542. Retrofpect of German Literature... Mathematics, &c. -{Sur. 
tive mode of writing on the moft abftrufe 
fubjects. The prefent, although neither 
a compendium, nor a fyftem of philofo- 
phic jurifprudence, confifts of a conneét- 
ed feries of eflays, which comprehend al- 
moft the whole territory of this fcience, 
and which the ingenious fiudent may 
eafily reduce to a fyftematic form. We 
cannot upon this occafion omit to mention 
another work by Prof. Maass, of which 
we poffefs the fecond edition, and which 
is confidered by the German literati, as 
well as in foreign countries, wherever 
that language is read, asthe moft valuable 
and lyftematic ‘* Azalyfis of the Power 
ond Influence of the Imagination.’ For 
want of room we cannot enter into a de- 
taued account of this philofophic publi- 
cation, which above all novels and ghoft- 
{tories amply deferved to be tranflated into 
the Englifh language, if the readers of 
folid and ufeful produétions were not fo 
much inferior in numbers to thofe of ab- 
furd and marvellous romances. 
MATHEMATICS. 
The principal new publication, fince 
our laft retrofpeét, in this extenfive field 
.of literature, is ‘* The complete Elements 
ef Geometry, according tole Gendre, Simp- 
“on, von Sinden, Gregorius a St. Vin- 
centio,”” and the ancients, by L. W. GiL- 
BERT, profefior, &c.-at Halle,, Part I, 
PP. 453, 8vo. with plates, 1798; or under 
atiother titie, A complete Syfiem of Ele- 
mentary and Higher Geomeiry.” The me- 
“ritorious author deferves the particular 
thanks of the tyro, as well as of every 
friend of geometry, for having furnifhed 
them with a compendium in which every 
ufeful piece of information relative to this 
difficult fcience is induftrioufly colleéted, 
for having deduced trom a few princi pal 
propolitions many others as confequences, 
and thus in a remarkable degree tacilita- 
.ted the underftanding and acquifition of 
the whole. Another new and interefting 
work, though confined to the arithme- 
tical department, is T. L. JorpDAn’s 
‘* Defcription of feveral neva Reckoning- 
Machines invented by himjelj,” part 1. Ma- 
chines without rotatory motionor wheels, 
and without tables of calculation. With 
three tabulay views, and four engraved 
Rous, pp..102. Svo. 1798." The au- 
thor fhews himfelf in this publication a 
man ct refleGtion and ingenuity ; and we 
await with anxiety the fecend part of his 
book, in which he promifes to deferibe 
fome {till more pertect machines ; we can- 
not, however, refrain trom obrerving, that 
he ought to be lefs ipaving of his tables, 
and at the fame time endeavour to render 
them as accurate and courciponding with 
the text as the nature of the work will 
admit. ‘* Tables, fhowing the Contents of 
Cafes, with an Explanation of their Ufe,’” 
being a werk which was crowned with the 
prize given by the Royal Danith Society 
for the encouragement of the {ciences, by 
S. BRuwUN, with a plate, pp. xxxi. and 
84. 8vo, Although theie tables are chiefly 
calculated for the Danith meafures, yet 
they may be eafily reduced to any other 
ftandard. The author divides the whole 
into two principal feétions, one treating 
of full cafks, and the other of cafks not 
filled: for the former, Mr. B. on 55 
pages lays down 32 tables, which are ar- 
ranged according to the length of the 
calks, beginning with 25 and extending 
to 56 inches ; for the latter, he furnifhes 
us with 23 tables of proportion, which 
are fo calculated, that between the part 
of the bottom of the cafk played upon by 
the wine, and the likewife wet part of an 
imaginary bottom threugh the bung-hole 
parallel with the real bottoms, there is a 
medium taken according to a-certain rule, 
the {pace thus difcovered is commuted. 
into a circle of the fame proportion; and 
then the cafk, as far as it is filled with 
the liquor, is likewife reduced to a cylin- 
der of a fimilar proportion. «* The Ta- 
bles foewing the different Courfe of Ex- 
change, together with Inftrufions and Ex- 
plonations, how to make ufe of them,’ by 
A. CRAILSHEIM, 4to. 1798. All the 
calculations here relate to the mint-ftand- 
ard of 24 florins. The London ccurfe 
begins with 127 Frankfort Batzen, and 
extends to 1563 every operation is car- 
ried on by decimal fractions, fo that an 
of the tables may, with little trouble, be 
ufed for the exchange of Holland and 
Hamburg. The courtes of Paris, Augt 
burg, and Vienna, are likewife calculated, 
and the whole is arranged according to 
the manner adopted by VeGa in his fa- 
mous ‘‘ Logarithmical Tables,” of which 
we have given.a fhort account i our frit 
Reitrorpeci. _ a res 
NATURAL PHILOSOPHY. 
Initcad of having to recapitulate a long 
litt of works in this ufeful branch of 
icience, we can infert two only, which de- 
ferve particular notice. ‘“ilements of Na- 
tural Philofophy, in its Mathematical and 
Chemical parts,” by.,.J.: GS FIsGmeme 
Doégtor and Profeffor at Jena, pp. 820, 
8vo. with three quarto plates: In this 
publication the author has endeavoured to 
compre{s all the late chemical difcoveries, 
as well as to introduce the new metaphy- 
fical theory of Kant, which is now making 
hiatty ttrides towards producing a thorough 
revolution in the do&rine of phyfics. 
With - 
