48 Mr Buchanan, On a solar Calorimeter used in Egypt 



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

 is 13-02 inches. If 44*44 represent 360° of an arc then 13*02 

 represents 105*5°. From the common centre of the two circles 

 draw to the outer circumference two radii inclined to one another 

 at an angle of 105*5°. The construction 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 circumference ; we cut along it until we reach the 

 inner circumference, we then cut round this circumference along 

 an arc of 254*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 105*5° amplitude, 

 which remains, is the metal band which, when bent round until 

 its edges abut, forms the 45° mirror. 



Outer Mirror. Through B, draw 3 P S parallel to OP and on it 

 lay off B 3 A 3 = BA = 2 inches. From A 3 as centre, at the distance 

 A 3 B 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 4 . B S B 4 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 4 B 4 and B 4 A make 

 equal angles with the line B 3 B 4 . But 4 B 4 is the direction of the 

 incident ray at B 4 ; therefore B 4 A is the direction of the reflected 

 ray, and the ray which strikes the outer rim of the mirror is 

 reflected upon the upper extremity of the focal line. In the same 

 way it is evident that the incident ray 3 B 3 , which strikes the 

 inner rim of the mirror, is reflected along the line B 3 B and 

 falls upon B, the lower extremity of the focal line. Consequently 

 parallel rays which strike the mirror in points between B 4 and B 3 

 are reflected on AB and strike it in points between A and B 

 which are homologous as regards position with the points in the 

 mirror between B 4 and B 3 which are struck by the primary rays. 



In the isosceles triangle B 3 A 3 B 4 the angle A 3 is equal to the 

 angle A 3 AB, therefore 



T> A AT) 



= - 0*4 ; 



tan^l 3 



B 3 A S AB 

 ~ AB 3 ~ AB 3 ~ 





A 3 =111° 48'; 



and the angle at the base 



;=£(180°-vl 3 ) = 34 o 6'. 

 Further, the base 



B 3 B 4 = 2 x AB cos i = 331 inches. 



