329 
base of the branch, though in this case growing upwards, in consequence 
of the position of the branch being reversed. 
No. 4 6 is part of the stem of a holly-tree, which stood in its natural 
position when operated on. It shows, also, that the principal portions 
of newly formed wood have grown chiefly on the upper lips of the spiral 
denudations. 
No. 4 ¢ is part of a branch which grew as nearly as possible in a ho- 
rizontal position from the axis of the tree. It was denuded of bark over 
the upper half of its circumference, the bark on the lower half next the 
earth being still attached. The cells forming woody tissues in this in- 
stance have been produced for the most part in horizontal series, having 
little preponderance to the part nearest the base of the branch, which 
favours the correctness of M. Trecul’s views, as stated above. 
I have now, in this and a former paper, laid before the Academy the 
results, such as they are, of twenty years’ experiments on this subject, 
which may appear a long period ; but we cannot force the operations of 
* nature, and must, therefore, be content to wait assiduously on her if we 
desire to elicit trustworthy data, such as can be useful to future stu- 
dents following in the same path of investigations. 
Sie Witiiam Rowan Hamizton, LL.D., M.R.I.A., read the follow- 
ing paragraphs in continuation of his paper— 
ON ANHARMONIC CO-ORDINATES. 
11. To myself it naturally appears as a fourth advantage of the an- 
harmonic method, that it is found to harmonize well with the method of 
quaternions, and was in fact suggested thereby ; though not without sug- 
gestions from other methods previously known. 
12. Thus; if a, B, y denote three given vectors, 0A, 0B, oc, from a 
given origin o, while a, 4, ¢ are three given and constant scalars, but 
t, u, v are three variable scalars, subject to the condition that their sum 
is zero, 
t+a+v=0; 
then the equation, 
Yaa+wbB+v'ey 
: varwbtore ’ 
in which r is any positive and whole exponent, expresses generally that 
the Jocus of the point P is a curve of the r order, in the given plane of 
asc; which curve has the property, that itis met in 7 coincident points, 
by any one of the three sides of the given triangle anc. But the coefti- 
cients @ w” v" are examples here of what have been above called anhar- 
monic co-ordinates. 
OoP=p= 
Captain Buaxety read the following :— 
CAPTAIN BLAKELY’S REMARKS IN CONTINUATION OF HIS REPLY TO MR. MALLET 
AT THE MEETING OF THE ROYAL IRISH ACADEMY ON MAY 14, 1860. 
Mr. Cuarrman,—At the last meeting of the Academy a question was 
raised by Mr, Mallet, between himself, Dr. Hart, and me, as to whick 
