168 Mr. C. Fox on the Construction of the Oblique Arch. 



pear to have been clearly understood by the writer of the letter 

 in question. 



The two points to be determined are, whether my rule is 

 identical with Mr. Nicholson's; and if not, which is the better 

 of the two. 



That they are not identical I hope will be evident from the 

 following facts ; and which is the better of the two must be 

 left to the judgement of your readers. 



No one would for a moment hesitate to acknowledge the 

 obligations which practical men are under to that highly ta- 

 lented individual Mr. Peter Nicholson ; but on referring to 

 his Treatise on Masonry and Stone-cutting (plate 17), it 

 will at once appear that the intrado is the only surface de- 

 veloped, and the approximate line being laid down upon it, 

 all the courses are drawn at right angles to that line ; the 

 courses therefore are drawn with reference to the intrado 

 only. Now my plan is to make use of neither intrado nor ex- 

 trado for this purpose, but to lay down all the courses upon 

 a supposed intermediate surface: the two plans are therefore 

 not identical. 



Now the reasons why I conceive my plan to possess ad- 

 vantages superior to Mr. Nicholson's are these. On referring 

 to vol. viii. of this Magazine, Plate III. fig. 6, it will be seen 

 that the angles of the courses, as shown in the developed in- 

 trado and extrado, differ very considerably, even more than 

 16^: it will therefore be obvious, that if the angle of the in- 

 trado is adopted for the rule (as by Mr. Nicholson) then the 

 angle of the extrado will be wrong ; and again, if the angle 

 of the extrado were adopted for the rule, then the angle of the 

 intrado would be incorrect; for in either case the thrust 

 would not be in the direction of the abutment, which in every 

 arch is an essential point. 



Now to use my own words (vol. viii. p. 302), " It is evident 

 from fig. 7, that if spiral planes are considered as composed 

 of spiral lines, placed at various distances from the centre of 

 the cylinder, each of these lines will form a different angle 

 with the axis; and therefore, as an arch has always some thick- 

 ness, that although we have the inner edge of the spiral plane 

 placed at right angles to the thrust, yet every other portion 

 is gradually departing from a right angle, and is exerting its 

 force in an improper direction : thus an arch of this descrip- 

 tion can never exert its thrust in the direction of the bridge, 

 but is endeavouring to push the abutments obliquely." 



" To get the thrust strictly correct I have supposed the 

 arch to be cut into two rings of equal thickness (see fig. 8), 



