90 Experiments with Potassium and Sodium. 
0.26 6y9 =a? +627? =a.06777 and as many corresponding values 
for 2b. So for any greater iiila of prime factors, «767776? &c. 
Thus we see that an hypothenuse or a base may be found, upon 
which may be constructed any required number of right angled tri- 
angles, whose sides shall all be rational integers. 
5. When P is neither a square nor the sum of two squares; t the pro- 
duct P-Q cannot contain the sum of two squares, except where Q 
takes the forms P (m?-+-n?), P3(m?+-n?), 4P(m? + .—that 
is, when P and Q have a common divisor. 
For if Q be separated into any two parts whatever, (tien P and 
Q are prime to each other,) it is manifest that Pr+-Py=P-Q is not 
the sum of two squares, whether x and y are squares or not. 
6. Every number which is the sum of two squares that are prime 
to each other, is either a prime number, or divisible only by factors 
which are also the sum of oe oe 
==@5 cen a? +-b2=P- Q, which 
"For, if we suppose at 
has been shown to be ser 
Corollary. Hence, if A2=D?-+-C?; then cnege as was 
asserted in a previous remark. 
Arr. XI.—Experiments with Potassium and Sodium; by Jutivs 
T. Ducaret, M. D., Professor of Chemistry, in the Medical De- 
besa the University of Maryland. 
Suieidan says thata piece of Potassium put upon a bath of Mer- 
cury, gradually amalgamates, acquiring a rotary motion, due to its 
action on the water in the atmosphere, which evolves hydrogen. In 
dry air the amalgamation takes place without motion. But if pieces 
of Sodium be thrown upon Mercury, they are again thrown off with 
slight explosions, accompanied with light and caloric. On the other 
hand, Potassium burns on the surface of water, while Scdinith decom- 
poses it without producing combustion.* These effects of the two 
* I observed many years ago, that on hot water sodium scintillates, and bycis tis 
zes,—Ep. 
