Royal Institute of France. 467 
This memoir is an application of descriptive geometry to some 
very important questions. We conceive that we may arrive at 
one point from another by an infinity of different roads ; but these 
roads are not all equally favourable ; the inclination, for instance, 
ought not to exceed in any point the limits given by experience, 
and after which the moving powers no longer act with advan- 
tage: the limit of slope varies according to the method of effect- 
ing the transport of articles, whether on the backs of men or by 
wheeled carriages. The mathematical theory of M. Dupin en:- 
braces all the elements of this question considered in the most 
general manner. 
M. Brochaut read a paper on Gypsum, Messrs. Ramond and 
Brongniart are to examine it. 
Monday, March 18.—A letter was read from Sir C. Blagdon. 
He announces that they are at this moment constructing in 
Cornwall steam-engines destined to work under a pressure of 
seven atmospheres. The trials already made seem to indicate 
that they will be productive of immense advantages. In order 
to determine under what circumstances steam-engines ought to 
produce the maximum of effect, keeping in view the quantity of 
coal used, it is necessary to know the relation which may exist 
at different temperatures between the elastic force of the steam 
and the quantity of caloric necessary for its production. Already 
had some French manufacturers ascertained that the increase of 
the elastic force is superior to that of the caloric employed ; for 
they found an advantage in working their machines under pres- 
sures superior to that of the atmosphere; but the form of their 
boilers did not admit of their much exceeding this term. In En- 
gland they have gone much further, by means of an invention of 
Mr. Woolf’s, and which is combined in such a way as to employ 
the steam at very high pressures. It seems also that the steam- 
engines of this able engineer contain another useful modification, 
and which consists in the heated steam never being in immediate 
contact with the piston of the large cylinder, as it is in the com- 
mon machines; in the latter case, as is well known, the piston 
soon loses its accurate adjustment, because the steam dissolves 
the greasy substances which lubricate it. In Mr. Woolf’s ap- 
paratus the steam enters into a first cylinder, and there it presses 
on the surface of a column of oil, which it forces to enter into an 
interior cylinder, in which is the piston: it thus raises the piston 
without touching it, and lets it fall as soon as it is condensed. It 
is clear that this mechanism may be also applied on both sides of 
the piston, so as to produce a double effect. 
Gg2 XCVI, In. 
