362 
Consequently, if 8 represent the angle at base of the cone of maximum 
volume under total surface, we shall have 
sin 0,=sin pf. 
The angle at the summit of the cone of maximum volume under its 
conical surface is, therefore, equal to the angle at the base of the cone 
of maximum volume under its total surface, and the theorem announced 
immediately follows. It also readily appears that upon the same base 
the cone of maximum volume under total surface is double that of 
maximum volume under conical surface., 
Rey. William Reeves, D. D., read the first part of a paper ‘‘On the 
Ancient Order of Culdees in Ireland.”’ 
Rozert M‘Donnett, M. D., read a paper— 
ON THE ORGANS WHICH IN THE COMMON RAY ARE HOMOLOGOUS WITH THE 
ELECTRICAL ORGANS OF THE TORPEDO. 
THe very beautiful structures which exist in the electric as well as 
the non-electric rays, as appendages of the anterior branches of the fifth 
pair of nerves, were regarded by Geoffroy St. Hilaire and others as the 
representatives of the electric organs of the torpedo. The fact, however, 
of their existence in the torpedo along with, although not united with, 
the electric organs, is sufficient to render this view untenable. 
1. Savi, who has given an accurate description of them in the torpedo, 
as well as a beautiful drawing, considers them as an apparatus for the 
secreting of mucus. For reasons, however, not to be entered on at pre- 
sent, the view taken by Jacobson, Treviranus, and, more recently, by 
Leydig, that these are organs of sensation, seems the correct one. 
2. The existence of the true so-called ‘‘ system ofthe lateral line” in 
the electric, as well as the non-electric fishes, enables us also to set aside 
this apparatus as not being homologically related to the electric organs, 
as has been supposed by some authors. 
3. The organ described by its discoverer, Dr. Stark, of Edinburgh, 
as an electrical apparatus, in the tail of the flapper skate and other rays, 
on aecount of its form and position, can hardly be considered the true 
homologue of the electric organ of the torpedo; nor am I aware that any 
of the authors who have examined it have, in their subsequent re- 
searches concerning this tail-organ, put forth such a notion. Possibly 
the pseudo-electric tail-organs of the rays may yet be shown to be ho- 
mologically related to the electric organs of the Gymnotus electricus. 
I believe, however, that I have lately discovered in the non-electric 
rays the organs which are the true homologues of the batteries of the 
torpedo ; and it is the object of the present communication to indicate 
the anatomical relations of these organs, and briefly to state how I 
have been led to make them out. 
If the skin be carefully removed from the upper surface of the head 
q 
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