532 
Fifteen drawings of Irish antiquities, or of things in different mu- 
seums considered illustrative of ancient weapons found in Ireland, were 
presented by Mr. G. V. Du Noyer, as an addition to the collection of si- 
milar drawings already deposited by that gentleman in the Academy. 
Two MS. volumes of a Journal kept in Dublin from 1801-4, and the 
Journal of a Tour in Ireland, &c., in 1804, in three volumes, were pre- 
sented to the Library by Mr. James Tighe. 
Thanks were returned to the donors. 
The Academy then adjourned. 
MONDAY, JUNE 24, 1861. 
The Very Rev. Dean Graves, D. D., President, in the Chair. 
Tur Ruy. J. H. Topp, D. D., read a paper on some additional leaves of 
the Book of Lismore, recently recovered by his Grace the Duke of De- 
vonshire, and exhibited the’MS., in its collective form. 
Ir was Resotvep,—That the special thanks of the Academy be re- 
turned to his Grace the Duke of Devonshire for the opportunity afforded 
to its members of becoming acquainted with the contents of the Book of 
Lismore, through the Rev. Dr. Todd’s description, and of personally in- 
specting this very curious and valuable manuscript. 
Siz W. R. Hamriron, LL. D., read a paper— 
ON GEOMETRICAL NETS IN SPACE. 
[1.] Wun any five points of space, ancpr, are given, whereof no four 
are supposed to be complanar, we can connect any two of them by aright 
line, and the three others by a plane, and determine the point in which 
these last intersect each other: deriving thus a system-of ten lines Ay, 
ten planes I1,, and ten points P,, from the given system of five points Py, 
by what may be called a First Construction. 
We may next propose to determine all the new and distinct lines A,, 
and planes II,, which connect the ten derived points P,, with the five 
given points P,, and with each other; and may then inquire what new and 
distinct points P, arise, as intersections* A - II of lines and planes already 
obtained : all swch new lines, planes, and points being said to belong to 
a Second Construction. And then we might proceed, on the same plan, 
to a Third Construction, and to indefinitely many others following: 
building up thus what Professor I/édius, in his Barycentrie Calculus,t 
has proposed to call a Geometrical Net in Space. 
* Intersections A* A of line with line (when complanar) are included in this class 
A+ II; and intersections TI - Il - II of three distinct planes, when not included at this 
stage, may be reserved for 4 subsequent construction, in which they naturally offer them- 
selves, as of the standard form A ‘TI. 
t Der Calcul Barycentrische, Leipzig, 1827, p. 291. Some first results connected with 
the subject were given, according to the writer’s recollection, in a Memoir by Carnot on 
Lransversals, to which he cannot at present refer. i 
