304 
aught we had shown to the contrary, 
might always take place) where GK is 
parallel to BF—this we have lett al- 
together unnoticed, though upon it de- 
pends the application of our reasoning, 
and the legitimacy of our conclusion, 
The demonstration of this case, it ap- 
peared to me, was unnecessary from 
the extreme ease of effecting it; and 
I, therefore, passed over it, in the same 
manner, as I did some other much 
slighter particulars. However, I feel 
curious to hear what plea can be urged 
by “A” for following my example :—he; 
who so scrupulously condescends to 
notify the slightest operation he per- 
forms, ought surely to have paid some. 
attention to this, the least obvious of 
all the facts which I adopted as the prin, 
ciples on which to found my solution, 
VIII. A word now to yourself, Mr. 
Editor, by way. of explanation.. That 
the “imputation” of obscurity and in- 
conclusiveness is removed, I think you 
will now allow, and removed, too, with- 
_ out reference either to the “ porisms or 
the pedantries of almost-forgotten au- 
thors.” Your suggestion seems to 
have arisen from mistaking the import 
of the note, which I appended to my 
demonstration. I did not say, or, at 
least, I did not intend to say, that the 
accompanying process was in any way 
dependent upon La Hire’s porism; but 
that the demonstration which I had 
employed in my new work was depen- 
dent upon that proposition. Of course 
it was to be understood that the po- 
rism itself was previously given. 
In conclusion, it may be proper to 
remark, that this theorem is capable of 
a far more general enunciation than 
that which I gave in your magazine for 
July. To instaace one extension—the 
’ points B and C may interchange their 
places so as throw K without the tra- 
pezium. Another is, that ABCD may 
be a re-entering or an intersecting tra- 
pezium—the stated properties still ob- 
taining. This case is not capable of 
demonstration by the method above 
employed, though it may be derived 
from principles nearly similar. 
These properties, however, form but a 
small part of the numberless hitherto un- 
investigated, butextremely beautiful ones 
which appertain to the trapezium: to 
develope which will call for the utmost 
resources of mathematical dexterity. 
On the 5th of August I presented to 
the “‘ Society of Inquirers of Bristol’ 
-a few of these ;amongst which was my 
general theorem, with a demonstration 
Mathematical Problem Demonstrated.” 
[Nov. l, 
perfectly unrestricted, and upon prin- 
ciples altogether new. The paper will 
probably appear through the usual me- 
dium of the society, the Philosophical 
Magazine; or, at all events, combined 
with other applications of the same 
principle, in my “ Stupres.”. One yet 
more general property I will just allude 
to—that the points ABFCDE, in lieu of 
being printed in the sides of the angle, 
formed by the projection of the figure, 
may be in the periphery of any conic 
section whatever, and GKH will be ina 
straight line stil!—Your’s, &c. 
_ Bristol, Sept. 2, 1825. T. 5. D. 
To the Editor of the Monthly Magazine. 
Simi 5 “eee | 
E do not make ail the use we 
might, either of our materials or 
of our knowledge. 
Thus the daburnum tree, which the 
French sometimes call the green ebony 
of the Alps, is one of the most beautiful 
of woods for furniture, yet it is seldom 
orever used for that purpose. _- ., 
It has been proved, in many parts of 
France, that the walnut-tree, if grafled, . 
produces ten-fold; yet, I believe, the 
walnut is seldom or ever submitted to 
that process, at least in this country. , 
Mr. Dawes, of Slough, discovered 
that the covering of a wall with dlack 
paint would facilitate the ripening of 
wall-fruit, and. yet not one wall in 
twenty thousand is so painted, Bs 
The knowledge that charcoal is the 
best ingredient in the foundation of 
buildings erected in moist places, is as 
old as Theodorus, who, according to, 
Diogenes Laertius,. proposed the form- 
ing the foundation of the Temple of ~ 
Ephesus with that material, because it 
would become so solid that no water 
could penetrate it. This, I say, has 
been known more than two thousand 
five hundred years, and yet I am-not 
aware that charcoal has.ever been used, 
in this country, for the purpose above 
referred to. 0. 0. 0. 
To the Editor of the Monthly Magazine. 
' Sm: ’ 
HE edition of Johnson’s Die- 
tionary into which I looked for, 
the meaning of the word Jdiotism was 
that of Todd (1818), which, I think, 
you should have also consulted before 
questioning the truth of my statement, 
as it is allowed to be greatly superior 
to any other. It contains, besides the 
quotation from. Judge. Hale, to which 
you alluded in the last number of your 
Saeed ' Magazine, 
