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Proceedings of the Eoyal Society 
teaching prevalent in the great English schools, according to which 
dead rules are substituted for living functions, and doctrines about 
sounds for the sounds themselves. Whosoever as a teacher of 
languages has seized on the great principle that the ear is the special 
organ used by nature in acquiring a knowledge of articulate sounds, 
will never commit the mistake of pronouncing eXcos, the divine 
attribute of mercy, with the same intonation that marks eA.eds,'a 
wooden block for washing mince- collojps. The G-reek language con- 
tains whole columns of such words, which the man who pronounces 
G-reek according to Latin accents must pervert and turn into non- 
sense. To teach any language with false accents and false quan- 
tities, and yet to inculcate rules about true accents and true quan- 
tities, is to declare the schoolmaster wiser than the Creator, and to 
insist on doing by a forced and painful process of memory what 
nature is willing to do for us by the pleasant habituation of the ear. 
2. Note on Action. By Professor Tait. 
The 
quantity represented by Jvds^ or its equivalent Jpdt, in any 
case of the motion of a particle, is known to possess important 
dynamical relations. The accidental discovery of a singularly 
simple geometrical representation of this quantity in the case of 
planetary motion led me to inquire whether the method involved 
might not be easily generalized. This note contains a sketch of 
some of the results of a hurried investigation of the point. 
G-raphical representations of the action in some common cases of 
motion readily suggest themselves. 
Thus, in the case of the parabolic trajectory of an unresisted 
projectile, the action through any arc of the path is proportional to 
the area included between that arc, the directrix, and two ordinates 
parallel to the axis ; while the time is, of course, represented by 
the intercept on the directrix. 
Again, in the case of the ordinary brachistochrone (the cycloid 
with its vertex downwards), the action and the time, corresponding 
to any arc from the cusp, are respectively proportional to the area 
and the arc of the corresponding segment of the generating circle. 
Numerous other simple cases might be given, but these are suffi- 
