396 J. P. Cooke on the Numerical Relations 
they are in reality. It should, therefore, be stated, that, in by 
far the larger number of instances, the deviations are within the 
limit of possible errors iu the determinations, leaving only a few 
exceptional cases to be accounted for. It must be remembered 
that, other things being equal, the amount of probable error is the 
greater the greater the atomic weight, so that a difference of 1:9 
in the case of iodine is not a greater actual deviation from the 
law than only 0-5 in thecase of chlorine. Indeed, it is very pos- 
sible that on more accurate determinations the atomic weight of 
iodine will be found to correspond to the law, which cannot be 
expected of that of chlorine. It is well known that many of the 
larger atomic weights, especially those of the rarer elements, can- 
not be regarded as fixed within several units. 
I have calculated, as well as the data I have would permit, 
the amount of probable error in the determinations of many of 
the atomic weights, and by comparing the results from different 
esses, and by different experimenters, I have endeavored 
to detect the existence of constant errors, which seem to be the 
great errors in all these determinations, those accidental errors 
which are made in the repetitions of the same process by equally 
careful experimenters being comparatively insignificant. The 
results of this investigation will be published in a subsequent 
memoir. It is sufficient for the present purpose to state, that, 
while they show that, in the greater number of cases, the appat- 
ent variations from the law are within the limit of probable error, 
there are yet several instances, where, after allowing for all possl- 
ble errors of observation, there is a residual difference. I do not 
therefore look alone to more accurate observations for a confirma- 
tion of the law, but, regarding the variations as ascertained ine 
i her the 
according to a numerical law, as the perturbations in astronomy 
are a necessary consequence of the very law they seemed at first 
to invalidate, or whether they are due to independent causes, can 
of course, for the present, be only a matter of speculation. There 
are, however, facts which seem to indicate that the variations are 
not matters of chance, but correspond to variations in the prop- 
erties of the elements. . ! 
From the beautiful discovery of Professor Schénbein we have 
learnt that oxygen has two allotropic modifications, and that be- 
sides its ordinary condition, it is capable of assumin nother 
highly active state when its properties resemble those of chlorine. 
Cyanogen is known only in a quiescent state. The other haloids, 
fluorine, chlorine, bromine, and iodine, are known only in a high'Y 
active state. Now it will be seen on examining the table, that 
the atomic weights of the highly active elements, as determined 
