178 On Fluxions. [Sser. 
the calcareous crusts of which were inflated with bubbles, so as to 
form a cancellated shell, in texture like pumice-stone. The most 
durable substances of animal bodies, such as the bones and teeth, 
are only partly vascular, since their ealcareous materials are fixed 
by chemical precipitants, and remain: under chemical laws, In- 
juries done to the horns of cattle, to the hoofs of animals, and to 
human nails, are never restored; these parts do not possess the 
power of self repair; and it is only by the mechanical wearing away 
that such injuries are obliterated. Indeed the beneficent construc- 
tion of animal nature is sufficiently manifested in the insensibility 
of all the exuvial coverings, and im the organic composition of 
many parts which are exposed to mechanical attrition, as the enamel 
of teeth, the horny beaks of birds, and the euticular or horny 
coverings of feet. The same beneficence appears to be extended to 
many parts of the internal organic substances, by which painful 
sensations are obviated, whilst the substances themselves being less. 
directly under the dominion of the vital superintendency become 
more permanent ; such parts are the tendons, ligaments, cartilages, 
cellular tissue, the gelatine and lime of bones; even water is an 
essential constituent of the animal fluids, and affords the necessary 
softness and flexibility to solids. But this subject, and its connexion 
with the vegetable composition and texture, extends far beyond the 
limits of a memoir; and I must therefore suspend my observations. 
(Fo be continued.) 
Sane Sn on 
ArTicLe FV. 
Further Observations on Fluaions. By Alexander Christison, Esq- 
F.R.S.E. Professor of Humanity in the University of Edin- 
burgh. 
(To Dr. 'Thomson.) 
MY DEAR SIR, Edinburgh, July 19, 1815, 
AN experienced mathematician will find no difficulty in the 
reasoning, Annals of Philosophy, vol. v. pp. 830 and 331; a 
learner, however, will understand that reasoning better if he sup- 
pose the accent, which is put after the y at the top, to be put not 
at the top, but half way down the side of the y in p. 330, line 40 ; 
and likewise wherever that letter so occurs afterwards with one or 
two accents, unless there be two letters in the numerator; and if 
he read i for z after the mark of equality in the last line but one 
of p. 330, and in the second line of p. 331. 
You may insert the following observations. 
It is evident from fig. 2, p. 32S, that the ratio of the increments 
is never the ratio of the fluxions; for at F H, 5 minus one centil- 
liouth to-+-is too small, and 5 plus one centillionth to 1 is too 
°. 5 6 
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