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of Edinburgh, Session 1871 - 72 . 
certain that if there is any it is extremely small. Hence, the 
constituent atoms, if aeolotropic as to permeability, must be so, 
hut to an exceedingly small degree. Le Sage’s second funda¬ 
mental assumption given above, under the title “ Constitution of 
u Heavy Bodies implies sensibly equal permeability in all direc¬ 
tions, even in an aeolotropic structure, unless much greater than 
Jupiter, provided that the atoms are isotropic as to permeability. 
A body having different permeabilities in different directions 
would, if of manageable dimensions, give us a means for drawing 
energy from the inexhaustible store laid up in the ultramundane 
corpuscles, thus :—First, turn the body into a position of minimum 
weight; Secondly, lift it through any height; Thirdly, turn it 
into a position of maximum weight; Fourthly, let it down to its 
primitive level. It is easily seen that the first and third of those 
operations are performed without the expenditure of work; and, on 
the whole, work is done by gravity in operations 2 and 4. In 
the corresponding set of operations performed upon a moveable 
body in the neighbourhood of a fixed magnet, as much work is 
required for operations 1 and 3 as is gained in operations 2 and 4; 
the magnetisation of the moveable body being either intrinsic or 
inductive, or partly intrinsic and partly inductive, and the part of 
its aeolotropy (if any), which depends on inductive magnetisation, 
being due either to magne-crystallic quality of its substance, or to 
its shape.* 
4. Note on Spherical Harmonics. By Professor Tait. 
While engaged in some quaternion researches with reference to 
Spherical Harmonics, which I hope soon to lay before the Society, 
I was led to imagine that some of my results might produce a 
simplification of the ordinary modes of treating the subject. The 
following is the result of the attempt. It seems to make the cal- 
* “ Theory of magnetic induction in crystalline and non-crystalline sub- 
“ stances.”— Phil. Mag., March 1851. “Forces experienced by inductively 
“ magnetised ferro-magnetic and dia-magnetic non-crystalline substances.” 
— Phil. Mag., Out. 1850. “Reciprocal action of dia-magnetic particles.”— 
Phil. Mag., Dec. 1855 ; all to be found in a collection of reprinted and newly 
written papers on electrostatics and magnetism, nearly ready for publication, 
(Macmillan, 1872). 
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