October 28, 1898.] 



SCIENCE. 



595 



To find the day of the week corresponding 

 to a given date, add to the day of the month 

 the index number of the month and the index 

 number of the year, then subtract the largest 

 multiple of seven that is less than the sum. 

 The remainder will be the number of the day 

 of the week. 



The index numbers of the months are as fol- 

 lows : 



January, 3 (in leap years, 2). 



February, 6 (in leap years, 5). 



March, 6. 



April, 2. 



May, 4. 



June, 0. 



July, 2. 



August, 5. 



September, 1. 



October, 3. 



November, 6. 



December, 1. 

 To find the index number of the year, for any 

 year from 1800 to 1899 inclusive, increase the 

 excess of the year over 1800 by one-fourth of 

 itself (discarding fractions) and subtract the 

 largest multiple of seven contained in the sum. 

 For dates in other centuries a multiple of 28 is 

 added or subtracted so as to bring the year 

 within the above limits, and, after finding the 

 index number for the resulting year, one is 

 likewise added or subtracted for each centes- 

 imal year not divisible by 400 that is passed 

 over (or of which the beginning is passed over). 

 If many years are to be passed over it is often 

 convenient to use multiples of 112. 



A few illustrations of the application of this 

 rule are here given. To find the day of the 

 week corresponding to August 20, 1898, we add 

 the index numbers of the year, 3, and of the 

 month, 5, to 20, and subtract 3 times 7. The 

 remainder, 7, indicates that this is the seventh 

 day of the week, or Saturday. If the index 

 numbers of all the months and of a given 

 year are known, it is ordinarily quicker to find 

 the day of the week mentally than to consult a 

 calendar of the given year. For July 4, 1776, 

 we add 28 to 1776 and find the index number 

 of 1804 to be 5 ; adding one for the year 

 1800 passed over gives 6, the index number of 

 1776 ; to which we add 2 + 4 ; subtracting 7 

 we have the remainder 5, indicating Thursday. 



For December 25, 2046, we deduct 224 from the 

 year and find the index number of 1822 to be 6. 

 Deducting one for the year 1900 passed over 

 (2000 is divisible by 400 and so is a leap year 

 and requires no deduction), we find 5 as the in- 

 dex number of the year 2046. Adding 1 + 25 

 we find that Christmas of that year will come 

 on Tuesday. 



As this subject is so simple it would be un- 

 necessary to give a deduction of the rule. But 

 it may be noted that if the index numbers of 

 the months are not remembered, that of one 

 month may be found by adding the index num- 

 ber of the year to the day of the month (for 

 any date for which the day of the week is 

 known) and subtracting the sum from the day 

 of the week increased by a multiple of seven.. 

 The index numbers of the remaining months 

 may then be obtained in succession, as the in- 

 dex number of any month, except Januarj', is 

 equal to that of the preceding month increased 

 by the number of days therein and diminished 

 by a multiple of 7. 



Dates given in old, or Julian, style should 

 first be changed to new, or Gregorian, style. 

 The Dominical letter of any year may be found 

 by deducting the index number of the year 

 from 5 or 12. Thus for 1898 we have 5 — 3 = 2, 

 indicating the second letter of the alphabet, or 

 B, as the Dominical letter. 



If in time it should be more convenient to- 

 calculate the index numbers of the years from 

 the excess of the years over 1900 instead of 

 1800, that modification of the rule may be 

 made if the index numbers of the months are 

 increased by 5 or diminished by 2. 



Edward L. Stabler. 



Brooklyn, N. Y. 



an apple canker.* 



Last spring I began investigating the cause 

 of the so-called apple canker. This disease at- 

 tacks the bark of the larger limbs, where all 

 stages of development may be seen from small 

 sunken areas to the large cankers of many 

 inches extent. In aggravated cases a portion 

 of the wood is laid bare. The bark becomes 

 swollen and rough in all directions from the 



* M. E. Waite, Rural New Yorker, February 5, 1898, 

 p. 82. 



