effects upon luminous stars. Thus if one member of a double star were dark, we could readily detect its existence, and even estimate its size, position, and motions, by observing those of its visible companion. It was a favourite notion of Huyghens that there may exist stars and vast universes so distant that their light has never yet had time to reach our eyes; and we must also bear in mind that light may possibly suffer slow extinction in space, so that there is more than one way in which an absolute limit to the powers of telescopic discovery may exist.

There are natural limits again to the power of our senses in detecting undulations of various kinds. It is commonly said that vibrations of less than sixteen strokes or more than 38,000 strokes per second are not audible as sound; and as some ears actually do hear sounds of much higher pitch, even two octaves higher than what other ears can detect, it is exceedingly probable that there are incessant vibrations which we cannot call sound because they are never heard. Insects may possibly communicate by such acute sounds, constituting a language inaudible and inscrutable to us; and the remarkable agreement apparent among bodies of ants or bees might thus perhaps be explained. Nay, as Fontenelle long ago suggested in his scientific romance, there may exist unlimited numbers of senses or modes of perception which we can never feel, though Darwin's theory would render it probable that any useful means of knowledge in an ancestor would be developed and improved in the descendants. We might doubtless have been endowed with a sense capable of feeling electric phenomena with acuteness, so that the positive or negative state of charge of a body could be at once estimated. The absence of such a sense is probably due to its comparative uselessness.

Heat undulations are subject to the same considerations.

It is now apparent that what we call light is the affection of the eye by certain vibrations, the less rapid of which are invisible and constitute the dark rays of radiant heat, in detecting which we must substitute the thermometer or the thermopile for the eye. At the other end of the spectrum, again, the ultra-violet rays are invisible, and only indirectly brought to our knowledge in the phenomena of fluorescence or photo-chemical action. There is no reason to believe that at either end of the spectrum an absolute limit has yet been reached.

Just as our knowledge of the stellar universe is limited. by the power of the telescope and other conditions, so our knowledge of the minute world has its limit in the powers and optical conditions of the microscope. There was a

time when it would have been a reasonable induction that vegetables were motionless, and animals alone endowed with power of locomotion. We are astonished to discover by the microscope that minute plants are if anything more active than minute animals. We even find that mineral substances seem to lose their inactive character and dance about with incessant motion when reduced to sufficiently minute particles, at least when suspended in a non-conducting medium f. Microscopists will meet a natural limit to their means of observation when the minuteness of the objects examined becomes comparable to the length of light undulations, and the extreme difficulty already encountered in determining the forms of minute marks on Diatoms appears to be due to this cause.

Of the errors likely to arise in estimating quantities by the senses I have already spoken (vol. i. p. 320), but there are some cases in which we actually see things different from what they are. A jet of water often appears to be a continuous thread, when it is really a wonderfully or

f Jevons, Proceedings of the Literary and Philosophical Society of Manchester,' 25th January, 1870, vol. ix. p. 78.

ganized succession of small and large drops, oscillating in form. The drops fall so rapidly that their impressions upon the eye run into each other, and in order to see the separate drops we require some device for giving an instantaneous view, such as illumination by the electric spark, or the use of the revolving disc called the phenakistiscope.

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Maxwell, Theory of Heat,' p. 301.

There long appeared to be a strong presumption that all comets moved in elliptic orbits, because no comet had been proved to move in any other kind of path. The theory of gravitation admitted of the existence of comets moving in hyperbolic orbits, and the question arose whether they were really non-existant or were only beyond the bounds of easy observation. From reasonable suppositions Laplace calculated that the probability was at least 6000 to 1 against a comet which comes within the planetary system sufficiently to be visible at the earth's surface, presenting an orbit which could be discriminated from a very elongated ellipse or parabola, in the part of its orbit within the reach of our telescopes h. In short, the chances are very much in favour of our seeing elliptic rather than hyperbolic comets. Laplace's views have been confirmed by the discovery of six hyperbolic comets, which appeared in the years 1729, 1771, 1774, 1818, 1840, and 1843, and, as only about 800 comets altogether have been recorded, the proportion of hyperbolic ones is quite as large as should be expected. Some remarkable speculations have recently been published by Mr. A. S. Davies, as to the probable character of the orbits of comets, which, after moving freely through space, become attached to this planetary systemk.

When we attempt to estimate the numbers of objects which may have existed, we must make large allowances for the limited sphere of our observations. Thus probably not more than 4000 or 5000 comets have been seen in historical times, but making allowance for the absence of observers in the southern hemisphere, and for the small probability that we see any considerable h Laplace, Essai Philosophique,' p. 59. Todhunter's History,'

Pp. 491-94.

i Chamber's Astronomy,' 1st ed. p. 203.

k 'Philosophical Magazine,' 4th Series, vol. xl. p. 190; vol. xli. p 44.

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