Instructions for the Observation of the Eclipse, 1582 INSTRUCTION FOR THE OBSERVATION OF THE ECLIPSE OF THE MOON AND THE MEASUREMENT OF SHADOWS, WHICH HIS MAJESTY ORDERS TO BE MADE IN THE YEAR 1582 IN THE SPANISH CITIES AND TOWNS OF THE INDIES, IN ORDER TO DETERMINE THEIR LONGITUDE AND LATITUDE; ALTHOUGH THERE MAY BE OTHER MATHEMATICAL METHODS FOR DOING THIS, THOSE WHICH FOLLOW HAVE BEEN CHOSEN BECAUSE THEY ARE SIMPLER.
Firstly, the eclipse of the moon during the year 1582 will occur on June 19, after midnight in Spain and sometime after nightfall in the Indies, depending on the greater or lesser distance and longitude of each province. But since these, as well as the computation of the time differences, are in doubt the following is to be done.
One or two days before the eclipse, in an open and exposed spot on which the sun shines at rising and setting, construct a plane surface with a ruler and a level, at least a yard square. Make it on a surface of hard clay, lime, cement, plaster, or wood, so that it is smooth and level , no higher in one part than in another. With a set of dividers, which may be made of wood, if no other type is available, draw two circles in the middle, one within the other with a common center, which is the point in the center of the circle where one point of the dividers is placed to draw it. For one circle the dividers are to be opened one-third yard from point to point, and for the other, a third and one-half.
Once these circles are drawn, drive into the center point a nail or style of iron or wood. It must be straight, smooth, and thin, and exactly one third yard long, not counting the part driven into the plane surface. It must be vertical, not bent or inclined in one section or another. This may be accomplished and checked by making equal measurements with the dividers between the top of the style and various points on the circumference of one of the circles.
This done, after sunrise watch carefully for the direction and point along the circumference of the larger circle at which the shadow of the style is entirely enclosed in it, and at the precise time that the tip of the shadow touches the circumference, neither inside nor outside, but right on it, make a mark on the line in the center of the tip of the shadow. Do the same for the smaller circle, when the shadow enter it. At some times and some places, it may well happen that the shadow will not become this short; but whatever the case, as the shadow grows shorter, use something as a movable marker to follow the tip and determine that it is still growing shorter. At the point where the shadow is shortest, which will be exactly noon, make another mark, and from it measure with the dividers the precise distance to the base of the style along the direction in which the shadow is cast. On a piece of paper draw two straight ink lines, one precisely the length of the shadow at its shortest, and the other equal to the length of the style from its base to the tip, not including the part driven into the platform. Label in writing each of these lines, identifying the measurement of the shadow and that of the style. State in which direction the shadow fell when it was measured: whether north or south. State the day, month, and year when this observation of the shadow was made.
In the afternoon, after the shadow begins to lengthen again, watch with the same attention for the time when it extends to the smaller circle (if it had fallen within it), and make a mark on the circumference at the precise point on which the tip of the shadow falls, as was done when the shadow entered. Then do the same with the outside larger circle, making another mark where the shadow commences to leave it.
Having marked the two points of entry and exit of the shadow in each of the circles, make a third point on the circumference of each, halfway between the first two, so that from the point where the shadow entered the larger circle to this third point the distance is equal to that between this third point and the point where the shadow left. Do the same with the inside, smaller circle. Remove the style, and place a good straight ruler from this middle point on one circle to that of the other, and draw a long line that crosses the circles and the platform; this is to be called the meridian line, because it will run directly north and south. If it is well drawn, it will pass through the point where the shadow was shortest, and also through the center hole into which the style was driven, dividing each of the circles into two equal parts or half-circles. Then divide these in half by making a point halfway around the circumference of each half-circle, spaced equally from the points where the meridian line intersects them and runs beyond. With these halfway points established on the half-circles, draw another line with the ruler which passes through all of them and traverses the platform, crossing the meridian at right angles at its midpoint, where the style was. This line will run directly east and west; thus each of the circles will be divided into four equal parts.
Before the day of the eclipse, make an instrument in the following form, which will be simple to do. On the straight side of a plank, which is at least a yard wide and long, make a circle by putting one point of the dividers in the center of the plank, and the other point open exactly one-third yard. At the point or center where the base point of the dividers rested, place a thin vertical style of iron or some other material, one-third yard long, and straight and square, so that it does not lean in one direction more than another, like that used for the measurement of the shadow. At the base of the style next to the plank, tie a thin thread with a loose knot and a small weight at the end which will extend beyond the circumference of the circle, but not beyond the edge of the plank.
Allowing sufficient time on the day of the eclipse, place this instrument on edge over the platform on which the shadow was measured, facing the side opposite that on which the noon shadow fell. If the shadow fell toward the north, the instrument should face south, or if the shadow fell to the south, the instrument should face north. The instrument should lie lengthwise along the east-west line, and should be adjusted along it very carefully so that it does not deviate to either side. It should not be inclined to the north or south, but exactly vertical; this can be checked with the leveling thread which hangs from the style.
With this in place, mark a point on the circumference of the half-circle at the place where the leveling thread, hanging from the style crosses it.
In the evening, when the full moon starts to rise in the east, have a number of people observe whether the moon rises perfectly rounded, as it will if it is not eclipsed upon rising, or whether it appears lopsided on some part of its roundness, or totally obscured. If it rises perfectly round, continue observing to determine when it begins to be obscured. When this is clearly observable, mark the point on the circumference of the circle on the instrument where the middle of the shadow of the style falls. After the darkness of the moon has passed, continue watching for the time when the moon recovers all of its light. When it is completely clear of darkness, and again round, make another mark on the circular line where the shadows of the style falls. If in the same location the shadow does not reach the edge of the circle, make the mark at the very tip of the shadow at its maximum extent.
This done, make a circle of the same dimensions as that on the instrument on a large sheet of paper (not parchment) made of four sheets joined at the edges so that it will be as large as the plank. On it mark the point where the leveling thread crossed the circular line, and the points indicated by the shadow of the style on either side of the leveling point, and exactly as far from it as they were on the plank. next to each point, indicate with written labels which pertains to the level,which to the beginning of the eclipse, and which to the end. In addition, indicate the end of the instrument that was toward the east during the observation. The drawing on paper should in all respects represent precisely the figures observed on the instrument. Make a duplicate, and another of the paper showing the measurements of the style and shadow for noon. Along with the names of the people who made the observations, send each duplicate separately to his majesty in care of the Royal Council of the Indies.
Even if because of cloudiness or other hindrance the eclipse cannot be observed, measure the length of the noon shadow on that day, or on another on which it can be done. Send this measurement and that of the style, as directed above, with a report of the day, month, and year when it was taken. Report any reason for not being able to take it on the day of the eclipse.