350 On a solar Calorimeter used in Egypt 



AB S = 5 inches. Through B draw B 2 parallel to AB 3 and 

 make BBo=$ inches. Join B 2 B 3 . B 2 B, is obviously the line 

 representing the principal section of the mirror inclined at 45 

 to the axis. Its length B^B S = \/8 = 2-83 inches. If the line 

 B Z B S be continued until it cuts AB produced in Z>V, then B Z B 

 is the generating line of the complete cone of which the 45 

 mirror is a portion. Its length is obviously V5O = 7*07 inches. 

 The flat band which, when bent round until its edges abut, 

 forms the reflecting surface of the 45 mirror is specified by 

 the following construction. 



On a sheet of paper, or on the silvered sheet of metal, 

 describe from the same centre two circles with radii of 7x37 

 and 7*07 - 2*83 = 4-24 inches respectively. The circumference 

 of the greater circle is 44*44 inches. The upper rim of the 

 45 reflector has a radius of 5 inches, therefore its circum- 

 ference is 31*42 inches. The difference between these two 

 circumferences is I3'O2 inches. If 44*44 represent 360 of an 

 arc, then 13-02 represents IO5'5. From the common centre 

 of the two circles draw to the outer circumference two radii 

 inclined to one another at an angle of IO5'5. The construc- 

 tion is then complete. If it has been carried out on the sheet 

 of metal from which the actual mirror is to be constructed, 

 we first cut out the disc of 7^07 inches radius ; we then apply 

 the shears to the point where one of the radii cuts the cir- 

 cumference ; we cut along it until we reach the inner circum- 

 ference, we then cut round this circumference along an arc of 

 2 54'5> when we arrive at its inner section with the second 

 radius, which is then followed until the outer circumference 

 is reached. The annular disc, less the sector of IO5'5 ampli- 

 tude, which remains, is the metal band which, when bent 

 round until its edges abut, forms the 45 mirror. 



Outer Mirror. Through /> 3 draw O. A P :} parallel to OP and 

 on it layoff B 3 A 3 = BA = 2 inches. From A 3 as centre, at 

 the distance A 3 3 describe a circular arc. Join AA 3 and 

 produce the line AA 3 till it cuts the arc in B 4 . Join B 3 B t . 

 B z Bt is the line of section of the outer mirror. For, having 

 in view the properties of triangles and of parallel lines, it is 

 clear that the lines O^B^ and B 4 A make equal angles with 



