26 
metrical reasoning, that the common tangent planes of the spinode de- 
velope and the node-couple develope are stationary planes of the one or 
the other of the two developes, that is, 7’ =0, and the reasoning seems 
correct as far as it goes, but it was not shown how the demonstration 
would (as it ought to do) fail in the case of a surface having a double or 
cuspidal curve. Ishowed also that in the case where the common tan- 
gent plane is a stationary plane of the spinode develope (that is for the 
planes #’), the spinode curve and the node-couple curve touch instead of 
simply intersecting, it would seem that the tangent plane at such point 
is to be counted once, and not twice, in reckoning the number f’ of such 
tangent planes; the like remark applies, of course, also to the points of 
intersection 6 of the double and cuspidal curves. 
The Rey. Dr. Lioyp read a paper— 
ON THE EFFECT OF A DISTANT LUMINARY, SUPPOSED MAGNETIC, UPON THE 
DIURNAL MOVEMENTS OF THE MAGNETIC-NEEDLE. 
Tr has been usual to ascribe the ordinary diurnal variations of the mag- 
netic needle to the influence of solar heat, either operating directly upon 
the magnetism of the earth, or generating thermo-electric currents in 
its crust. The credit of these hypotheses has been of late somewhat 
weakened by the discovery of a dunar diurnal variation in the three 
magnetic elements; while, at the same time, new laws of the solar 
diurnal change have been established, which are thought to be incom- 
patible with the supposition of a thermic agency. There has been, ac- 
cordingly, a tendency of late to recur to the hypothesis that the sun and 
moon are endued with magnetism, whether inherent or induced; and 
it is, therefore, of importance to investigate the effects which bodies, so 
constituted, would produce on a needle at the earth’s surface, and to 
compare them with those observed. In the present communication the 
author has endeavoured to solve this question, on the supposition that 
the assumed magnetism of these luminaries is original and permanent. 
The results prove the insufficiency of the hypothesis to explain the phe- 
nomena. 
We shall suppose, for simplicity, that the centre of the acting mag- 
net is in the plane of the equator. So far as the diurnal change is con- 
cerned, we may suppose it to be fixed; accordingly, we may take that 
centre as the origin of co-ordinates, the line connecting it with the cen- 
tre of the earth as the axis of x, and the plane of the equator as the 
plane of (zy). Then, if (x, y, ) be any point of the fixed magnet, pm 
the quantity of free magnetism contained in the element ds of the mag- 
net at that point, m a magnetic element on the earth’s surface, and 
(a, 6, c) its co-ordinates, the force exerted by » on m is 
mpds | 
2 ? 
Pp 
in which p denotes the mutual distance of the points (a, 6, c) and 
