684 KANSAS CITY REVIEW OF SCIENCE. 



tedious processes of calculation. But it is easy to learn and quick to use ; and 

 what tyro in this line would not be truly gratified, after half a minute's calcula- 

 tion, with ascertaining by his own work the nearest hour or so when an eclipse, 

 18.36 and so on years in the future, will take place. He may find also when 

 they have occurred in the past. An almanac for any year will give a starting 

 point in the matter, for there is no year without two eclipses. There are gener- 

 ally four; occasionally six, and never more than seven in one year. 



If you have taken the pains to gather up the almanacs for eighteen consecu- 

 tive years, or in some other way have obtained a catalogue of all the eclipses 

 that occurred in this period, then you have the times at which seventy of these 

 interesting phenomena of the heavens took place — forty-one of the sun and twen- 

 ty-nine of the moon. This would afford quite a basis for operation. 



I presume that most, if not all, readers of the Review understand what eclipses 

 are, and what causes them ; that an eclipse of the sun must occur at new moon 

 and an eclipse of rhoon at full moon. In passing we will glance at the nodes 

 and lunations. You know that the moon's orbit, or path, is slightly inclined to 

 the earth's orbit, which is the sun's apparent path. This angle of inclination is 

 5° 8'. Now the points where these orbits intersect, or cross each other, are 

 called nodes. And that one where the moon crosses the sun's path from north 

 to south is the descending node, and the point of moon's crossing from south to 

 north of the ecliptic is the ascending node. They are on opposite sides of the 

 earth, and a line joining them and passing through the earth is called the line of 

 nodes. Now these nodes are not stationary, but move backward, or to the west, 

 on the ecliptic (earth's orbit) at the rate of 19^° in a year. So that the sun, after 

 passing one node, comes round and meets the same node again about twenty days 

 less than one year, or in 346^ days ; and we will call this a node-year. Then 

 nineteen node years will contain 6,585.78 days. 



A lunation is the«time from one new moon to another, the mean length of 

 which is twenty-nine days, twelve hours, forty-four minutes, three seconds. Now 

 223 of these lunations are equal to 6585.32 days, a period of time very nearly 

 equal to the nineteen node-years. And here we get the Saros ; which in years, 

 days, etc., is eighteen years, about eleven days, seven hours and forty- three min- 

 utes. I say about eleven days, and there is rather a critical point here which 

 must be observed. When four leap-years come in the Saros, we use eleven daysj 

 but there are frequently five leap-years in the Saros, when but ten days can be 

 used with the eighteen years. And at the close and beginning of centuries which 

 do not contain 400 without a remainder, sometimes only three leap-years occur 

 in the Chaldean period, and then we must count in twelve days. But the seven 

 hours and forty-three minutes must be used in all cases. 



It may be noted that the difference between nineteen node-years and 223 

 lunations is 0.45 of a day, or nearly eleven hours; and in this time the sun moves 

 28' of arc to or from the node, as the case may be. Note, also, that if the sun 

 and moon are in the line of nodes at the middle of the eclipse, the eclipse will be 

 central on the earth's equator. Then at the next eclipse, when 18.03 years have 



