* 110 
That the telegraphic signals now em- 
ployed in the navy originated in this 
way, may be inferred from this circum- 
stance, that Sir Home Popham, to whom 
the service is dzrect/y indebted for them, 
was a midshipman under Capt. Thomp- 
son, when the latter acted as commodore 
on the coast of Guinea station; as was 
also the late Captain Eaton, who pre- 
served a copy of the above literal signals 
until his death. Sir Roger Curtis, who 
has with much ingenuity contrived a 
plan of nautical correspondence, similar 
to that introduced by Sir Home Popham, 
but who has not been equally successful 
im its adoption, likewise served under 
Captain Thompson. 
Thus did the literal signals, which, 
mong other uses, had the singular ap- 
plication described above, apparently 
lead to the telegraphic signals, the utility 
of which is now so generally acknow- 
ledged. The latter were, at the glorious 
battle of Trafalgar, the medium by which 
the memorable sentence, ‘* England ex- 
pects every man. to do his duty,” the 
conception of the greatest hero our-naval 
annals record,.was re-echoed throughout 
the fleet already prepared ‘* to conquer 
or to die.” S. 
= ie 
To the Editor of the Monthly Magazine. 
SIR, 
S the method of describing the Ca- 
tenaria, in a recent publication on 
Arches and Abutment-piers, may excite 
some discussion, during the erection of 
the bridges proposed to be built over the 
Thames, from the Strand and Vauxhall ; 
and as the properties of this line are ad- 
mitted, by all writers on arches, to be of 
the utmost importance in determining 
the relations of an arch, the following 
comparison of the hne investigated by 
Dr. David Gregory, mm his Paper on the 
Catenaria, in the Phil. Trans. Aug. 1697, 
with the ling shewn in the publication 
alluded to, may not be uninteresting to 
_ many of the readers of your Magazine. 
Previous to the erection of Blackfriar’s 
bridge, there arose much controversy, 
through the periodical publications, rela- 
‘tive to the principles of equilibration, 
and the proper form of the arches of 
that bridge; and a gentleman then 
stated, that the catenary was the best 
form ; the absurdity of this position was 
soon detected, and, by some unfortunate 
citcumstance, the following passage has 
crept into~ Dr. Hutton’s Mathematical 
Dictionary, under the article Catenary.: 
‘¢ In 2697, Dr. David Gregory published 
Of the Catenaria and the common 
/ 
[Sept. 1, 
an investigation of the properties before 
discovered by Bernouilli and Leibnitz, in 
which he pretends, that an inverted ca- 
tenary is the best figure for an arch of 
a bridge.”—~his mistatement should be 
corrected. : 
The following is an extract from Dr. 
Gregory’s paper :—=‘* It appears from 
mechanics, that three powers are 1 
equilibrio, when they have the same ratio 
as three intersecting right lines, which . 
are parallel to their directions, or which 
are inclined to them in a given angle, be- 
ing terminated by their mutual concourse. 
Therefore, if Dd denote the absolute 
ravity of the particle Dd as it must-be 
a chain of uniform thickness, then"d > 
will represent that part of the gravity 
which acts perpendicularly on Did by 
which it happens (because of the flexibi- 
lity of a chain moving about @) that 
d D {endeavours to reduce itself to a 
vertical direction; therefore if d d or 
the fluxion of the ordinate BD, be sup- 
posed.constant, the action of the gravity 
exerted perpendicularly on the correspond- 
ing parts of the chain dD. will also be 
constant or every where the same.” 
No one will accuse Dr. Gregory of _ 
having pretended, that an inverted ca~- 
tenary is the best figure fur an areh of a 
bridge, who has read merely this quota- 
tion from his invaluable paper. It is-al- 
most needless to: say, that Dr, Gregory 
has never advanced sucha position, nor 
can any work of his lead to the supposi- 
tion, that he would be so loose i his 
conclusions as to say, that the catenary, 
or any other arch, is the best figure for a 
bridge, knowing, as he must have done, 
how variable are the forms of the extra- 
dosses of bridges. 
This is not the only aspersion which 
Dr. Gregory’s paper has met with. ‘The 
author of the Treatise of Arches and 
Abutment-Piers, in his introductory de- 
-finitions and remarks, aceuses him of 
having said, that * the invered curve of 
a catenaria, composed of equal rigid po- 
lished spheres, in a plane perpendicular 
to the horizon, weuld keep its figure in 
the one situation as in the other.”—Et is 
true, he saysin a note, ‘* although Dr, 
Gregory dogs not say equal, he evidently © 
means it; ve it has been so understood 
by others, and refers to Dr. Hutton’s Re- 
creations in Mathematics.”—If such a 
statement had been made, it must be a 
misprint, as Dr, Hutton states, that a 
catenarian arch may have an horizontal 
extrados, and be an arch of equilibration, 
which is irreconciigable with an arch 
equally 
