DIVING 



1815 



DIVISIBILITY OF NUMBERS 



depths, to visit perhaps with the fabled mer- 

 maids, must have been thought of as a de- 

 lightful adventure by boys and girls and their 

 romantic elders for many ages. When men 

 began to sail the seas and ships were often 

 wrecked, there was added the romance of 

 sunken treasure, which even to this day is the 

 chief inspiration of deep-sea diving. 



The Diving Bell. In ancient times there 

 were professional divers for recovering wreck- 

 age who worked, as do the modern pearl divers 

 of the Orient, without mechanical appliances. 

 But of course they were unable to stay under 

 water more than two or three minutes, and 

 both Greek and Roman historians tell of curi- 

 ous inventions made to enable them to keep at 

 work longer. One of these, the diving bell, is 

 supposed to have been revived by Roger Bacon 

 in 1250. If you turn a dish upside down and 

 push it straight downward into the water, the 

 air inside will be carried down with it, as you 

 may see by the bubbles that come up if you 

 tip the dish slightly; the diving bell was just 

 a huge inverted dish with tubes through which 

 fresh air could be supplied. Men could work 

 inside it for several hours. 



How a Modern Diver Works. Before going 

 below the surface, a diver of to-day dons a 

 waterproof suit. At the neck of the suit is a 

 metal ring into which a helmet is screwed. The 

 helmet is provided with windows, to enable the 

 diver to see, and with two rubber tubes; 

 through ope of the latter a supply of air is 

 pumped from above, and the other serves to 

 carry off the foul air. The helmet is made of 

 copper. Formerly a diver had to communi- 

 cate with those above the surface by jerking 

 a rope, but modern diving outfits include tele- 

 phones. A loud-sounding receiver is placed in 

 the crown of the helmet and a transmitter is 

 fixed between the windows, or eyes, directly 

 opposite the diver's mouth. This apparatus 

 has been so perfected that it is now possible 

 for the attendant above to speak to several 

 divers at the same time and for the divers 

 themselves to be put in direct communication 

 with each other. 



To enable a diver to sink to the bottom and 

 to preserve his balance while there, his boots 

 have leaden soles and he wears two sheets of 

 metal weighing about forty pounds each, one 

 over his chest, the other on his back. Each 

 boot weighs sixteen pounds. He also carries 

 necessary tools in a strong leather belt, and is 

 provided with electric lights, either powerful 

 arcs of 3,000 candle power connected with dyna- 



mos above, or electric torches supplied with 

 their own batteries. 



Until recently it has not been possible for 

 divers to work at a great depth, but in 1907 the 

 British government perfected apparatus which 

 was used 200 feet below the surface, and in 

 1915, when a torpedo boat sank at Honolulu, 

 divers of the United States navy reached a 

 depth of 288 feet. C.H.H. 



DIVISIBILITY OF NUMBERS. When one 

 number can be divided by another, giving no 

 remainder, we say the first number is "divis- 

 ible" by the second. We sometimes say "ex- 

 actly divisible," but this is not necessary since 

 "divisible" is used to signify "exactly divisible." 

 The divisor in such cases is called a "divisor" of 

 the number, meaning an "exact divisor"; for 

 example, in 160-^8=20, 160 is "divisible" by 

 8, and 8 is a "divisor" of 160. 



Tests for Divisibility. Divisibility by 2. A 

 number is divisible by 2 if it ends in 0, 2, 4, 6 

 or 8; as 20, 18. 



Divisibility by 3. A number is divisible by 

 3 if the sum of its digits is divisible by three: 

 for example, 17841. The sum of its digits is 1+ 

 7+8+4+1, or 21, which is divisible by 3. Here 

 we use the word digit to mean the number for 

 which the digit stands. 



Divisibility by 4- A number is divisible by 4 

 if it ends in two zeros, or if the number repre- 

 sented by the last two digits is divisible by 4; 

 for example, 700, 132, 86388. 



Divisibility by 5. A number is divisible by 

 5 if it ends in or 5; for example, 80, 65, 700. 



Divisibility by 6. An even number the sum 

 of whose digits is divisible by three is divisible 

 by 6; for example, 174, 42726. 174 is an even 

 number; the sum of its digits (1+7+4=12) is 

 divisible by 3, and 174 is divisible by 6. 174-r- 

 6=29. See that the same is true of 42726. 



Divisibility by 8. A number is divisible by 



8 if it ends in three zeros, or if the number 

 represented by its last three digits is divisible 

 by 8; for example, 16000, 19648, 2048. 



Divisibility by 9. A number is divisible by 



9 if the sum of its digits is divisible by 9; for 

 example, 27648 (2+7+6+4+8=27); 604071 

 (6+4+7+1=18). 27 is divisible by 9, and 

 27648 is divisible by 9. 18 is divisible by 9, 

 and 604071 is divisible by 9. 



Divisibility by 11. Find the sum of the al- 

 ternate digits beginning with the first digit of 

 the number; find the sum of the alternate 

 digits beginning with the second digit of the 

 number. Find the difference between these 

 sums. If this difference is zero or a number 



