1 70 Mr. M. Smith on the Phtcnomena of Lunar Eclipses. 



the former: you will then have two sets of parallel lines (re- 

 sembling staves for music), with a blank space between them 

 equal to the excess of the diameter of the cylinder above an 

 inch. Now place the cylinder upright in a window exposed 

 to the sun, and at a distance of 107 inches*, or nearly nine 

 feet therefrom : place the card so that the shadow of the cylin- 

 der may fall thereon ; and it will be found that the shadow 

 will fill all the central space, antl also one of the sixteen small 

 spaces, this small space being the amount of the augmentation 

 of the shadow : for it is evident that if the shadow were pro- 

 jected from the centre of the sun, it would at all distances 

 from the cylinder be equal thereto, and would therefore fill all 

 the space between the two outer lines. If, on the other hand, 

 the shadow were projected from the limb of the sun, it would 

 be reduced one inch at the distance of 107 inches, and would 

 consequently only fill the space between the two inner lines ; 

 but as it is found experimentally to exceed this magnitude by 

 one of the sixteen small divisions, it proves that to an eye 

 placed at the visible limit of the shadow, one sixteenth part of 

 the sun's semidiameter would be seen. This cjuantity amounts 

 exactly to one mijiute of a degree, which is consequently the 

 augmentation of a shadow cast by any object of which the 

 boundary is a right line. It appears, then, tiiat the shadow of 

 an object is projected from a point in the sun's disc one minute 

 within his limb, and therefore fifteen minutes from his centre; 

 which circumstance must be particularly attended to in the 

 construction of sundials, for otherwise they will always err 

 exactly one minute of time fi-om the truth, being too fast in the 

 forenoon and too slow in the afternoon, the shadow being 

 cast from a point in the sun's disc one minute within that limb 

 which is nearest to the meridian. As this is a circumstance 

 not generally noticed by authors who have treated on dialling, 

 it is highly probable that dials are often constructed without 

 attention being paid to it; in which case, if a watch were set 

 by such a dial in the forenoon, it would be found to vary two 

 minutes from it in the afternoon. 



The reason why the augmentation of the earth's shadow in 

 a lunar eclipse falls short of one minute is, that the object 

 which casts the shadow is not terminated by a right line, but 

 by a curve ; hence an equal proportion of the sun's disc will 

 be uncovered with a smaller portion of his diameter. A due 

 consideration of this point will prove that the augmentation 

 of the shadow cannot be sensibly affected by any variation of 



• Accurately 105'5 inches when the sun is in perigee, and 109 inches 

 when he is in apogee ; this being the number of diameters of the sun which 

 he is distant from the earth. 



the 



