( 234 ) 
For the sake of comparison we may note, that formerly at the 
temperature 15° C. and in a field of 7700 C.G.S. units the increase 
was found to be: 
in the position I 6,5 1. 14,9 
Physiology. — “The resorption of fat and soap in the large and 
the small intestine’. By Dr. H. J. HAMBURGER. 
(Will be published in the Proceedings of the next meeting). 
Mathematics. — “On an application of the involutions of higher 
order”. By Prof. J. CARDINAAL. 
1. One of the best known problems of the theory of the pencil 
of conics is the determination of the number of particular conics in 
such a pencil, where one rectangular hyperbola, two parabolae and 
three pairs of straight lines are obtained. The corresponding problem 
of geometry in space, namely the determination of the number 
of particular quadrie surfaces in a pencil of those quadries (pencil 
of S*), offers more difficulties. 
It is true, it is easy to prove that there are three paraboloids in 
a pencil of S*; but more difficult is it to trace the number of other 
particular’ groups of surfaces. The surfaces of revolution cannot be 
reckoned amongst these, having to satisfy two conditions. However, 
the orthogonai (rectangular) hyperboloids can be, as it will be 
proved that these are bound by one condition only. 
My purpose in this communication is to investigate first how 
many rectangular hyperboloids appear in a general pencil of S* and 
consecutively to prove that the construction may be brought back 
to a problem of synthetic geometry in the plane, a problem where 
the theory of involutions of higher order must be applied. 
2. According to definition an hyperboioid is rectangular when 
the cyclic planes are- normal to two generatrices. With CLEBscH !) 
we however think it preferable to choose a definition, in which we 
make use of the section of the hyperboloid with the plane at infi- 
nity. To investigate the rectangularity we set to work as follows: 
1) CLEBSCH-LINDEMANN : Vorlesungen über Geometrie, (“Lessons on Geometry”), 
Vol. II, Part 1, p. 195, where we also find the literature of this subject mentioned. 
