A method of measuring the spots may now be described. It is not likely indeed that the ordinary observer will care to enter upon any systematic series of measurements. But even in his case, the means of forming a general comparison between the spots he sees at different times cannot fail to be valuable. Also the knowledge—which a simple method of measurement supplies—of the actual dimensions of a spot in miles (roughly) is calculated to enhance our estimate of the importance of these features of the solar disc. I give Mr. Howlett's method in his own words:—
"Cause your optician to rule for you on a circular piece of glass a number of fine graduations, the 200th part of an inch apart, each fifth and tenth line being of a different length in order to assist the eye in their enumeration. Insert this between the anterior and posterior lenses of a Huygenian eye-piece of moderate power, say 80 linear. Direct your telescope upon the sun, and having so arranged it that the whole disc of the sun may be projected on the screen, count carefully the number of graduations that are seen to exactly occupy the solar diameter.... It matters not in which direction you measure your diameter, provided only the sun has risen some 18° or 20° above the horizon, and so escaped the distortion occasioned by refraction.[16]
"Next let us suppose that our observer has been observing the sun on any day of the year, say, if you choose, at the time of its mean apparent diameter, namely about the first of April or first of October, and has ascertained that" (as is the case with Mr. Howlett's instrument) "sixty-four graduations occupy the diameter of the projected image. Now the semi-diameter of the sun, at the epochs above mentioned, according to the tables given for every day of the year in the 'Nautical Almanac' (the same as in Dietrichsen and Hannay's very useful compilation) is 16' 2", and consequently his mean total diameter is 32' 4" or 1924". If now we divide 1924" by 64" this will, of course, award as nearly as possible 30" as the value in celestial arc of each graduation, either as seen on the screen, or as applied directly to the sun or any heavenly body large enough to be measured by it."
Since the sun's diameter is about 850,000 miles, each graduation (in the case above specified) corresponds to one-64th part of 850,000 miles—that is, to a length of 13,256 miles on the sun's surface. Any other case can be treated in precisely the same manner.
It will be found easy so to place the screen that the distance between successive graduations (as seen projected upon the screen) may correspond to any desired unit of linear measurement—say an inch. Then if the observer use transparent tracing-paper ruled with faint lines forming squares half-an-inch in size, he can comfortably copy directly from the screen any solar phenomena he may be struck with. A variety of methods of drawing will suggest themselves. Mr. Howlett, in the paper I have quoted from above, describes a very satisfactory method, which those who are anxious to devote themselves seriously to solar observation will do well to study.
It is necessary that the observer should be able to determine approximately where the sun's equator is situated at the time of any observation, in order that he may assign to any spot or set of spots its true position in relation to solar longitude and latitude. Mr. Howlett shows how this may be done by three observations of the sun made at any fixed hour on successive days. Perhaps the following method will serve the purpose of the general observer sufficiently well:—
The hour at which the sun crosses the meridian must be taken for the special observation now to be described. This hour can always be learnt from 'Dietrichsen's Almanac'; but noon, civil time, is near enough for practical purposes. Now it is necessary first to know the position of the ecliptic with reference to the celestial equator. Of course, at noon a horizontal line across the sun's disc is parallel to the equator, but the position of that diameter of the sun which coincides with the ecliptic is not constant: at the summer and winter solstices this diameter coincides with the other, or is horizontal at noon; at the spring equinox the sun (which travels on the ecliptic) is passing towards the north of the equator, crossing that curve at an angle of 23½°, so that the ecliptic coincides with that diameter of the sun which cuts the horizontal one at an angle of 23½° and has its left end above the horizontal diameter; and at the autumn equinox the sun is descending and the same description applies, only that the diameter (inclined 23½° to the horizon) which has its right end uppermost, now represents the ecliptic. For intermediate dates, use the following little table:—
| Date. (Circiter.) | Dec. 22 | Jan. 5 | Jan. 20 | Feb. 4 | Feb. 19 | Mar. 5 | |
| June 6 | May 21 | May 5 | Apr. 20 | Apr. 5 | Mar. 21 | ||
| Inclination of Ecliptical Diameter of Sun to the Horizon.[17] | Left | Left | Left | Left | Left | Left | Left |
| 0° 0' | 6° 24' | 12° 14' | 17° 3' | 20° 36' | 22° 44' | 23° 27' | |
| Right | Right | Right | Right | Right | Right | Right | |
| Date. (Circiter.) | Jan. 21 | Dec. 7 | Nov. 22 | Nov. 7 | Oct. 23 | Oct. 8 | |
| July 7 | July 23 | Aug. 6 | Aug. 23 | Sept. 7 | Sept. 23 |
Now if our observer describe a circle, and draw a diameter inclined according to above table, this diameter would represent the sun's equator if the axis of the sun were square to the ecliptic-plane. But this axis is slightly inclined, the effect of which is, that on or about June 10 the sun is situated as shown in [fig. 14] with respect to the ecliptic ab; on or about September 11 he is situated as shown in [fig. 13]; on or about December 11 as shown in [fig. 12]; and on or about March 10 as shown in [fig. 15]. The inclination of his equator to the ecliptic being so small, the student can find little difficulty in determining with sufficient approximation the relation of the sun's polar axis to the ecliptic on intermediate days, since the equator is never more inclined than in [figs. 12] and [14], never more opened out than in [figs. 13] and [15]. Having then drawn a line to represent the sun's ecliptical diameter inclined to the horizontal diameter as above described, and having (with this line to correspond to ab in [figs. 12]-[15]) drawn in the sun's equator suitably inclined and opened out, he has the sun's actual presentation (at noon) as seen with an erecting eye-piece. Holding his picture upside down, he has the sun's presentation as seen with an astronomical eye-piece—and, finally, looking at his picture from behind (without inverting it), he has the presentation seen when the sun is projected on the screen. Hence, if he make a copy of this last view of his diagram upon the centre of his screen, and using a low power, bring the whole of the sun's image to coincide with the circle thus drawn (to a suitable scale) on the screen, he will at once see what is the true position of the different sun-spots. After a little practice the construction of a suitably sized and marked circle on the screen will not occupy more than a minute or two.
| Fig. 12. | Fig. 13. |
| Fig. 14. | Fig. 15. |