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340 Description of ad Burning Mirror. 
having a diameter of five decimetres, and that they receive 
perpendicularly the solar tays. The images reflected by 
the elasses of my mirror being larger than the images re- 
flected by these circular vlasses; it is evident that my results 
will be something too stnialls 
The apparent diameter of the sun being 32 minutes, it is 
evident that every point of a glass reflécts: a luminous ee 
the section of which through ‘the axis forms an angle of 39° 
This being granted, let AB, fig. 3, be the diameter of a 
circular glass, and let this diameter he five decimetres. Let 
us suppose that the straight line CD, drawn from the centre 
. of the sun on the centre of this lass, is perpendicular on its 
plane. By the straight line AB and by the straight line 
CD let us draw a plane, and let the straight Jines AE, BF 
be the intersections of the secting plane and of the surface 
of the bundie of ligbt reflected by this glass. If the 
straight lines EA, FB are prolonged, they Will meet in a 
point G, and form an anele of 32 minutes. In fact, the ap- 
parent diameter of the sun being 32 minutes, each point of 
the alass necessarily reflects a luminous cone, the section 
of which by the axis forms an angle of 32 minutes. Let 
the straight line HA be the axis of the luminous cone re- 
flected by the point A of the glass, and the right line KB 
the axis of the luminous cone reflected by the point B. It 
isevident that the aneles EAH, FBK, will beeach 16. But 
the angles FAH, F BK, are equal to the angles EGC, FGC, 
since the’ three straight lines HA, CG, KB, are parallel ; 
therefore the angle EGF is equal to the sum of the anoles 
EAH, FBR, which are 39”. - Therefore the angle EGF ts 39%, 
It now remains to calculate at what distance from: the 
mirror the image reflected will be double, triple, quadruple, 
&c. to the surface of the reflectine glass. For this .pur- 
pose I first calculate the distance GD, making this pro- 
ai a : tang. AGD': R's: AD’: GD+> or ‘rather, tang. 
PRR ey RESO SOP? ward 1" tind that GD'is ‘53,72: 
in ‘afterwards try at what distance from the glass the re- 
flected image is double, triple, quadruple, &e. to the surface 
of the’ glass. Let us suppose that it is double in LM, 
triple in NO, quadruple in EF, &c. 
In order to find the distances DP, DO, DC, &e. I con- 
duct myself as tollows ; ; 
In order to find DP, T form this proportion : 
AB: LM : :GD: GP; or.rather 1.2: aS 3572)": er 
on account ine AD being the half of LM, when the sur- 
face of the glass is the half of the i image reflected, 
- : . 
Knowing 
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