Notices of Books. 
[January, 
1 14 
Stability of Motion . By E. J. Routh. (Adams’s Prize.) 
This is an essay of somewhat uneven interest. The able and 
elegant discussion of the conditions that an equation may have 
no positive roots and no imaginary roots with the real part positive 
is very interesting, both in method and result ; but the remainder 
of the work takes (perhaps necessarily) too much the form of 
enquiry into special and limited cases. We are inclined to think 
that the line of investigation as slightly sketched in Chapter VIII. 
would have yielded results of more general theoretical interest. 
But the subordination of theoretical developments to practical 
application seems to us the defect of this laborious and original 
essay. 
Spherical Harmonics. By the Rev. M. M. Ferrey. 
An exceedingly clear and well-arranged account of the leading 
properties of these functions, with continual reference to their 
application to the theory of the potential. Possibly too great care 
has been devoted to giving algebraically simple proofs of the pre- 
liminary propositions, which might have been exhibited in closer 
connection by a free use of Green’s theorem. One is surprised, 
too, to find no mention of Prof. Maxwell’s representation of solid 
harmonics as derived from — by axis-differentiation. But if these 
are faults they are alone. The concluding chapter on Ellipsoidal 
Harmonics, as the author happily terms Lame’s functions, is 
an especially good introduction to this elegant extension of the 
spherical analysis. 
Inductive Metrology ; or the Recovery of Ancient Measures from 
the Monuments. By W. M. Flinders Petrie. London : 
Hargrove Saunders. 1877. 
This work gives a very elaborate comparison of the measures ot 
all the great nations of antiquity with those of modern times. 
Measurements from more than 600 buildings have been considered, 
and as many as 10,000 measurements have been examined. 
Among the results obtained may be mentioned the proof of “ the 
exact identity of the American mound-builders’ unit with the 
Hebraio- Persian cubit, which had a wide and ancient diffusion in 
the old world. The close similarity of the Mexican unit with the 
widespread 21-4 unit of the old world ; and the similarity also of 
the pre-historic British, and Christian Irish unit to this. The 
close similarity of the Phoenician unit to a principal unit of pre- 
