Mr. M. Smith on the Phcenomena ofLimar Eclipses. 1G9 



of its surface, or about 50 seconds of its diameter ; the reason 

 of which will appear from the following consideration. 



Suppose that during a partial lunar eclipse a curve were 

 described on the lunar disc, exactly to pass through all those 

 points in which the limbs of the sun and earth appear in con- 

 tact : it is evident that all that portion of the lunar disc lying 

 within that curve will have no solar light, and would thei-efore 

 be invisible or eclipsed : it is further evident, that an infinitely 

 small portion of solar light will not suffice to render the sur- 

 face of the moon visible, but that a certain definite portion of 

 light is necessary for tliat purpose. Let therefore another curve, 

 exterior to the former and every where at the distance of 50 

 seconds from it, be described ; and it may easily be conceived, 

 that although the space situated between these two curves will 

 be enlightened by a small portion of the solar rays, it will not 

 be sufhciently illuminated to become visible by reflection ; con- 

 sequently, that this latter curve, and not the former, will be 

 the visible boundary of the eclipse : and hence the shadow ap- 

 pears enlarged, by extending a small space into the penum- 

 bra. The precise quantity of this augmentation, perhaps, can 

 only be determined by observation : — atlmitting it to be 50 se- 

 conds, it may be found by computation that the shadow ap- 

 pears to terminate where the light is reduced to about the 

 120th part of the whole. It may further be observed, that 

 whatever be the amount of this augmentation, it may without 

 sensible error be considered a constant quantity, the variation 

 therefrom never amounting to more than a single second, be- 

 ing chiefly dependent on the semidiameter of the sun, and not 

 on the parallax of the moon : it is, however, probable, that the 

 augmentation may vary during the progress of an eclipse, be- 

 ing always greatest at the beginning and end, and least at the 

 limits of total darkness, a smaller portion of light sufficing to 

 render the moon's surface visible in the latter cfise than in the 

 former. 



To prove tliis augmentation by experiment, jirocure a cy- 

 linder of which the diameter is not less than an inch and a 

 quarter, nor gi'eater than an inch and a half. (The outer 

 tube of a pocket telescope is a very convenient object for this 

 purpose.) Measure the diameter of this cylinder very accu- 

 rately, and on a card draw with a pencil two parallel lines 

 about three or four inches in length, and distant from each 

 other the diameter of the cylinder. Between these two lines 

 draw two other lines parallel with the former, and each half 

 an inch distant therefrom : you will then have four parallel 

 lines and three spaces. Divide each of the two outer spaces 

 into eight equal parts by means of seven lines all parallel with 



Vol.66, No. 329. Sept, 1825. Y the 



