in Orthographic Projection. 



383 



tions of two of the axes remains that of equality, while that 

 with the third one is different, that single projection will, in 

 like manner, give two lines of sight. In order, however, to 

 obtain the facility of execution which belongs to the isometri- 

 cal method, these proportions must be integral, and not only 

 so, but capable of being expressed by means of the plotting 

 scales commonly used by draughtsmen. Taking these scales 

 at 10, 25, 30, 40, 50, and 60 to the inch, there are possible 

 two arrangements of the former sort, giving three lines of 

 sight each, data for which are subjoined ; there may be a great 

 variety of the latter sort giving two lines of view each, data 

 for three of the best of which are also subjoined, giving to the 

 draughtsman altogether (including the isometrical) 13 different 

 directions of view. 



The three axes are represented by o a, o b^ o c. 



(1.) For the scales 40, 50, and 60 to the inch. In this ar- 

 rangement all the lines parallel to o a, and all oblique lines are 

 to be laid down from scale 40 ; those parallel to o 6 from scale 

 50, and those parallel to o c by scale 60. 



Angle aoh=: 99.23 

 6 c = 156.60 

 coa = 103.47 



And a being 100, 



06 = 137.9 

 6c = 143.7 

 <ra=i 132.7 



