372 PHILOSOPHICAL TRANSACTIONS, [aNNO 1739- 



side A H, the moon's distance from the earth. Also the side e a is the half of a 

 chord of the lunar atmosphere touching the moon's body at a ; therefore the 

 sine of the increase e h a, will be to the sine of the horizontal refraction, as the 

 semichord a e is to a h, the moon's distance. 



Hence it follows, that the increase of the moon's diameter is insensible ; for, 

 if it amounted to 2|", supposing the horizontal refraction 3', i.e. at least 30 

 times greater than it can be supposed, as will be proved hereafter, then the 

 semichord e a would be equal to 276 French leagues, and thus far exceed a like 

 chord of the terrestrial atmosphere. Therefore, whether the moon is covered 

 with an atmosphere or not, her diameter will always be observed the same : so 

 that the observation of the lunar diameter can never be sufficient for resolving 

 the problem. 



But the solar eclipses afford better means for deciding the point ; for the ex- 

 treme rays bounding the cone of the lunar shadow, as they touch the moon's 

 body, and pass through her atmosphere, will be necessarily inflected toward 

 the axis of the cone ; hence the cone will become shorter and more obtuse. 

 But to know the quantity of that variation, it must be observed, that the ray 

 p A, fig. 4, or its parallel e g, which in case there be no atmosphere, would be 

 the limit of the lunar shade f a c, would be refracted towards the axis c A, at 

 the ingress of the atmosphere g, and at the egress h : hence the semi-angle of 

 the cone of the lunar shade will be increased by double the horizontal refraction 

 in the lunar atmosphere. 



Hence it follows, that in the supposition of a lunar atmosphere, a total eclipse 

 of the sun will begin later, and end sooner, than without one ; also, that in 

 some certain cases, there would be no total eclipse ; which, yet, the diameters 

 of the sun and moon, observed in the same degree of anomaly, would require ; 

 for in these cases the cone of the lunar shade might be so constructed, as not 

 to reach the earth's surface. 



In the same manner, the duration and quantity of partial eclipses would be 

 also diminished ; and they would thus begin later, and end sooner, on the 

 supposition of a lunar atmosphere, than without one ; and in certain cases, 

 there would be no eclipse at all, when there would otherwise be one. 



Such then would be the phaenomena in case there were an atmosphere about 

 the moon. Let us now consider what is really observed. In the first place, as 

 the axis of the lunar shade extends to 55 semidiameters of the earth, when 

 greatest, and to 52-l when least ; and as the least distance of the moon from 

 the earth is 54 of the earth's semidiameters ; if the lunar atmosphere were 

 capable of a horizontal refraction of 8", the semi-angle of the conical shadow 

 would be increased by double the quantity, that is 16"; therefore it would be 



