1801.] 
‘This day, returning to the fpot, 
To view the buth fo richly blown, 
With tearful eye I marked its lot ; 
For all the crimfon bloom was gone. _ 
&© Now far away thy plofloms glide, 
'  €€ Along the ftream, that laves thy feet 
t¢ Ah! cruel was yon faithlefs tide, 
«¢ To rob thee of thy flowers fo fweet! 
te Thy fate demands a pitying tears 
«¢ Yer why, fweet mourner, thus com- 
plain ? 
6¢ For fmiling fpring fhall foon appear, 
** To fwell thy ruby buds again, 
— 
Proceedings of Learned Societies. 
© Like thee the artlefs maiden fmiles, 
*¢ Adorn’d with beauty’s mildeft grace ¢ 
« Till robb’d by man’s infidious wiles, 
‘¢ The virgin bloom forfakes her face.’® 
But when ¢o Aer thall {pring appear, 
Soft beauty’s germ again to break Pam. 
Not all the rofes of the year 
Can animate her faded cheek. 
Ye wintry winds! O, freeze the wave! 
That caufed yon rofy {weet-briar’s doom 5 
And O! ye lightnings, blaft the‘flave, 
That dares defpoil a virgin’s bloom! 
Lrverpool. 
PROCEEDINGS OF LEARNED SOCIETIES. 
rem REE TT ote 
NATIONAL INSTITUTE OF 
FRANCE... 
{Continuation of the Sitting in Meffidor, Year g) 
ILLUSTRATIONS relative to a POINT of 
HISTORY of the TRIGONOMETRICAL 
TABLES.-—The TRIGONOMETRICAL 
TABLES Qf BORDA, publifbed by DE- 
LAMBRE. 
HESE Tables are purely logarithmi- 
cal. The decimal-divifion of the 
circle for which they were conftru&ed, is, 
doubtleis, more commodious than the fex-. 
_agefimal-divilion. Thefe figns, compofed 
each of thirty decrees, which divide the 
Cucunvference into twelve parts, while 
,each degree is fab-divided into fixty mi- 
nuites, and the minute into fixty feconds, 
is too remote from the fimple and uniform 
procefs of the arithmetical {fyfem, which 
proceeds invariably ‘by tens, not to occa- 
fion frequently very ferious inconveni- 
\encesin practice. They had been acutely 
obferved, near two centuries ago, by 
Brices, who, with a view to remedy 
+ them, without too openly fhocking the re- 
» ceived fyftem, had propofed to banifh, at 
leaft, the minutes and the feconds, which he 
replaced by tenths and hundredths of a 
degree. The tables which he compofed to 
»accredit his mitigated fyfiem, and which 
have appeared, fince his death, through the 
cares of, Gellibrand, were fo exact and 
complete, and the new logarithms which 
she employed in them, gave to his work 
fuch a fuperiority over all that had appear- 
ed till then, that he would infallibly have 
introduced the happy change which he 
»propoted, if Viacq, printing at the fame 
time his Artificial Trigonometry, in which 
the logarithms of Briggs were adapted to 
the ancient divifion of the circie, and ta- 
sbles 3; ‘fix-times larger than thofe 
yet Briggs, had not furnithed aitrongmers 
caMontTuty Mac, No. 79. 
wy . 
= 
with a fpecious pretext to adhere to their 
ancient routine. 
The French geometers and aftronomers, 
in propoting a total change in the divifion 
of the circle, had, inlike manner, to firug- 
gle with the tables of Vlacq,, become . 
fill more commadious in the editions of 
Gardiner and of Callet. They were obliged 
to give to their new tables abr ree or four- 
times lefs extent than thofe ef Vlacq. In 
both thefe points they have fuccecdet. 
The firt part included a contiderable 
augmentation of volumes ; but this incon 
venience could not retard Citizen Prony, 
appointed to raife a monument which was 
to furpafs all-that had been executed or 
even conceived of the greateft in this kind. 
Borda wanted tables more for ufe (plus 
ufuelies) 5 3; it was requifite, therefore, that 
in refpect of extent they fhould come near 
‘to thofe of Briggs, and then he found him~- 
felf under the fize of Viacq, Gardiner and 
Callet. .He made it his fad, therefore, 
to bring himéelf to their level, and he fuc- 
ceeded very ikilfully. 
Thefe little regifters of the proportional 
parts, fo commodious, which accompany 
the logarithms of the numbers, could not, 
as yet, have place in the tables of the 
finufes.and tangents. Borda is the firft, 
and the only one hitherto, who introduced 
them into his. He kept an account of the 
inequality of the differences; he has, 
moreover, re-eftablifhed the fecants, long 
fupprefied by Vlacq and all his editors 5 
and {uch are the means by which he has 
been, able to compenfate for the fimaller 
fize of his tables, that their ufe is, at lealt, 
as expeditious and asexaét as that of the 
fexagelimal tables, the molt commedious 
and the molt generally known. poe 
Different caufes have retarded the pub- 
lication of this work, the manufcript of 
which was finifled in1792. ‘The fcru- 
Uu pulous 
