374 



SCIENCE OF G ^RDENING. 



Part IL 



357 



dividing the given line into four parts ; forming the ends by segments of which the 

 two outermost points are the centres, and the sides by segments proceeding from a line 

 passing at right angles through the centre of the given line {Jig- 3S7. b). 



1918. The gardener s oval, or one in which both diameters are given, is thus formed. 

 Bisect the long diameter by the transverse one, itself thus bisected by the other. Divide 

 half the transverse diameter into three parts. Take one of these parts, and set it off 

 from both extremities of the long diameter. Fix there two pins or stakes, and fix a 

 third stake one part from the end of the transverse diameter ; double a line and put it 

 round these stakes, of such a length that when stretched, it may touch the extremities of 

 one of the diameters. Then, with a pin in this extremity, move it completely round, 

 and so strike out the oval (^g. 357. c). The long and short diameters are more easily 

 divided arithmetically ; thus, supposing the given length of the oval be ninety feet, and 

 its width sixty feet ; then the third part of half of the width is ten feet, and this distance 

 set back from the extremities of the diameters gives the situation of the stakes at once. 



3u58 



1919. A sjriral line, or volute, may be sometimes re- 

 quired in gardening, for laying out labyrinths or curious 

 parterres. The width or diameter of the spiral being 

 given {Jig. 358. i, h), bisect it, and divide each half into 

 as many parts as the spiral is to form revolutions (Jig. 358. 

 g to h). Then, from the centre draw all the halves of 

 the spirals which are on one side of the diameter line 

 {be, de, fg, hi) ; and from the point where the first semi- 

 spiral intersects the diameter line (6), as a centre, draw 

 all the others {de,fe, hg ). 



1920. Uniting three points in a curved line. A very 

 useful problem both in laying down plans on paper, and 

 transferring them to gardening, is that which teaches how, 

 Jrom any three points {Jig. 359. a, b, c), not in a straight 

 line, to Jind the centre of a circle whose circumference shall 

 pass through them. Imagine the three points connected 

 by two straight lines ; bisect these lines by others {g and e), 

 perpendicular to them, and where these intersect (at g) 

 will be found the centre of the circle whose circumference 

 shall pass through the three points. 



1921. The method of laying out polygons on even 

 ground, or any geometrical figure, will be perfectly sim- 

 ple to such as can perform the problems on paper ; all 

 the difiTerence on the ground is, that the line is used in- 

 stead of the compasses, with or without the assistance of 

 the square and arithmetical calculation. 



1922. Laying out the ground-lines of gardens, parterres, or any large figures on plain 

 surfaces, is merely a mixed application of geometrical problems. It is only necessary 

 to premise, that a straight line is found by placing rods upright, so as they may range 

 one behind the other at convenient distances, and so accurately adjusted, that the one 

 next the eye may conceal all the rest. A plan 

 of a garden, &c. (Jig. 360. a) being given 

 with a scale and north and south line attached, 

 first find its extreme dimendons, and supposing 

 you have space sufficient for laying it out, find 

 the central lines {fig. 361. a,a,b, b), and lay 

 them down first, distinguishing them by rows 

 of stakes ; then from tfiese set off the lines of 

 the central plot, if any, the walks, alleys, walls, 

 &c., distinguishing them by strong stakes, 

 which may remain till the ground is put into 

 proper form. 



1923. In laying out polygonal gardens, or 

 plots, or ponds {Jig. 360. b), when the dimen- 



360 



