in which they may be 

 placed; they will bo satisfied upon this point, and they will have 

 discovered that by working out these problems their practice in 

 drawing them is rendered easier, and they will have found the 

 result to be satisfactory. We have said before, there is no 

 necessity, even if it were possible, to go through all the 

 geometrical rules that can be applied to the subject when 

 drawing from nature; but wo do assert that it is necessary 

 to know them, because, from having practised them upon subjects 

 under given conditions, we can satisfactorily account for the 

 position of every line we draw, let them be placed as they may. 

 There arc many who take great delight in drawing from nature, 

 who affirm that perspective is a science not at all necessary to 

 them, although they allow that it is essentially so for architects. 

 This is a mistake, which may be coupled with another, into which 

 they frequently fall, viz., that "it is too difficult to learn." 

 They contend that " if the eye is properly educated, nothing 

 more is required." This vague expression is one we have heard 

 very often, and, of course, many who use it have no definite 

 idea of what they mean by it. We ask such, what they wish 

 us to understand by the " education of the eye?" The eye is 

 not an instrument like the hand, which must have some con- 

 siderable and practical experience in order to carry out the 

 intentions; tho eye has no practical duty to perform, it is simply 

 the medium through which is conveyed to the mind the form, 

 positions, and proportions of the objects to be represented; and 

 since positions and proportions are not arbitrary, it follows that 

 some kind of education is necessary to guide our judgment and 

 practice in dealing with them : in other words, the mind must 



