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fully said, that the student may expect his chief profit to be intellectual "in the widening of the range of thought and conception, in the pleasure attending the discovery of simple law working out the most complicated results, in the delight over the beauty and order revealed by the telescope in systems otherwise invisible, in the recognition of the essential unity of the material universe and of the kinship of his own mind with the infinite. reason that formed all things and is immanent in them."

The five points made in this statement covering the scope of astronomy and revealing, to some extent, the unique character of the study for scholastic uses, open to view the grand possibilities of the theme. Much more could easily be said in the same line, but that is not necessary or desirable now.

2. How shall astronomy be taught? If we have rightly in mind the value of this branch as a means of training, and have given it proper place in courses of study mapped out for use, then comes the important query how shall this study be taught? As we have said in these pages more than once recently, the teaching of astronomy is now rapidly undergoing a change which is to increase its efficiency and to bring it rapidly and widely to favorable notice in public school instruction. That change is coming in the uses that are to be made of textbooks. Too generally the text-book in this branch of study is made the end of the student's effort. When he has learned what the book contains the impression often follows that good progress has been made in gaining knowledge of the subject which may be very far from the truth. Something like what is now called the "laboratory method" will certainly take the place of a large part of the time and effort put forth by an immature student to get the meaning of the author who has written a scholarly book which is more a manual or a ready hand-book in the science than it is a suitable text-book for a novice. The fact is apparent and it has been recently the source of much discussion in the minds of those who teach. The trend of things is towards the inductive idea, or, what is the same thing, the "laboratory method," so called. This means that students should have test exercises, in astronomy, as those in physics now do who go to the laboratory for work, there to fix their knowledge of the principles of this science which is given in the text-book or in the lecture room. It is at once seen that such a step as this will put the student to the test of independent knowledge of the things he can see, chart, or

reason out as compared with what he can learn and remember from a text-book. The difference between these two kinds of knowledge is very great.

(TO BE CONTINUED.)

LECTURE-ROOM DEMONSTRATION OF ORBIT OF BODIES UNDER THE ACTION OF A CENTRAL ATTRACTION.

R. W. WOOD.

Not remembering to have seen any attempt to show experimentally in the lecture room the motion of bodies acted on by a central attractive force varying inversely as the square of the distance in elliptic, parabolic, and hyperbolic orbits, I have made a few experiments with a view of determining how well these curves could be imitated by the motion of a small steel ball around a magnetic pole. The results were so good that I feel warranted in making them known, and believe that the experiment may be found useful in making more cheerful that portion of the course usually rather destitute of pyrotechnics.

The apparatus used was very simple, consisting of a circular glass plate about 40 cm. in diameter, with a small hole in the center through which projected the somewhat conical pole piece of a large electro-magnet (Fig. 1). The surface of the plate was smoked, and it was made level as nearly as possible, the axis of the magnet being of course vertical.

A small, highly polished ball of steel about 5 mm. in diameter (from a bicycle bearing), when projected across the plate, traced its path in the soot and left a permanent record of its motion.

Under these conditions gravity exerts no direct influence on 'the motion, and we have only the initial velocity and the central attractive force to deal with, together with the loss of velocity due to friction. There are several other circumstances which make the conditions unlike those existing in the case of two gravitating bodies in space, and taking everything into consideration, it is quite surprising what good results were obtained.

The ball was blown out of a short piece of glass tubing held in the plane of the plate with varying initial velocities, and curved orbits obtained which were at least good imitations of the ellipse parabola and hyperbola.

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Figure 2 is a photograph of a plate showing all three forms, the black spot in the center being the hole occupied by the magnet pole; the arrows indicate the direction of the motion.

Number 1 was produced with low initial velocity, and is a very fair representation of an ellipse, with the attractive force in one focus. The loss of velocity due to friction caused the ball to "fall into the Sun" after completing one revolution, a one year's existence of the system.

On another trial an ellipse (spiral, strictly speaking) was obtained that was almost re-entering, the miss being not more than a couple of millimeters, while in the one figured it was nearly a centimeter.

The right hand branch of No. 2 resembles a parabola, and was produced by a somewhat higher initial velocity. It will be noticed that the ball moved to its perihelion position in a path rather like a hyperbola, and on rounding the pole, its velocity having been diminished somewhat, moved off in a parabola. It would be more exact probably if we called this curve an ellipse of great eccentricity, since the conditions governing the formation of a parabolic orbit would be difficult even to approximate. Numbers 3 and 4 are hyperbolæ, produced by still higher initial velocities.

None of the orbits shown in the figure are as perfect as some that have been obtained by accident on other plates. It is quite difficult to make a plate showing all three forms with only four or five trials, as the velocity has to be nicely adjusted; conse

* Figure 2 has been reproduced by the engraver from an untouched photograph.-Ed. Physical Review.

quently the curves shown in the figure must not be taken as samples of the best that can be produced by a large number of trials.

The hyperbola is of course the easiest to produce, and the parabola the most difficult. Some device for regulating the initial velocity and aim would be conducive to more uniform results.

Polarization of the steel ball is apt to give trouble, and I have obtained some repulsion orbits where the ball turns back before reaching the center, which are very pretty, but not desirable. when one is trying to illustrate central attraction. Soft iron balls would be preferable to steel on this account, but they are not on the market so far as I know, and the others answer the purpose well enough.

ASTRONOMICAL PHENOMENA DURING 1900.

ECLIPSES,

In the year 1900 there will be three eclipses, two of the Sun and one of the Moon.

1. A Total Eclipse of the Sun, May 28, will be visible as a partial eclipse throughout North America and Europe and in the western part of Asia, the northern part of Africa and the extreme northern part of South America. This is the most important astronomical event which can be predicted for the year, and will be especially interesting to Americans, since the path of totality passes across easily accessible portions of the United States (See POPULAR ÅsTRONOMY, No. 69, Nov. 1899, for chart of path of totality across the Southern States.)

Doubtless most of the Observatories in this country will send expeditions to observe the eclipse and to obtain all possible data concerning the wonderful corona of the Sun, which can be seen only when the Sun's disc is wholly covered by the Moon. The duration of totality is short in this eclipse; only 2m 8.8 at maximum, and that when the shadow falls upon the middle of the Atlantic Ocean. At the most favorable points in the United States totality lasts only about 1m 30%, so that there is little time in which to make the very important and very delicate observations which are desired. Photographic and automatic processes will be employed wherever possible, thus reducing the observer's duties to a minimum and making a miscarriage of operations, due to the observer becoming confused, improbable. The great uncertainty in the case is the state of the sky. A cloud of two minutes duration over the Sun would render all preparations useless. A series of weather observations has been undertaken by the U. S. Weather Bureau, during the month from May 15 to June 15 in the last three years, at a large number of points along the path of totality, for the purpose of determining the probability of clear or cloudy weather at those localities. Professor Bigelow's discussion of these observations (POPULAR ASTRONOMY, No. 69,) seems to show that chances are about three to one in favor of clear weather at stations

near the Atlantic coast and about six to one in favor of clear weather in the interior of Georgia and Alabama. We may therefore have confident expectation of some good results from all the effort and money which will be expended upon this total eclipse.

The path of totality begins in the Pacific Ocean off the coast of Mexico, crosses northern Mexico and the Gulf of Mexico, passes almost centrally over the city o of New Orleans, touches Mobile, Alabama, Raleigh, North Carolina, and Norfolk, Vir. ginia. Across the Atlantic no prominent islands lie in the track of the shadow. It touches land again on the west coast of Portugal, crosses Spain and the Mediterranean Sea, passes over Algiers and several other points on the north coast of Africa and ends near the north end of the Red Sea.

ELEMENTS OF THE ECLIPSE.

Greenwich Mean Time of conjunction in right ascension, May 28, 2h 57m 02.7.

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2. A Partial Eclipse of the Moon, June 12, will be visible generally throughout North and South America, Europe and Africa. It will, however, be of almost no importance, since the obscuration will be so very slight, only .001 of the Moon's diameter being covered by the umbra of the shadow at the middle of the eclipse.

Elements of the ECLIPSE.

Greenwich mean time of conjunction in right ascension, June 12, 15h 31m

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Moon's declination - 22 12
Sun's equa. hor. parallax

57 .2
8 .7

Hourly motion

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Moon's equa. hor. parallax 57 29 .7

CIRCUMSTANCES OF THE ECLIPSE.

Sun's true semidiam. 15
Moon's true semidiam. 15

44 .8

39 .2

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Magnitude of eclipse 0.001 (Moon's diameter 1.0).

3. An Annular Eclipse of the Sun, Nov. 21, will be visible in South Africa and Australia. This will be regarded of little importance, because the

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