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VI. 



ON THE SHAPE OF THE EAETH'S SHADOW PEOJECTED 

 ON THE MOON'S DISC DUEING THE PAETIAL 

 PHASES OF AN ECLIPSE. By A. A. EAMBAUT, M.A. 



[Read February 14, 1888.] 



Having observed during the partial lunar eclipse of August 3rd, 



1887, and during the partial phases of the eclipse of January 28th, 



1888, that the outline of the shadow appeared to the naked eye to 

 diverge from the circular form, and to be more deeply curved 

 where it approached the limb of the moon, whereas in the telescope 

 no such divergence could be detected, it occurred to me that this 

 effect might possibly be due to parallax. 



Although on further consideration it appeared that the parall- 

 actic displacement is much too small to account for the abnormal 

 shape of the shadow observed, I thought it might be of interest to 

 ascertain how far the outline of the shadow could be affected by this 

 cause. 



The investigation of this question is the object of the present 

 Paper. 



If we take as origin of rectangular co-ordinates a point on the 

 earth's surface in the plane containing the centres of the sun, 

 earth, and moon, the plane of xy coinciding with this plane, and 

 the axis of x passing through the moon's centre, and if the co-ordi- 

 nates of the earth's centre referred to these axes are £, r], 0, the 

 equation of its surface will be 



(x-iy + {y-tf + z* = R\ 



the surface being taken, with sufficient accuracy for the purposes 

 of this investigation, to be a sphere of radius R. 



If a, j3, are the co-ordinates of the vertex of the shadow-cone, 

 the equation of its surface is 



[(•- if + (y- *y + ; 2 - ^ 2 ] x [(« - iy + (/3 - >,) 2 - ^ 2 ] 



