the mercury in the barometer is also affected by capillary attraction, which depresses it by a constant amount depending mainly on the diameter of the tube. The requisite corrections can be estimated with accuracy sufficient for most purposes, more especially as we can check the correctness of the reading of a barometer by comparison with a standard barometer, and introduce if need be an index error including both the error in the affixing of the scale and the effect due to capillarity. But in constructing the standard barometer itself we must take greater precautions; the capillary depression depends somewhat upon the quality of the glass, the absence of air, and the perfect cleanliness of the mercury, so that we cannot assign the exact amount of the effect. Hence a standard barometer is constructed with a wide tube, sometimes even an inch in diameter, so that the capillary effect may be rendered almost zero.13 Gay-Lussac made barometers in the form of a uniform siphon tube, so that the capillary forces acting at the upper and lower surfaces should balance and destroy each other; but the method fails in practice because the lower surface, being open to the air, becomes sullied and subject to a different force of
In mechanical experiments friction is an interfering condition, and drains away a portion of the energy intended to be operated upon in a definite manner. We should of course reduce the friction in the first place to the lowest possible amount, but as it cannot be altogether prevented, and is not calculable with certainty from any general laws, we must determine it separately for each apparatus by suitable experiments. Thus Smeaton, in his admirable but almost forgotten researches concerning water-wheels, eliminated friction in the most simple manner by determining by trial what weight, acting by a cord and roller upon his model water-wheel, would make it turn without water as rapidly as the water made it turn. In short, he ascertained what weight concurring with the water would exactly compensate for the friction.14 In Dr. Joule’s experiments to determine the mechanical equivalent of heat by the condensation of air, a considerable amount of heat was produced by friction of the condensing pump, and a small portion by stirring the water employed to absorb the heat. This heat of friction was measured by simply repeating the experiment in an exactly similar manner except that no condensation was effected, and observing the change of temperature then produced.15
We may describe as test experiments any in which we perform operations not intended to give the quantity of the principal phenomenon, but some quantity which would otherwise remain as an error in the result. Thus in astronomical observations almost every instrumental error may be avoided by increasing the number of observations and distributing them in such a manner as to produce in the final mean as much error in one way as in the other. But there is one source of error, first discovered by Maskelyne, which cannot be thus avoided, because it affects all observations in the same direction and to the same average amount, namely the Personal Error of the observer or the inclination to record the passage of a star across the wires of the telescope a little too soon or a little too late. This personal error was first carefully described in the Edinburgh Journal of Science, vol. i. p. 178. The difference between the judgment of observers at the Greenwich Observatory usually varies from 1/100 to 1/3 of a second, and remains pretty constant for the same observers.16 One practised observer in Sir George Airy’s pendulum experiments recorded all his time observations half a second too early on the average as compared with the chief observer.17 In some observers it has amounted to seven or eight-tenths of a second.18 De Morgan appears to have entertained the opinion that this source of error was essentially incapable of elimination or correction.19 But it seems clear, as I suggested without knowing what had been done,20 that this personal error might be determined absolutely with any desirable degree of accuracy by test experiments, consisting in making an artificial star move at a considerable distance and recording by electricity the exact moment of its passage over the wire. This method has in fact been successfully employed in Leyden, Paris, and Neuchatel.21 More recently, observers were trained for the