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sets of experiments, when calculated out, would he found to 
indicate a law of error, differing considerably from the 
ordinary law of simple errors of experiments or observa- 
tions, and that the mean value of the minus differences 
would be very sensibly greater than that of the plus 
differences. I therefore calculated the means of the two 
sets of experiments, and the differences of all the breaking- 
weights from these means, and grouping these differences 
according to their order of magnitude, I projected the 
results on ruled paper, but instead of a tolerably regular 
curve having only one maximum I obtained a curve having- 
two well marked maxima. It was therefore at once evident 
that some unsuspected condition or disturbing cause had 
operated during the experiments to produce an undue 
number of breaking weights considerably above, and also 
considerably below, the general average. The effect, in fact, 
was somewhat similar to that which would be produced by 
a series of throws of a number of dice, some of which were 
weighted on one side, while others were weighted on the 
opposite side. I concluded, therefore, that many of the 
bars used by Mr. Spence had their sides of very unequal 
strength, and that it depended upon the position in which 
a bar was placed when tested, whether its breaking weight 
would be high or low. With the strongest side of the bar 
placed downwards the breaking weight would be high, but 
witli the weakest side downwards the breaking- weight 
would be low. Either of the other two sides placed lowest 
would in general give a breaking weight of intermediate 
value. If in two sets of experiments A and B a greater 
number of bars happened to be placed with their weakest 
sides downwards in set A than in the set B, then the mean 
of A would be less than that of B ; and this, in fact, appears 
to have actually taken place in Mr. Spence’s experiments. 
Thus, if we divide the set of 70 experiments made at a 
temperature of 70° Fahr. into two sets of 35 each, the mean 
breaking weight of the first 35 is 3cwt. 2qr. 231bs., and 
that of the second 35 is 3cwt. 3qr. 25-51bs., the difference 
being lqr. 2-51bs., or 2| times greater than the difference 
