or moon, according as it is high in the heavens or near the horizon, should be sufficient to make us cautious in accepting the plainest indications of our senses, unassisted by instrumental measurement. As to statements concerning the height of the aurora and the distance of meteors, they are to be utterly distrusted. When Captain Parry says that a ray of the aurora shot suddenly downwards between him and the land which was only 3000 yards distant, we must consider him subject to an error of sense1.

It is true that errors of observation are more usually errors of judgment than of sense. That which is actually seen must be truly seen so far; and if we correctly interpret the meaning of the phenomenon, there would be no error at all. But the weakness of the bare senses as measuring instruments, arises from the fact that they import varying conditions of unknown amount, and we cannot make the requisite corrections and allowances as in the case of a solid and invariable instrument.

Bacon has excellently stated the insufficiency of the senses for estimating the magnitudes of objects, or detecting the degrees in which phenomena present themselves. Things escape the senses,' he says m, 'because the object is not sufficient in quantity to strike the sense: as all minute bodies; because the percussion of the object is too great to be endured by the senses: as the form of the sun when looking directly at it in mid-day; because the time is not proportionate to actuate the sense: as the motion of a bullet in the air, or the quick circular motion of a firebrand, which are too fast, or the hour-hand of a common clock, which is too slow; from the distance. of the object as to place: as the size of the celestial bodies, and the size and nature of all distant bodies;

1 Loomis, On the Aurora Borealis.' Smithsonian Transactions, quoting Parry's Third Voyage, p. 61.

m Novum Organum.'

from prepossession by another object: as one powerful smell renders other smells in the same room imperceptible; from the interruption of interposing bodies: as the internal parts of animals; and because the object is unfit to make an impression upon the sense: as the air or the invisible and untangible spirit which is included in every living body.'

Complexity of Quantitative Questions.

So

One remark which we may well make in entering upon quantitative questions, has regard to the great variety and extent of phenomena presented to our notice. long as we deal only with a simply logical question, that question is merely, Does a certain event happen? or, Does a certain object exist? No sooner do we regard the event or object as capable of more or less, than one question branches out into many. We must now ask, How much is it compared with its cause or necessary condition? Does it change when the amount of the cause changes? If so, does it change in the same or opposite direction? Is the change in simple proportion to that of the cause? If not, what more complex law of connection holds true? This law determined satisfactorily in one series of circumstances may be varied under new conditions, and the most complex relations of several quantities may ultimately be established.

In every question of physical science there is thus a series of steps of progress, the first one or two of which are usually made with ease, while the succeeding ones demand more and more careful measurement. We cannot lay down any single invariable series of questions which must be asked from nature. The exact character of the questions will vary according to the nature of the case, but they will usually be of a very evident kind, and we may readily illustrate them by actual examples. Suppose,

for instance, that we are investigating the solution of some salt in water. The first is a purely logical question: Is there solution, or is there not? Assuming the answer to be in the affirmative, we next inquire, Does the solubility vary with the temperature, or not? In all probability some variation will be found to exist, and we shall have at the same time an answer to the further question, Does the quantity dissolved increase, or does it diminish with the temperature? In by far the greatest number of cases salts and substances of all kinds dissolve more freely the higher the temperature of the water, but there are a few salts, such as calcium sulphate, which follow the opposite rule. A considerable number of salts resemble sodium sulphate in becoming more soluble up to a certain temperature, and then varying in the opposite direction. We next require to assign the amount of variation as compared with that of the temperature, assuming at first that the increase of solubility is proportional to the increase of temperature. Common salt is an instance of very slight variation, and potassium nitrate of very considerable increase with temperature. Very accurate observations will probably show, however, that the simple law of proportionate variation is only approximately true, and some more complicated law involving the second, third, or higher powers of the temperature may ultimately be established. All these investigations have to be carried out for each salt separately, since no distinct principles by which we may infer from one substance to another have yet been detected. There is still an indefinite field for further research open; for the solubility of salts would probably vary with the pressure under which the medium is placed; the presence of other salts already dissolved may have effects yet unknown. The researches already effected as regards the solvent power of water must be repeated as regards alcohol, ether, carbon

bisulphide, and other media, so that unless general laws can be detected, this one phenomenon of solution can never be exhaustively treated. The same kind of questions recur as regards the solution or absorption of gases in liquids, the pressure as well as the temperature having then a most decided effect, and Professor Roscoe's researches on the subject present an excellent example of the successive determination of various complicated laws".

There is hardly a single branch of scientific research in which similar complications are not ultimately encountered. In the case of gravity, indeed, we arrive at the final law, that the force is invariably the same for all kinds of matter, and depends only on the distance of action. But in other subjects the laws, if simple in their ultimate nature, are disguised and complicated in their apparent results. Thus the effect of heat in expanding solids, or the reverse effect of forcible extension or compression upon the temperature of a body, will vary from one substance to another, will vary as the temperature is already higher or lower, and will probably follow a highly complex law, which in some cases gives negative or exceptional results. In crystalline substances the same researches have to be repeated in each distinct axial direction.

In the sciences of pure observation again, such as those of astronomy, meteorology, and terrestrial magnetism, we meet with many interesting series of quantitative determinations. The so-called fixed stars, as Giordano Bruno divined, are not really fixed, and may be more truly described as vast wandering orbs, each pursuing its own path through space. We must then determine separately for each star the following questions :

1. Does it move?

2. In what direction?

n Watt's Dictionary of Chemistry,' vol. ii. p. 790.

3. At what velocity?

4. Is this velocity variable or uniform? 5. If variable, according to what law? 6. Is the direction uniform?

7. If not, what is the form of the apparent path?

The successive answers to such questions in the case of certain binary stars, have afforded a proof that the motions are due to a central force coinciding in law with gravity, and doubtless identical with it. In other cases the motions are usually so small that it is exceedingly difficult to distinguish them with certainty. A coincidence of motions in some constellations has been pointed out by Mr. Proctor, and the parallactic effect due to the sun's proper motion has been surely detected; but the time is yet far off when any general results as regards stellar motions can be established.

The variation in the brightness of stars opens an unlimited field for curious observation. There is not a star in the heavens concerning which we might not have to determine

1. Does it vary in brightness?

2. Is the brightness increasing or decreasing?

3. Is the variation uniform, that is, simply proportional to time?

4. If not, according to what law does it vary?

In a majority of cases the change will probably be found to have a periodic character, in which case several other questions will arise, such as

5. What is the length of the period?

6. Are there minor periods within the principal period?

7. What is the form or law of variation within the period?

8. Is there any change in the amount of variation?