IV 
Introduction 
the central line. Since the angular distances from the center are projected toward the tangent, all points which transit 
describe hyperbolic curves. Thus we have a network of declination and time threads. For measuring differences 
of declination the central vertical line is graduated like a scale, and since the field of view permits the whole solar 
image to be seen, the scale-reading can be expressed in seconds of arc with the aid of the known apparent diameter 
of the sun. As one division has a linear value of $ inch (with an angular value of about 23"), the tenths, and some¬ 
times the twentieths, can readily be estimated. The differences of right ascension are measured by the diurnal motion 
with the aid of a chronograph. In order to avoid a correction which would arise from the projection above mentioned 
upon the plane, the transits were so arranged that use was made either of the line passing through the center of the 
field or of symmetrically situated pairs of lateral threads. 
“ The eyepiece used is a so-called negative one of the Huyghens form, having two plano-convex lenses with focal 
lengths of 3.90 and 1.75 inches. The magnification is approximately 75, and the field of view is 38', so that it 
embraces on each side 3' more than the whole solar disk. The eyepiece is drawn out 1.45 inches in order to make 
the image distinctly visible at the distance of the projection board from the eye lens—15.43 inches. The actual mag¬ 
nification of the image is here about 140 times, or the number which we obtain if the magnification given above is 
multiplied by the quotient of the distance of the table divided by the distance of distinct vision (7 to 8 inches). 
“ Further explanation is required of the conversion of the scale-distance into arc whereby the distance in declina¬ 
tion of a spot from the sun’s center is measured. On account of the size of the angles under which the rays fall upon 
the paper, the tangents can no longer be held to be proportional to the arc, and the value of a scale-division decreases 
from the center of the field toward the edge. These angles have their vertex at the position for the eye; or rather, in 
this case, where the eyepiece is drawn out, in more general terms in the point through which all rays pass after 
emergence from the eyepiece, and therefore the distance of this point from the board is concerned. Instead of com¬ 
puting this from the dimensions of the system of lenses, we in practice get a knowledge of this most simply by 
pointing the telescope toward the brightly illuminated sky and rendering the emergent pencil visible (as by blowing 
smoke upon it). Let us denote this distance, expressed in scale-divisions, by D , the angle of the cone of the sun’s disk 
formed at the intersection by G; g is similarly the angle at the same point between the spot and the sun’s center, p is 
the apparent radius of the sun, 5 its magnitude read off from the table, 5 the distance of the spot from the sun’s 
center. Then we have 
therefore 
_ 5 s 
tan G -—, tang=- , 
. £ tan G 
whence -- 
5 tan g 
g_ s g tan G 
P G P ' S ' G ’ tan g * 
But the last is the difference in declination of the spot and the sun; therefore 
tan G 
~G~ 
g 
tan g ’ 
which is most conveniently adapted to calculation in the form 
0 2 2 
log A8=logs-flog £+- log sec G — log secg . 
^ 3 3 
A small table of double entry, with the arguments 5 and p, gives AS directly. For the apparatus here D= 119F0, and 
on the average G = i9° 30'. The diameter of the solar image measures somewhat over ten inches on the paper. 
“ The transits for right ascension are as a rule taken four times, twice before and tw r ice after reading off the declina¬ 
tions, each time over one thread. When the number of spots is large, as has often been the case in recent years; and 
several groups fall at the same hour-angle, each section has to be determined for itself. The usefulness of the 
chronograph should be particularly recognized in such cases as this where the objects follow each other in rapid 
succession—often separated by only a fraction of a second. The clock is regulated to mean time so that the 
differences of right ascension are obtained without further reduction, since the departure of the rate from apparent 
solar time does not come into consideration, never exceeding 3 ^ 6 . The accuracy obtained, as well as the sim¬ 
plicity of the reduction and the whole procedure will be the more readily perceived from the following example. 
The separate groups of each day are distinguished in order of right ascension by the capital letters, the separate 
spots of the groups in the same order by the small letters with the attached exponents; but the most conspicu¬ 
ous spot of each group is assigned the letter without an exponent; different nuclei in the same penumbra receive 
subscripts. This mode of designation is preferable to that of current numbers. 
