HISTORIC SKETCHES. 



Fig. 85. 



In Tig. 85 another contrivance U represented, which affords a 

 ueful moans for drawing an ellipse by mechanical aid. A 11 and 

 CD are two flat pieces of wood or metal fastened together in tin- 

 centre so as to form a flat cross, having its four arms of equal 

 length. Along the central line of each transverse piece a deep 

 broad groove is out in such a manner that anything drawn down 

 the groove c B may pass freely at the centre, B, into either of 

 the other grooves in the remaining' arms of the cross. In these 



grooves travel two pins, 

 attached by clamping 

 screws to the beam v o, 

 which is also fitted with a 

 socket atone end, in which a 

 pencil may be placed. The 

 method of describing the 

 ellipse with this kind of el- 

 liptic compasses, which is 

 called a trammel, is as fol- 

 lows : The beam, F o, is 

 placed on the top of the 

 cross-piece, c D, having the 

 pencil point at M, the pin K 

 at K, the centre of the ellipse required to be described, and the pin 

 H at D. As the beam, r o, is turned slowly to the right, tho pencil 

 point traces out the curve from M to N, while the pin that was at 

 D travels up the groove D K towards E, and tho pin K travels along 

 the groove K B towards B. On the completion of the curve M N, 

 the beam F G is lying on tho surface of the cross-piece A B, and in 

 the same direction with it, the pin H having travelled from D to 

 B, while tho pin K has travelled from E to B. Tho process is 

 then repeated in tracing out the next quarter of the ellipse from 

 N to o, the pin at H moving from E towards c, while the pin at 

 K returns from B to E. The pins continue to travel in this 

 manner up and down the grooves, from the centre to either end, 

 and from either end to tho centre, until the whole of the curve 

 M N o F is traced out by tho movement of the pencil point at L, 

 from M to N, from N to o, from o to p, and from P to M. 



PROBLEM LIX. To describe an ellipse of which the axis major 

 and axis minor are given. 



In Fig. 86 let x represent the axis major, and Ythe axis minor 

 of tho required ellipse. Draw two straight lines, A B, c D, of 

 indefinite length, at right angles to one another, and intersecting 

 each other in the point E. From tho point E, set off E F, E o, 

 along EC, ED, each equal to half of x ; and along E A, E B, set off 

 EH, B K, each equal to half of T. From tho point H or K 

 as a centra, with a radius equal to E F or B o, describe arcs 

 cutting F a in L and H. The points L and U are tho foci of the 

 ellipse required, and the curve F H o K can then be traced by tho 

 aid of a pencil and piece of thread, as shown above. 



If, however, it be necessary to determine points through which 

 the curve may be traced by hand, draw straight lines through 

 the points F, o, H, K, parallel to H K and F o, so as to form the 

 parallelogram N Q p o. Then to trace tho part H F K of tho 



x curve of the ellipse, di- 



Y vide the straight lino 



E F into as many equal 

 parts as possible in the 

 points a, b, e, d, e, etc., 

 and divide the straight 

 line F N into the same 

 number of equal parts 

 in the points/, g, h, t, k, 

 etc., and the straight 

 line F o also into the 

 same number of equal 

 parts in the points I, m, 

 n, o, p, eto. Then 

 from the point H draw 

 straight linos passing 

 through the points a, 



Fig. 86. 



6, c, d, e, in E F, and through /, g, h, i, It, in N F ; and from the 

 point K draw straight lines also passing through the points a, b, c, 

 d, e, in E F, and through Z, m, n, o, p, in F o. The points of inter- 

 section, 1, 2, etc., of the lines drawn from H through/, and from 

 K through a, from H through </, and from K through b, and so on, 

 are points in the curve, and the curve may be traced by hand by 

 drawing a curved line carefully through these points of intersec- 

 tion. The other half may then bo completed in a similar manner. 



HISTORIC SKETCHES. XXI. 



7 CHARLKS KinVAUD STUAJtT AND THE REBELLION 

 OF 1745.-U, 



As soon as the Pretender discovered himself to the people of 

 Moidart, where he landed, they declared themselves willing to 

 join him ; and in a few days came Macdonald of Kinloch- 

 Moidart, Macdonald of Glongary, Cameron of Lochiel, Stuart 

 of Appin, and the Frasers, with some 2,000 men. The royal 

 standard was now reared, and Prince Charles found himself 

 so strong that about tho middle of August he appeared in force 

 near Fort William, and two companies of royal troops, who 

 were sent against him, were cut to pieces or taken prisoners. 

 On the 4th of September possession was taken of Perth, and on 

 the 5th tho Pretender was publicly proclaimed there. The 

 titular Duke of Perth, the Marquis of Tullibardine, Lord George 

 Murray, and several other noblemen joined him ; and in spite 

 of the preparations which were being made by Kir John Cope, 

 King George's commander-in-chief in the north, the prince's 

 army moved towards the Forth. Glasgow was summoned, bnt 

 returned no answer ; so the army marched to Edinburgh and 

 occupied it, the garrison retiring to the castle. At Edinburgh 

 the prince resolved to wait till he was joined by certain influential 

 men, who had sent to him promising assistance. 



Sir John Cope, who had made strenuous exertions to muster 

 a force capable of crushing tho insurgents, now pushed forward 

 with infantry, cavalry, and artillery, and on the 20th of Septem- 

 ber (Edinburgh having surrendered on the 16th) his vanguard 

 reached Preston Pans, in the immediate neighbourhood of 

 Edinburgh. About three a.m. the next morning the Highlanders 

 attacked the English troops, and some of the English dragoons 

 having shamefully ridden away, the infantry were unsupported, 

 a panic ensued, many of the English were killed or taken pri- 

 soners, and a complete victory was won for the Pretender. 



A vain attempt was made to reduce Edinburgh Castle, which 

 resolutely held out for King George ; and then, about the end 

 of October, the prince removed his quarters to Dalkeith, where 

 he was joined by Gordon of Glen bucket, Lord Pitsligo, and the 

 Earl of Kilmarnock, and whither also were brought the sup- 

 plies of warlike stores, money, and accoutrements which had 

 been sent to him from France. 



King George was abroad when the Pretender landed, most of 

 his troops were in Flanders, and there were not more than 

 6,000 regular troops in England to oppose the rebels. The 

 king came over forthwith, troops were detached from the army 

 in Flanders, the militia were called out, associations of volunteers 

 were formed, and by the beginning of November there were 

 14,000 men in arms in the north of England, besides a con- 

 siderable body of loyal Scots to the north of Fort William. 

 Marshal Wade was given the command in chief, and was taking 

 steps to secure the English towns of importance, when he was 

 apprised of the Pretender's march southwards. 



Charles Edward had been assured that the English country 

 gentlemen only waited his coming to rise against the govern- 

 ment, and that if he marched at once into England he would 

 swell his ranks to such a size that no force the government 

 could bring would be able to withstand him. The orders were 

 therefore given for the Highlanders to march south, and south- 

 wards they went, about 7,000 strong, and crossed the Tweed 

 on the 6th of November. Wade was concentrating his troops 

 in and about Newcastle, by which town he expected the rebels 

 would pass, when he heard that Carlisle had surrendered, city 

 and citadel, on the 15th of November. On the 20th the rebels 

 marched to Ponrith, thence to Kendal, and arrived at Lancaster 

 on the 24th. On the 27th they reached Preston, and on the 28th 

 an advanced party entered Manchester. The inhabitants of 

 the chief towns were compelled to aid the Pretender both by 

 money and goods ; but few people joined the army, and none of 

 the English gentry. On the 1st of December the Pretender 

 entered Macolesfield, and on the 4th Derby, which was the 

 most southern point to which he penetrated. Divisions sprang 

 up among the rebel chiefs, some voting for a march direct to 

 London, which, judging after the event, seems the wisest thing 

 they could have done ; others voting, in view of the large army 

 which the Duke of Cumberland had formed in Staffordshire, 

 and of the strong force which Marshal Wade had in the north- 

 eastern counties, for an immediate retreat into Scotland. The 

 Pretender yielded to the voice of the majority, and on the 6th 

 of December gave orders for the retreat. 



