VALUE OF THE BRITISH ASSOCIATION UNIT OF RESISTANCE. 
251 
also is the other in the same proportion. Thus tire accuracy of our result is not 
impaired by the uncertainty of this correction. In fact, although to determine the 
resistance of our coil It in absolute measure we require to determine accurately a 
ratio of 1 to 3000, and this determination has generally been held to be one of the 
main objections to our method, yet to determine the value of the B.A. unit we have 
in addition to compare a ratio of 160 to 1. Thus, in fact, to determine the value of 
the B.A. unit the ratio to be compared is 160 to 3000, or about 1 to 19, and this is a 
much easier experiment to make. 
Our 160 and 3000 have both been expressed in terms of the resistances of the box, 
and even though there may be some considerable error in the actual values of these 
resistances, the error in the ratio of any two of them is a quantity very small indeed. 
In conclusion, we would refer to another objection which has been made to the 
method. Nearly the whole of the battery current is allowed to flow through the 
coil V, 'whose resistance is about 1 ohm ; the effect of this must be to heat V and 
alter its resistance, thus producing error. We shall show that the error in our case is 
vanishingly small. 
The electromotive force of the battery was at most about 5 volts, and the total 
resistance of the primary circuit was about 80 B.A. units. The coil V was of German- 
silver wire, about 450 centims. being used to make it; the wire thus was very thick, 
its radius being ‘06 centim. The wire, silk covered, was loosely wound in a coil and 
enclosed in a brass case, which was immersed in water. 
From these data we find that the amount of heat developed per minute in the coil 
will be '055 unit. 
If we suppose all this heat to be retained, the rise of temperature will be ’015° C. 
per T, and the increase of resistance '0000045 B.A. unit, and this will be too small tc 
affect our results. As a matter of fact, it is clearly impossible for all the heat to remain 
in the coil, and the correction is, cl fortiori, too small to be considered. 
During the second series of experiments a hole was bored in the brass case of the 
coil and a thermometer inserted. The thermometer agreed throughout in its readings 
with that in the water bath in which the coil was immersed. 
Thus we conclude as the final result of this series of experiments that the value of 
the B.A. unit is '98635 ohm. 
The agreement between the individual experiments of the series is remarkable. 
They are, however, open to the objection that the conditions under which they were 
taken remained unaltered in some essential particulars. Thus the rods used to 
separate the primary and secondary coils were the same throughout, while the battery 
was also the same. It was decided, therefore, to make a second series of observations 
m which these quantities were varied. This was done during November and December, 
1881. Mr. Dodds had left Cambridge, and his place was taken by Mr. E. B. Sargant, 
of Trinity College. 
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