580 Dinhur Castle, its Gardens and its Gardeners. 



of land are commonly found to be ; so, instead of giving his 

 lessons on paper, which is a common practice, he marked off 

 with his picket staves a large square, and showed that by mul- 

 tiplying the base side by the perpendicular, the number of 

 square links, or feet, or yards, would be found. After Bauldy 

 had understood how to find the contents of a square, he next 

 formed a parallelogram, and showed that the area is found by 

 multiplying the length by the breadth. He next formed the 

 rhombus, and directed them to multiply the base by the perpen- 

 dicular height, and they would find the area : he also showed 

 them the difference between the rhombus, and the rhomboides 

 from the rhombus. He proceeded to the triangle, and showed 

 them various ways of finding the area ; first, by multiplying the 

 base by a perpendicular demitted from the opposite angle, half 

 the product is the area ; or, by multiplying the base by half of 

 the perpendicular, or the perpendicular by half of the base. After 

 the triangle he formed the trapezium, and, dividing it into two 

 equal parts by a diagonal line, and demitting perpendiculars from 

 the other angles and multiplying the diagonals by the sum of the 

 two perpendiculars, showed them that half the product is equal 

 to the area. Next in order he described the trapezoid, the 

 regular polygon, the circle, circular ring, segment of a circle,, 

 and the ellipse. 



Having gone over the various forms in wliich the different 

 parts of our earth are commonly found, or a combination of 

 them, he found that he had not time to measure the fields which 

 he intended. The sun was descending towards the highland 

 mountains, and the long shadows of the evening were gathering 

 around them, so it was agreed that they should draw their opera- 

 tions to a close, and resume them again at an early opportunity. 



When they were leaving the field the attention of Bauldy 

 appeared to be fixed upon a beautiful Lombardy poplar that 

 was growing near the place where they were. At last he said, 

 " Weel master, I hae aften wondered what the hight o' that tree 

 may be, but I dinna ken how to reach the top o't." — "But you 

 may soon know the height of it, Archibald, without going to 

 the top of it," replied his master. " The sun has not yet set, 

 and the shadow of the tree is very distinctly seen upon the field, 

 so that the length of the tree's shadow may be easily known." 

 He knew the length of one of his picket staves, and measured 

 its shadow and also the shadow of the Lombardy poplar ; he 

 applied the rule of three to the three given numbers, and in a 

 few minutes he told Bauldy that the height of the tree was 

 about 70 ft. Bauldy thanked his master for the information he 

 had given him, and added that it was " a braw thing to hae 

 lair, for it made them that made a gude use o't like a different 

 set o' folk althegither." — "I am glad to see you, Archibald," 

 said the master, " so desirous to obtain useful acquirements, and 



