- _ Royal Society of London. 179 
all the cases of plane triangles, independently of any tables, 
formule respecting the increments and fluxions of the 
Sines and tangents of arcs and angles,—the solutions of 
quadratic and cubic equations by tables of sines and tan- 
gents,—and rules for the admeasurement of altitudes by the 
barometer and thermoaicter. and 
Such are the principal topics discussed in the volume be- 
fore us: our mathematical readers will at once see their va- 
Jue and importance. We could have wished that some of 
these had been treated more at large ; especially the different, 
kinds of projection, and the application of the: fluxions of 
trigonometrical quantities to astronomical and other pro~ 
blems ; and we should also have been gratified to see the de- 
Monstrations accompanying their respective rules, instead of 
being separated from them,—and to find no theorem, whe- 
ther simple or complex, but what was demonstrated. We 
are, however, aware that all this could not be:comprehend- 
ed in a single volume ; and we therefore hope the present 
edition will experience the encouragement it so richly de- 
Serves, that Mr. Bonnycastle may be enabled in-a future 
edition to extend the utility of his performance, by making 
the additions we now suggest. Taking the work, however, 
as it is, we think it by far the best on trigonometry that has 
yet been published in the English language; and we are 
conscious, that in recommending this treatise to general fa- 
your, we are equally discharging an act of justice to the 
‘author, and of service to the public. 
ee 
———_——————— eee Eee 
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XXXI. Proceedings of Learned Societies. 
ROYAL SOCIETY OF LONDON. 
Os Thursday the 6th of November the Royal Society as- 
sembled, after tlie summer vacation, at its apartments, So- 
merset-House, when the right honourable colonel Greville, 
vice-president, took the chair. The reading of the Croonian. 
Lecture on muscular motion, by J, Peirson, Esq. com- 
menced. lo a 
oT M 2 On 
