THE ANGLE OF ELEVATION. 



137 



applied as in our figure." Gardeners 

 generally take the angle formed by the 

 rafter and plumb-line, and call that the 

 angle of the roof ; but the true angle is 

 that formed by the rafter and horizontal 

 line, as elsewhere noticed. " If the 

 quadrant is numbered both ways, the 

 proper angle is immediately obtained." 



To find the angle of elevation formed by 

 the roofs of hothouses, the following very 

 plain and practical rules have been given 

 in the "Gardeners' Chronicle," 1843, p. 

 721. There are many other ways to find 

 this out, and those who have studied tri- 

 gonometry will recollect the problems 

 bearing on the case. We adopt the two fol- 

 lowing, as they are sufficiently simple to be 

 understood by very moderate capacities : — 



" By means of a Gunter's scale and a 

 pair of compasses, the pitch or elevation 

 of roofs may be found easily as follows : 

 Draw a horizontal line, and from the end 

 of this another at right angles, by a square 

 or otherwise ; on the former, set off as 

 many equal parts, say half-inches, as the 

 house is feet in width, between where the 

 outer side of the rafter touches the front- 

 wall plate and the back wall ; and on the 

 other as many of such parts as the back 

 wall is feet in height, measuring from a 

 point on a level with the front-wall plate 

 to the under side of the rafter at top. A 

 line drawn between the points marking 

 the above measures will form the slant- 

 ing side of a triangle, corresponding with 

 the pitch or elevation of the roof. It 

 only remains to ascertain the number of 

 degrees which the angle contains. With 

 the distance of 60° form a line of chords, 

 marked cho. on Gunter's scale ; place one 

 foot of the compasses in the angular point, 

 and with the other describe an arc, inter- 

 secting the lines representing the base 

 and roof; the distance between these 

 lines at the points of intersection by this 

 arc, will extend from the beginning of the 

 line of chords to the number of degrees 

 Fig. 132. which the angle con- 



Z b tains, or, in other 

 words, to the number 

 of degrees of eleva- 

 tion. Or a simple 

 way is the following : 

 Describe the triangle 

 a b c, on which let a c 

 represent the width, 

 and b c the height of the back wall above 



VOL. I. 



the front-wall plate ; then place the instru- 

 ment called a protractor, with its middle 

 line at a, and the line a b will intersect 

 on the protractor the angle required." 



In following out the same subject, we 

 cannot do better than transcribe the fol- 

 lowing data for determining the angles of 

 glass roofs as laid down by Wilkinson. 

 " The angle contained between the back 

 wall of the forcing-house and the inclined 

 plane of the glass roof, always equals the 

 sun's altitude, when its rays fall perpen- 

 dicular on that plane, provided that the 

 inclination of the plane to the horizon 

 be at an angle not less than 28° 2', nor 

 greater than 75°. Within the above 

 limits the sun's rays are perpendicular 

 twice in the year — once in going to, and 

 once in returning from, the tropic. Hence, 

 then, having determined in what season 

 we wish to have the most powerful effects 

 from the sun, we may construct our 

 houses accordingly by the following rule : 

 Make the angle contained between the 

 back wall of the house and its roof equal 

 to the complement of the latitude of the 

 place, less or more, the sun's declination 

 for that day on which we wish its rays to 

 fall perpendicularly. From the vernal 

 to the autumnal equinox, the declination 

 is to be added, and the contrary. Thus, to 

 apply those principles to the slope of roof 

 recommended by Knight for ripening 

 grapes in July, say at London, we have — ■ 



Latitude of London, . . . 51° 29' 

 Sun's declination on the 21st of July, 17° 31' 



33° 58' 



— or 34° nearly. 



In continuation, Mr W. says, "As we 

 want the genial warmth of the sun's rays 

 most in spring, therefore, for general pur- 

 poses, that construction would perhaps be 

 best which gives us the greatest quantity 

 of perpendicular rays then. If the incli- 

 nation were 45°, the sun's rays would be 

 perpendicular about April the 6th and 

 September the 4th ; and as the rays 

 would vary very little from the perpendi- 

 cular for several days before and after the 

 6th of April and the 4th of September, 

 the loss of rays arising from reflection 

 would, as appears from the annexed table; 

 be nearly a minimum. Even at the winter 

 solstice, the loss by the obliquity of the 

 angle of incidence would be only two in 

 one thousand more than when the rays 



s 



