128

BURNING MIRRORS.

surface of the earth. Supposing' the heat of the air inordinary weather to be 65°, in sultry weather 75°, giving anaverage medium of 70°, even without allowing for the mostpotent operation of a mid-day sun. Taking the degree 70as the average effect, the calculation will appear as follows:the accumulated power of this lens, presuming the effect tobe equal over the entire surface, the concentrated heat atthe focus would be equal to 73,938°.

Those who had an opportunity to examine the effect ofthis lens, will remember, that the external part of the focaleffect was less intense than near the centre; but it beingconceived possible that the refraction of the light and theeffect of the caloric fluid, may not take place at the sameangles. It has, therefore, been thought by the ingeniousauthor of those calculations, 1 from whence this memoir isextracted, to deduct one-fourth thereof as a compensation;after which there remains 55,454°, as the expression of itspower.

And as the application of the second lens reduced itsfocal diameter to half an inch, the effect, w itliout allowancefor the reduction of its power, would be equal to 221,816°,deducting one-fourth for a second transmission, there re-mains 166,362°, as the expression of its power.

Admitting the solar rays emanated from a point, the focusof the lens would be also a point; for the rays transmittedthrough one edge of the lens would meet those transmittedthrough the other edge, so that the focus would be withoutparts, or a mere mathematical point; but as the sun isknown to measure 31' 32' during his apogee, and 32' 28"during his perigee, the focus must necessarily be 0.7105parts of an inch at Midsummer, and 0.7594 at Christmas .The length of the luminous axis at Midsummer, must, fromthe same cause, be 3.428 inches, and at the opposite period3.557; because the dimensions of the focus are actuallydependent on the apparent diameter of the sun, its semi-diaineter being to be added to increase the measure of theconverging rays on the opposite sides, the tangent of whichis the semi-diameter of the focus; and by the same meansthe length of the axis is discovered, adding to and subtract-ing from the converging angle, by which means the pointsat which they meet on the axis are discovered. Those twopoints disclose the commencement of the luminous appear-ances thereon.

The variation between the above calculated diameter of

1 Dr. Rees.