A year consists of 12 calendar months, the number of days in each of which are usually remembered by means of the following lines :— Thirty days hath September, When the sun is exactly south of any place on the earth's surface, it is 12 o'clock at that place; and the interval which elapses before the sun next assumes the same position is called a day. The period of time required by the earth to revolve round the sun is called a solar year, and is 365 days 5 hours 48 minutes 50 seconds, very nearly. Taking the civil year as 365 days, the time lost in the calendar will be 5 hrs. 48 min. 50 sec. in 1 year, or 23 hrs. 15 min. 20 sec. in 4 years. Hence, if every fourth year be reckoned as leap year, the time gained in the calendar will be 44 min. 40 sec. in 4 years, or 74 hrs. 26 min. 40 sec. in 400 years. If, however, only one of the centenary years in every 400 years be reckoned a leap year, the time gained in the calendar will be reduced to 2 hrs. 26 min. 40 sec. in 400 years, or about 1 day in 4,000 years. The following rule, therefore, for leap year renders the calendar sufficiently accurate for every practical purpose : Rule. Every year which is exactly divisible by 4 is a leap year, except the centenary years, which are only reckoned leap years when they are exactly divisible by 400. REDUCTION is the process of changing a quantity from one denomination to another without altering its value. Thus, if £1 be changed for 20 shillings, the value remains the same, only it is expressed in a different denomination; so if 12 pence be changed for I shilling, the denomination only will be altered, but not the value. To illustrate the principle of Reduction, we will suppose the diagrams (1) and (2) to represent sectional views of the Issue, or money-changing department of a bank, in which the rooms are arranged according to the several denominations of the coins, as shown in the diagrams. We will suppose, further, that each room is called by the name of the coins which are exchanged in it for those of a higher or lower denomination, and that there is no direct communication between any two rooms, unless a certain number of the lower denomination exactly make one of the higher. If a person wishes to change £4 175. 9d. into farthings, a little consideration will show him that the readiest way to do it is by beginning with the pounds (see Diag. 1), and change them into 80 shillings in the pound room, then descend to the shilling room, and there change the 80 shillings, together with the 17 shillings (97 shillings altogether) into pence; he will receive (12 times 97, or) 1,164 pence, and this with the 9 pence will make 1,173 pence; descending to the pence room, he will change this for (4 times 1,173, or) 4,692 farthings. This is called Reduction descending, and the operation may be exhibited thus :— 20 Multiply the pounds by 20, and £4 175. 9d. add in the shillings thus:-o and 7 are 7; twice 4 is 8, and I are 9; next multiply by 12, and add in the 9d.; 12 times 7 is 84, and 9 are 93; 12 times 9 is 108, and 9 are 117; lastly, multiplying by 4 we get 4,692 farthings. 975. 12 1173d. 4 4692 q. Again, if a person wishes to change 4,379 farthings into pounds, F |