distinctness of vision he ascribed principally to the use of a graduated dark glass, constructed under his direction by Mr. Simms. It consists of a long wedge of red glass and a long wedge of green glass, their edges turned the same way, combined with an equivalent wedge of colorless glass, its edge turned the opposite way. Nobody would suppose without trial how fastidious the eye is as to the proper intensity of shade, and how distinctly, when intent on clear vision, it rejects a shade in the most trifling degree lighter or darker. He thought it highly important that such shades should be used for observing the transits of Venus. It is desirable also that the color left by the shade. glass should be agreeable to the observer's eye.

Still there is one caution which must not be put out of sight. The selection of places depends entirely upon the portion of the Earth which is illuminated at the times of ingress and egress; and if the tables of the movements of Venus are erroneous in 1882 to the amount of an hour's motion, the illuminated face of the Earth will be altered to the amount of two or three hours' rotation of the Earth, and the selections of stations may be totally changed. It is therefore most important that the tables of Venus should be thoroughly examined, and where necessary rectified. A great mass of observations of Venus exist, already reduced so far as to require only the very last step of substitution of errors of planetary elements. The Astronomer Royal referred particularly to the Greenwich Planetary Reductions from 1750 to 1830, to the reduction of certain Cambridge observations, to the reduction (in the annual Greenwich volume) of the Greenwich observations down to the present time, and to the discussion of some of the Greenwich observations by Mr. Main and Mr. Glaisher. And he took the opportunity of expressing his opinion that fifty pounds spent on calculations with an object like this would confer much greater benefit on astronomy than a thousand pounds employed in the foundation and equipment of an observatory.

On viewing the expense and the risk of the determinations of the Sun's distance by transits of Venus, as well as the distance of time, which must necessarily place them beyond the knowledge of many observers of the present day, it appears natural to consider whether other methods cannot be used, less stringent as to the moment of ob servation, requiring less co-operation of observations, and occurring at an earlier time. Such are the direct determinations of the parallaxes of Venus and of Mars, when near to the Earth, by simultaneous observations at northern and southern stations, as in figure 1, or by successive observations at the same observatory when it is brought to different positions by the Earth's rotation, as in figure 6.

Venus cannot be compared with stars on the meridian. She may be compared with stars in extra-meridional observations before sunrise or after sunset, but she is then uncomfortably bright, and rarely well defined; and she has only one illuminated limb admitting of ob servation, and therefore in the comparison of observations made at different stations there is great risk of error from difference in the estimation of her semi-diameter. Moreover, she does not remain long in the position nearest the Earth, and the nearer she is the more con

tracted are the daily hours of observation.

It seems unlikely that trustworthy results will be deduced from the observations of Venus.

Figure 6.

Parallax of Mars

м

The circumstances of Mars in opposition to the Sun (figure 6) are much more favorable. Mars may then be compared with stars through the whole night; he has two observable limbs, both admitting of good observation; he remains much longer in proximity to the Earth, and the nearer he is the more extended are the hours of observation.

Here, however, a circumstance is to be considered which has not previously called for attention. The orbit of Mars is much more eccentric than those of Venus and the Earth. At some oppositions, therefore, he will be so far from the Earth that little advantage will be derived from attempting to observe his parallax. (It is understood that such observations were made in the United States expedition of a few years past, which, from the great distance of Mars, must have been nearly useless.) At other oppositions he is almost as near as Venus is about conjunction. The following table expresses roughly the distance of Mars from the Earth, at some of the nearest and some of the most distant oppositions. The unit of measure is the Earth's mean distance from the Sun:

The years 1860, 1862, and 1877 are, therefore, favorable for the determination of parallax. But they require the following special considerations:

When, as in figure 1, the method of comparison of observations made at a northern observatory and a southern observatory is employed, the most favorable position of the planet is that of verticality to the point midway between the two observatories. The north latitude of the northern observatories (Greenwich, Berlin, Pulkowa) is greater than the south latitude of the southern observatories, (Cape of Good Hope, St. Jago.) Hence, cæteris paribus, a north declination of Mars will be preferable to a south declination. In this respect the opposition of 1862 is preferable to that of 1860.

But there is another method of making observations for parallax not applicable to Venus, but applicable to Mars, namely, by observing the displacement of Mars in right ascension, when he is far east of the meridian and far west of the meridian, as seen at a single observatory. Thus, in figure 6, conceive the pole of the Earth to be turned. towards the eye, and conceive the Earth and Mars to be stationary in space, the Earth, however, rotating round its axis. By the diurnal rotation, an observatory is carried from the position A to A'; and, at

one of these times, Mars is seen in contact with one star, and at the other time with another star. These observations give the means, as in figure 1, of determining the distance of Mars. And though. in fact, both the Earth and Mars are moving, yet the effects of those motions can be so exactly calculated as to give to the determination the same accuracy as if both were at rest.

In order to compare the value of this method with that of observations on the meridian at two observatories, we must estimate the length of the base line A B in figure 1, or A A' in figure 6. The greatest meridional base line, from Pulkowa to the Cape of Good Hope, is Earth's radius x 2 sine 47° nearly. The measure of the greatest base line A A' depends on the latitude of the observatory. At Greenwich it is Earth's radius X 2 sine 38° 30'; at the Cape of Good Hope and at St. Jago (Chili) it is about Earth's radius X 2 sine 57°; at Madras it is nearly Earth's radius X 2 sine 77°. Thus it appears that at each of the three last-mentioned observatories the base line which can be obtained is considerably greater than the best which can be obtained by meridional combination of two observatories. At Madras the angle to be measured would be about 44". To this is to be added that the method is attended with no expense whatever; that the observations which are compared are made with the same telescope and by the same observer, or the same series of observers; that there is none of the tediousness, the wearying correspondence, or the doubt, which are inseparable from observations requiring distant co-operation; and that the observer is supported by the feeling that his own unassisted observations will give a perfect system of means for deciding one of the most important questions in astronomy. The Astronomer Royal expressed his opinion that this method is the best of all.

In order to use the process to the greatest advantage, Mars ought to be visible at six hours' distance from the meridian on each side, and therefore his declination ought to have the same name as the latitude of the observatory. Thus 1860 will be a favorable year for the Cape of Good Hope and St. Jago; 1862 will be favorable for North American and European observatories. It is scarcely necessary to discriminate between them for Madras, where both years are good; 1862, however, is preferable to 1860.

The first equipment for this observation, on the necessity for which special stress must be laid, is an equatorial, firm in right ascension. Many modern equatorials are deficient in this important quality. It would be well in using them to apply a temporary mechanism for fixing the instrument in right ascension, such as its construction may permit. The next, which will be found advantageous, though not strictly necessary, is the apparatus for the American or chronographic method of transits, by which the number of observations may be greatly increased, and something will be gained in the accuracy of each. These, with the ordinary clocks and chronometers, &c., of an observatory, are all that are required.

The principal rules for the observer would be: To make the obser vations, as near as practicable, to the six-hour intervals from the

meridian on both sides, and to repeat the observations in continued sequence morning and evening, morning and evening. If different observers are employed, to take care that each observer is charged as often with morning as with evening observations. To determine the difference between the right ascension of Mars and the right ascensions of two stars, one having greater N. P. D. and the other smaller N. P. D. than Mars. To use the same stars in at least two observations of different names, morning and evening, and in as many more consecutive observations as can be conveniently arranged. When it becomes necessary to change the selection of stars, to observe both the old pair and the new pair in one morning or evening observation. In all cases to observe, by such alternation as is most agreeable to the observer, both limbs of Mars, (the preceding and the following.) The observations might with advantage commence a fortnight before opposition and terminate a fortnight after it.

In the nature of external preparation, applying generally to all observatories, the principal requisite is a chart of the apparent path of Mars in considerable detail, giving the place of the planet for every hour or every few hours, and giving the places of all the stars, little and great, in its neighborhood. The observer in possession of this will be able to select stars of such a magnitude as he judges most agreeable to his eye, and at such intervals as will be convenient for his system of wires; and to attend rigorously to the condition of always comparing the planet with two stars, one of greater and one of less N. P. D. It might be proper that the color of the stars should be noted, in order that, to avoid possible inequalities of refraction, stars of the same color as Mars (if there are such) may be selected. It would not, perhaps, be too much to expect such charts for 1860 and 1862 from the superintendents of our national ephemerides.

On reviewing the whole subject, the Astronomer Royal presses on the attention of astronomers the importance of observing Mars in 1860 and 1862; and for this purpose the necessity of speedily making the preparations, instrumental and literary, which he has described, especially that of the charts of stars with the path of Mars. At the same time he urges that the future astronomical public will not be satisfied unless all practical use is made of the transits of Venus of 1874 and 1882; and that for these a thorough discussion of the elements of the orbit of Venus, the determination of some distant longitudes, and a reconnoissance of Wilkes's land must be effected within a few years.

REPORTS ON THE STATE OF KNOWLEDGE OF RADIANT

HEAT, MADE TO THE BRITISH ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE, AT THE MEETINGS IN 1832, 1840, AND 1854.

By the REVEREND BADEN POWELL, M. A., F. R. S, Savilian Professor of Geometry in the University of Oxford.

REPORT FOR 1832.

IN attempting to give a condensed account of the present state of our knowledge of the science of Radiant Heat, it appears to me that I shall be best consulting the design of such a report by offering, in as brief a form as possible, a sketch of what has been formerly done in this department; and thence proceeding to a more detailed survey of what is now doing. And we shall proceed with greater clearness if we distinguish the several different departments into which the subject divides itself, agreeably to certain known distinctions in the properties and species of heat acting under peculiar circumstances. All these have been too commonly confounded together under the general and vague name of Radiant Heat, whence not unfrequently the most erroneous views have resulted. By distributing our subject, however, under the few well-marked divisions which the scanty results of observation as yet supply, we shall at once secure perspicuity in our views, and be treating the subject in a way most accordant with the inductive process: which, it must be distinctly avowed, has not yet enabled us to advance to any such comprehensive knowledge of the facts as can warrant us in generalizing them, or in ascribing to a common principle the radiation of heat from a mass of hot water, from a flame, and from the sun.

We shall take each of these principal divisions separately, and under each shall consider what is known in reference to those properties to which experiment has been directed.

DIVISION I.

Radiation of heat from hot bodies below the temperature of luminosity.

We regret to state that since the date of the present Report of the Smithsonian Institution, we have received intelligence of the death of the gifted author of these admirable articles. In his departure from this life science has been called to mourn a successful and industrious investigator, an able defender, and an accomplished expounder of her principles. As a scholar, a writer, and a christian gentleman, we can but seldom hope to look upon his like again. The republication and wide diffusion of these reports, in a collected form, will, we trust, be considered of importance in the advance of science, and we hope to be able to publish a continuation of them by some worthy successor of Professor Powell. J. H.