26 



THE POPULAE EDUCATOR. 



directed to VPSE. The edge a b of the shadow on the ground 

 of the block is directed to VPSI, and its extent cut off at 6 by a 

 ray from c to VPSE ; b d, which is necessary to complete the 

 outline of the visible portion of the shadow cast by the block, 

 is directed towards VP 1 . 



PROBLEM LIV. (Fig. 92). A cross, the face of which is 

 inclined to the PP at an angle of 40, casts its shadow on a 

 plane inclined at 30 with the horizon ; the horizontal trace of 

 the plane is perpendicular to the pp. The sun is in the picture, 

 that is, its rays are parallel with the picture, its elevation 55 ; 

 other conditions at pleasure. 



Draw anywhere across the HL the line a b at an angle of 55 

 for the directing ray of the sun's elevation. Draw the line c d 

 at 30 with the ground line representing the inclination of the 

 plane receiving the shadow. Draw a line through PS parallel 

 to c d ; this will be the trace of the inclined plane receiving the 

 shadow, and upon which the vanishing points for the retiring 

 edges of the shadow upon the inclined plane are to be found ; 

 thus, draw lines from VP 1 and VP 2 parallel to a b, producing VP 3 

 and VP 4 . 



The learner will naturally pause here to inquire why these 

 lines should be drawn, and to this query we must reply 

 as follows : If there had been no inclined plane upon which 

 the shadow falls, the whole of the shadow would have been 

 horizontal, and consequently the retiring lines of the shadow 

 would have vanished on the HL at VP 1 and VP 2 respectively ; 

 but as the plane containing the shadow becomes inclined, 

 so will the trace of the plane be inclined also, elevating 

 or depressing the vanishing points proportionately. Con- 

 struct the perspective elevation of the cross according to 

 previous instructions. The rays from the angles of the cross 

 must be drawn parallel to a b ; the horizontal projections of the 

 shadow, as o m, must be drawn parallel to the PP (see Lesson 

 XVI., page 260), as far as the horizontal trace of the inclined 

 plane c PS. Afterwards the shadows of the perpendicular edges 

 of the cross which fall upon the inclined plane must be drawn 

 parallel to c d, as m n, the length of whica is determined by 

 the ray en; n f is the shadow of e r, and is drawn in the 

 direction of VP 3 ; / g is the shadow of r h drawn parallel to 

 c d, because r h is a perpendicular line ; g Ic, the shadow of 

 h i, is drawn towards VP 4 ; k s, the shadow of i p, is drawn 

 towards VP 3 . The remaining edges of the shadow upon the 

 inclined plane will not be difficult, if the pupil carefully con- 

 siders the positions of the lines of the cross ; the shadows of 

 those which are perpendicular must be drawn parallel to c d ; 

 those which would retire, had the shadow been on the ground, 

 to VP 1 nuist vanish at VP 8 ; and those which would retire to 

 VP 2 must be directed to vp 4 . After the shadow leaves the 

 inclined plane at the horizontal trace c PS at z, it then falls 

 upon the ground, consequently the edge z I will go to VP 1 , and 

 the shadow of v w, which is q t, will vanish at vp 2 . The learner 

 should go through this problem three or four times, taking the 

 inclinations of ab to the H L and c d to the ground line at 

 different angles to those which have been used in this problem. 



PROBLEM LV. (Fig. 93). Again, to show how to determine 

 the vanishing points of shadows which fall upon inclined planes, 

 we have borrowed a subject from " Malton's Perspective." In 

 that work the subject is a ladder inclined against a house ; we 

 have chosen a pole, a b, instead, to make the explanation more 

 simple. ' c VP 1 is the trace of the inclined plane of the lower 

 roof ; D vp 1 is the trace of the inclined plane of the upper roof. 

 These are found by drawing a line from the vanishing point of 

 the horizontal edge of the roof to the vanishing point of the 

 inclination (see Lesson X., Problem XXXII., Vol. III., p. 333). 

 The trace of the plane of the shadow is from A to B, found by 

 drawing a line from the vanishing point of the object, tlie pole, 

 casting the shadow, through the vanishing point of the sun's 

 elevation, VPSE ; this contains the vanishing points for the, 

 shadow of the pole, projected upon the inclined roofs, and are 

 found where the traces of the inclined planes intersect the trace 

 of the plane of shade. To begin with the shadow on the ground : 

 Because this portion, a c, is horizontal, therefore its vanishing 

 point is on the HL at VP 3 ; c d vanishes at B, because the plane 

 of the wall containing c d vanishes through VP 1 ; d e vanishes 

 at A, the vanishing point of the pole, because the plane of the 

 wall containing d e is parallel with the pole ; e f at VP 4 , 

 where the trace of the plane of the roof intersects the plane of 

 shade ; similarly, g h to VP 5 . and g f similarly to c d at B. 



HISTORIC SKETCHES. XLYI. 



RUSSIA AND PETEE THE GEEAT. 



IN the year 1697, five years before the death of William III., 

 a foreigner of singular personal appearance, of rough exterior, 

 and still rougher manners, applied to the English authorities to 

 be allowed to work as a shipwright's labourer in one of the 

 royal dockyards. Not only was permission granted for him to 

 work as he wished at Deptford dockyard, but orders were given 

 to the superintendent there to let the stranger see as much as 

 possible of the shipbuilder's art, and to afford him every infor- 

 mation he might desire. A good house (one that belonged to 

 the Evelyn family, and in which John Evelyn, the accomplished 

 diarist and author, wrote and studied) was taken for him and 

 his companions at Deptford, so that he might live near his 

 work, and in the dockyard he laboured early and late, and 

 possessed himself to a remarkable extent with the knowledge 

 of a skilled shipwright. This was not the only object he had 

 in entering himself at the yard. He knew, none better, that 

 example is worth a hundred precepts, and that he could appeal 

 from those of his subjects who did not think it became them to 

 work, to his own example, by which he had shown them both 

 how to work and why they should work. 



This shipwright and dockyard labourer was Peter the Great, 

 Czar of Russia, who a few months before had quitted his capi- 

 tal, Moscow, to see and learn new things for his kingdom, of 

 which the most important knowledge that he possessed was 

 that it sadly needed reformation in every department. Resolved 

 to bring his countrymen out of the barbarism in which they 

 were immersed, and aware that this could only be done by the 

 introduction of civilised elements from without aware, too, of 

 the superstitious horror the Russians had for either leaving 

 their own country themselves or for allowing strangers to enter 

 it he conceived the idea of making a tour of the principal 

 capitals of Europe, where he might learn for himself what was 

 worthy to be introduced, and where he might enlist artificers 

 and scientific men in his service to come to Russia and teach his 

 subjects. At the same time he sent ambassadors to the several 

 courts of Europe, that Russia might be represented, and that 

 he might know from authentic sources what was going on in 

 the world of politics. Amsterdam was the first city that ar- 

 rested his attention, where the great amount of shipping, of 

 which he was exceedingly fond, drew him with peculiar force. 

 He worked in a dockyard there for some time, living like any 

 other labourer, and refusing to allow any distinction to be made 

 between him and his fellows. After acquiring all the know- 

 ledge he could pick up in Amsterdam, he came over to England. 



Rough, even brutal in his manners for what was he but the 

 chief barbarian of his empire ? the Czar Peter had talents 

 which were superlatively great, as compared with those of any 

 one else in his dominions. He had the wisdom to see wherein 

 his people were wanting, and to recognise the means of supply- 

 ing their wants ; he had the magnanimity to disregard all the 

 carping criticisms of those who, having been born in more civi- 

 lised countries, affected to despise the wild men of the north ; 

 and he had the courage to persist in improving, in spite of 

 themselves, a nation whose leaders hated to be reformed, and 

 whose fears and superstitions whispered them to cling to the dead 

 past rather than to draw life and energy from the living present. 

 Rough manners, as indicative of a strong will, were perhaps 

 essential to the fulfilment of Peter's purpose. A soft-speaking, 

 gentle-handed man would never have curbed the hitherto un- 

 bridled licence of a savage soldiery, nor have overcome the pig- 

 headed, unreasonable opposition of priests and landlords, who 

 only saw in the enlightenment of the nation the downfall of 

 their own power. 



The Czar Alexis, grandfather of Peter the Great, was the first 

 native prince who seems to have thought the Russians capable 

 of being anything more than mere savages. Not until his suc- 

 cession to the throne had the empire sufficiently recovered from 

 the repeated incursions of the Mongolian Tartars, of the Poles 

 who devastated whole districts, and kept possession of strong 

 towns like Smolensko and from the still more fatal wounds 

 inflicted by civil war, to allow of attention being turned to the 

 general amelioration of the empire. Hitherto the history of 

 Russia consisted of accounts of savage life on a large scale, of the 

 conflicts which one set of great chiefs waged with another, of the 

 struggle for supremacy between the head of the state a.nd the 



