TRANSACTIONS OF THE SECTIONS. li 
of eliminating between Fr=p, F’x=q, Fx being any quantic in x of the nth degree, 
so that this equation will be of the (7—1)th order in g, and the mth order in p. 
In the Philosophical Magazine for October and December, and in the Proceed- 
ings of the Mathematical Society of London, will be found further developments of 
the theory of these circular inyolutes, which it is proposed to term Cyclodes. 
On the application of Quaternions to the rotation of a Solid. 
By Professor P. G. Tarr. 
ASTRONOMY. 
On the extent of evidence which we possess elucidatory of “change” on the 
Moon's Surface. By W. R. Bret, F.R.AS. 
The questions of change on, or fixity of the moon’s surface must be decided, as 
Webb (Celestial Objects for Common Telescopes, second edition, p. 68) remarks, by 
observation and not assertion. It is therefore important to gather up the fragments 
of our knowledge bearing on the evidence which we possess on these questions ; 
and we may remark, in the first place, that our real knowledge of the fixity of the 
moon’s surface does not at present depend upon “evidence,” using this term to 
designate the results of observation and not the deductions of theory ; nor can we 
possess any adequate evidence of this kind, as is manifest from the very cireum- 
stance that up to the present moment our records of the physical aspect of the 
moon’s surface are not only exceedingly scanty—in comparison with the countless 
thousands of objects of every variety of description which are revealed to us by 
eyen small instruments, let alone the increasing visibility of smaller objects due to 
larger apertures—but it is now becoming acknowledged that such records and the 
delineations accompanying them are not sufficiently precise and exact to enable us 
to refer to them as reliable witnesses in establishing ‘fixity ;” indeed it is difficult 
to conceive how the wnalterable state of the moon’s surface can be determined by 
“ observation.’ If, as has been asserted, all changes on the moon’s surface have 
ceased myriads of ages ago, we are certainly destitute of the records of ‘ observa- 
tion” of the real state of that surface at so remote a period. In fact our absolute 
Imowledge of “ fixity” can only date from the construction of the first lunar map, 
since which there are no traces of any grand convulsion. The establishment of 
“fixity ” can only have reference to those objects which have been more particu- 
larly observed during the intervening A pee and, as shown by Webb (Intellectual 
Observer, vol. xii. pp. 435, 436), if really established by a long course of ob- 
servation at any one point, it would be no argument for its universal prevalence, 
since a state of quiescence might be attained at very different epochs in different 
regions. 
ach being the case as regards “ fixity,” let us now inquire as to what evidence we 
possess on the subject of “change.” ‘The earliest attempts to perpetuate a know- 
ledge of the moon’s surface consisted in delineating the disk in the form of maps, 
accompanied in two instances with “‘ catalogues ” of the most striking and promi- 
nent objects ; but, as might be expected, such maps are greatly destitute of “ de- 
tail,’ especially of such a character as is necessary to pronounce on “ change.” 
Towards the close of the last century Schroter, seeing the importance of perpetuat- 
ing a knowledge of detail, bequeathed to us the result of his labours in this direction 
in the form of his ‘Selenotopographische Fragmente,’ taking up portions of the 
moon rather than attempting a delineation of the whole in detail. His successors, 
Lohrmann, Beer and Madler, and Schmidt, have followed in his steps, and pro- 
duced works abounding much more in detail than any of the predecessors of 
Schroter; Lohrmann’s sections and map, with the two maps of Madler, are well 
known. The larger portion of Lohrmann’s Sections, as well as the results ot 
Schmidt's labours, are still unpublished. Webb’s index map of the moon in his 
