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XXIII. On the Phcenomena of Lu7iar Eclipses. By Mr. 

 M. Smith. 



To the Editor of the Philosophical Magazine and Journal. 



Sir, 



IN all works on astronomy with which I am acquainted, and 

 in which the doctrine of" lunar eclipses is treated on, there 

 are two circumstances connected therewith which in ray opi- 

 nion have always been attributed to wrong causes : one of these 

 is, that the apparent semidiameter of the earth's shadow is al- 

 ways greater by about 50 seconds than theory indicates ; and 

 the other is, that the intensity of the shadow is extremely va- 

 riable, it sometimes rendering the moon entirely invisible, and 

 at other times permitting her to be very distinctly seen, of a 

 ruddy colour resembling tarnished copper. 



With respect to the first of these circumstances, namely, the 

 dimensions of the shadow, the rule for finding this, deduced 

 from theory, is as follows. Add together the horizontal pa- 

 rallaxes of the sun and moon, from which subtract the sun's 

 semidiameter, and the remauider will be the semidiameter of 

 the earth's shadow. But as the semidiameter of the shadow is 

 found by observation always to exceed this quantity by about 

 50 seconds, astronomers have directed this augmentation to 

 be made to the computed magnitude ; and not having disco- 

 vered the true cause of this enlargement of the shadow, they 

 have erroneously ascribed it to the earth's atmosphere. 



It will be a sufficient refutation of this error to observe, that 

 the earth's shadow could not be enlarged 50 seconds by such 

 means, unless the atmosphere were sufficiently dense at a height 

 of nearly sixty miles from the earth's surface to project a sha- 

 dow : and this is a supposition which I believe no one will 

 contend for ; particularly when it is considered that tlie atmo- 

 sphere, by refracting the sun's rays, must tend to diminish 

 rather than increase the shadow. I shall now show that this 

 enlargement of the shadow is occasioned by an obvious cause 

 which has hitherto been unnoticed, and is totally independent 

 of the earth having any atmosphere. 



In the first place, it is to be particularly observed that the 

 rule above given for computing the semidiameter of the shadow 

 is founded on the assumption, that a spectator placed in the 

 moon any where in the visible boundary of the shadow would 

 see the limb of the sun and that of the earth in contact ; — and in 

 this lies the mistake. A spectator so placed would see a certain 

 small portion of the sun's disc, amounting to about the 1 20th part 



of 



1 



