of Edinburgh, Session 1877-78. 535 
Again, it is easy to see tliat we have by the above equations 
A' = ac sin ~ cos - , 
A A 
» ff . o 
A =ac cos — sm - , 
so that, construct the figure how we will with four given lines, the 
ratio of the tangents of the halves of the pair of angles correspond- 
ing to 6 , &, is constant. This is the relation between True and 
Excentric Anomaly. And we have also the very simple expression 
A A' = ^ sin 0 sin 0', 
4 
so that the product of the areas of the crossed and uncrossed quad- 
rilaterals is equal to the product of the areas of the (construction) 
triangles whose sides are 
a, c, b — d , 
and a, c, b + d , 
respectively. Here again the letters may be interchanged at will ; 
which, in itself, is a curious theorem. 
While seeking a quaternion proof of the above theorem, I hit 
upon the following result. Given two opposite sides of a gauche 
quadrilateral in magnitude and direction. If one of these be fixed, 
and if the diagonals are to be of equal lengths, the locus of either 
end of the other is a plane. 
Professor Tait, in consequence of the lateness of the hour, post- 
poned his paper u On the Strength of the Currents required to work 
a Telephone.” He said that the title given in the billet did not 
fully describe the contents. These referred not only to various 
measurements of the actual currents employed, whether produced 
from a cell or a Holtz machine, or by induction, but also to the mode 
in which the sounds are reproduced. He stated that he believed it 
would soon be possible to employ the instrument for the study of 
internal changes of form in all bodies, and also that in its construc- 
tion magnets might be entirely dispensed with. He also stated that 
Mr James Blyth had with success substituted a copper plate for the 
