Affinities of the Elements of Water. 301 
Now it is obvious that, if this quantity be measured at the ordinary temperature 
of the atmosphere, and then near the boiling point of water, any difference that 
is found sufficiently great to be unconnected with the thermo-electric indications 
that sometimes arise from the dissimilarity of the electrodes, must belong to h.o: 
as the affinity of platinum for oxygen cannot be supposed to vary at such low 
heats. The actual experiments, however, require considerable care, and I am 
induced to describe them at more length than would be necessary, but for my 
hope that the detail may be of some use to any who may feel disposed to pursue 
this vestigation. 
The methods used to determine these quantities differ but little from those 
given by Mr. Wheatstone in the Memoir already referred to. ‘The most impor- 
tant deviation is in the measure of intensity. He assumes it to be the number of 
turns of the rheostat which must be added to the circuit, in order to reduce the 
deflection of a rheometer from 45° to 40°. For this I have ventured to substitute 
another, namely, the sum of the resistances required to bring the rheometer to 
45°. This is equivalent to assuming as the unit current one which produces that 
deflection. Supposing it attained by introducing into the circuit a resistance p’, 
the fundamental equation gives 
= z ————; hence E=R+r+/f’. 
R+7r+p 
Its advantages consist in giving a larger scale, and in being liable to less absolute 
errors. ‘These errors are of two kinds: the one of observation caused by the un- 
certainty of reading the divisions of the rheometer, and the varying contact of the 
rheostat ; the other arising from changes in the magnetic intensity of the needle. 
With Tespect to the first class, they are easily valued by the same application of the 
calculus of probabilities, which has so much advanced astronomy and other branches 
of physics. Comparing each observation of a series with their mean, it is possible 
to deduce what amount of error is as likely to affect a single observation as not. 
This is called the Probable Error; the value of the observation is inversely as 
its square, and that of the mean of the whole series as the same inversely, and also 
as their number directly. Now from a considerable series I find these probable 
errors are, with my apparatus, + 7.7; and + 5.1 for Mr. Wheatstone’s & and 
mine; while the quantities themselves are 118.9 and 236.4. The relative accu- 
