A curious instance of false negative inference is furnished by experiments on light. Euler rejected the corpuscular theory on the ground that particles of matter moving with the immense velocity of light would possess momentum, of which there was no evidence. Bennet had attempted to detect the momentum of light by concentrating the rays of the sun upon a delicately balanced body. Observing no result, it was considered to be proved that light had no momentum. Mr. Crookes, however, having suspended thin vanes, blacked on one side, in a nearly vacuous globe, found that they move under the influence of light. It is now allowed that this effect can be explained in accordance with the undulatory theory of light, and the molecular theory of gases. It comes to this—that Bennet failed to detect an effect which he might have detected with a better method of experimenting; but if he had found it, the phenomenon would have confirmed, not the corpuscular theory of light, as was expected, but the rival undulatory theory. The conclusion drawn from Bennet’s experiment was falsely drawn, but it was nevertheless true in matter.
Many incidents in the history of science tend to show that phenomena, which one generation has failed to discover, may become accurately known to a succeeding generation. The compressibility of water which the Academicians of Florence could not detect, because at a low pressure the effect was too small to perceive, and at a high pressure the water oozed through their silver vessel,33 has now become the subject of exact measurement and precise calculation. Independently of Newton, Hooke entertained very remarkable notions concerning the nature of gravitation. In this and other subjects he showed, indeed, a genius for experimental investigation which would have placed him in the first rank in any other age than that of Newton. He correctly conceived that the force of gravity would decrease as we recede from the centre of the earth, and he boldly attempted to prove it by experiment. Having exactly counterpoised two weights in the scales of a balance, or rather one weight against another weight and a long piece of fine cord, he removed his balance to the top of the dome of St. Paul’s, and tried whether the balance remained in equilibrium after one weight was allowed to hang down to a depth of 240 feet. No difference could be perceived when the weights were at the same and at different levels, but Hooke rightly held that the failure arose from the insufficient elevation. He says, “Yet I am apt to think some difference might be discovered in greater heights.”34 The radius of the earth being about 20,922,000 feet, we can now readily calculate from the law of gravity that a height of 240 would not make a greater difference than one part in 40,000 of the weight. Such a difference would doubtless be inappreciable in the balances of that day, though it could readily be detected by balances now frequently constructed. Again, the mutual gravitation of bodies at the earth’s surface is so small that Newton appears to have made no attempt to demonstrate its existence experimentally, merely remarking that it was too small to fall under the observation of our senses.35 It has since been successfully detected and measured by Cavendish, Baily, and others.
The smallness of the quantities which we can sometimes observe is astonishing. A balance will weigh to one millionth part of the load. Whitworth can measure to the millionth part of an inch. A rise of temperature of the 8800th part of a degree centigrade has been detected by Dr. Joule. The spectroscope has revealed the presence of the 10,000,000th part of a gram. It is said that the eye can observe the colour produced in a drop of water by the 50,000,000th part of a gram of fuschine, and about the same quantity of cyanine. By the sense of smell we can probably feel still smaller quantities of odorous matter.36 We must nevertheless remember that quantitative effects of far less amount than these must exist, and we should state our negative results with corresponding caution. We can only disprove the existence of a quantitative phenomenon by showing deductively from the laws of nature, that if present it would amount to a perceptible quantity. As in the case of other negative arguments (p. 414), we must demonstrate that the effect would appear, where it is by experiment found not to appear.