110 M.C. Lea on Numerical Relations existing, $c. 
his calculations are too unreliable to render the fact well estab : 
lished. 7 
The numbers adopted for the equivalents in the foregoing cal 
culations are those obtained by the latest and most reliable de 
terminations; they are taken from the table contained in 
Jahresbericht der Chemie of Kopp & Will for 1857, published im 
August, 1858, and the last which the author has been able 
obtain at the time of concluding this paper, and have been 2 
no case altered or modified in the slightest degree with a view 
to preserve or increase numerical relations, which by slight 
changes of this kind can be often rendered much more symmer 
rical. Dumas, in one of his highly interesting papers on this 
subject* (Comptes Rendus, xiv, 709, extracted in Kopp and 
Will’s Jahr. 1857) in his series a+ad+yd', adopts the equive — 
lents N=14, P=31, As=75, Sb=119, Bi 207 (see Jahresbericht, 
p. 35, where the equivalent of Bi is erroneously printed 108, by 
substitution of the values given for a,2, y,d, and @, 207 is ob 
tained): whereas the equivalent of Sb as lately found ie 
Schneider, confirmed by H. Rose, and adopted by Kopp & Wil 
is 120°3. In another place (Comptes Rendus, XLVI, 1027) Du 
mas has taken the equivalent of the same metal at 122, thus 
adopting alternately the numbers 119 and 122, neither the true 
one, according to the exigencies of the two series. The equy 
alent number of bismuth in the series just mentioned is take 
at 207, whereas it should be 208. In the series a-+ad we 
g=12, Ca=20, Sr=44, Ba 68, Pb 104—the last three show! 
be Sr 43°77, Ba 686, Pb 1085. So with Li, Na, K, V, Zr, & 
In the foregoing tables the calculated and received equiva : 
The analogies here presented, all depending upon the same of 
approximately the same number, extend therefore— 
To the series Pb, Sn, N, P, As, Sb, Bi. a oe 
To the series Hg, Cd, Ma, zn.” : 
To the esi AB, Go. fading: Mac¥ 4 
a group, including Mn, Fe, Co, Ni, U, Co, and some” 
the fie cee assed in the three preceding abies. 
_* The interesting of Prof. Cooke (Memoi vol. 
which the author's ateention al e (Memoirs Amer, Ac., 2d set.) ¥0° 7. 
more particularly referred to iv the ¢ Second rly a oe 
