NUM 



NUM 



is simply selective or distinctive, is a 

 pronoun, as in * one or another ' " {Pen. 

 Cycl.). If it be asked, in what century 

 the birth of a person occurs, who is born 

 in the year 1800, the answer is, — if born 

 in the year eighteen hundred (cardinal), 

 the birth occurs in the nineteenth cen- 

 tury ; if in the eighteen hundredth year 

 (ordinal), in the eighteenth. 



4. Numbers, Natural. The general 

 name for the whole scale of numbers, 

 1, 2, 3. &c. It is subdivided into the 

 scale of odd numbers, 1, 3, 5, &c., and 

 even numbers, 2, 4, 6, &c. These, again, 

 are subdivided into oddly odd numbers, 

 3, 7, 11, &c. ; evenly odd numbers, 1, 5, 

 9, &c. ; oddly even numbers, 2, 6, 10, &c. ; 

 and evenly even numbers, 4, 8, 12, &c. 



5. Number, Square, Cube, &e. When 

 any number is multiplied by itself any 

 number of times, the result is called a 

 power of that number. The second and 

 third powers are usually called the square 

 and the cube, which are incorrect names, 

 derived from certain connexions of these 

 powers with the square and the cube in 

 geometr}'. The division of numbers into 

 square numbers, 1, 4, 9, 16, &c. ; cube 

 numbers, 1, 8. 27, 64, &c. ; fourth powers, 

 1, 16, 81, 256, &c., and so on, may be 

 carried to any extent. 



6. Number, Prime and Composite. A 

 prime number is one which is not divi- 

 sible by any number except unity and 

 itself, as 1, 2, 3, 5, 7, 11, 13, &c. A com- 

 posite number is any number which is 

 not prime. 



7. Number, Abundant, Perfect, De- 

 fective. An abundant number is one, of 

 which the sum of all its divisors exceeds 

 itself: thus, 12 is an abundant number, 

 for 1 + 2-f 3-f4 + 6 = 16. A perfect num- 

 ber is one, oT which the sum of all its 

 divisors is equal to itself: thus, 6 is a 

 perfect number, for l-f-2-i-3 = 6. A de- 

 fective number is one, of which the sum 

 of its divisors is less than itself: thus, 10 

 is a defective number, for 14-2+5 = 8. 



8. Numbers, Figurate. A figurate 

 number is any one out of any of the fol- 

 lowing series, the first excepted, which 

 is only introduced as a basis : — 



I 2 3 4 5 6 &c. 



Each number is the sum of the numbers 

 in the preceding row : thus 10 is the sum 

 237 



of 1, 8, 6 ; 70 is the sum of 1, 4, 10, 20, 

 35; and 70 is the fifth number of the 

 third order of figurate numbers. 



9. Numbers, polygonal and pyramidal. 

 The principle of these numbers is sufll- 

 ciently explained under the article Figu- 

 rate Numbers (p. 136). The following 

 are some of the polygonal numbers : — 

 Triangular 13 6 10 15 21, &c. 

 Quadrangular 14 9 16 25 36, &c. 

 Pentagonal 1 5 12 22 35 51, &e. 

 Hexagonal 1 6 15 28 45 66, &c. 



Pyramidal numbers are formed by 

 summing the polygonal numbers; thus, 

 to find pentagonally pyramidal numbers, 

 take the pentagonal numbers : 



1 5 12 22 35 51, &c. 



1 6 18 40 75 125, &c. 



10. Numbers, Amicable. These are 

 numbers, each of which is equal to the 

 sum of all the divisors of the other. Such 

 are 



284 and 220 



17,296 and 18,416 



9,363,583 and 9,437,056. 



NUMBER of DIRECTION. A num- 

 ber not exceeding thirty-five, which 

 number is the limit of Easter day, this 

 day always falling between the 21st of 

 March and the 25th of April. 



NUMBERS for STARS. A mode of 

 denoting the stars adopted by Flamsteed, 

 who numbered them, not in order of 

 brilliancy, but in that of coming on the 

 meridian. Thus, 1 Orionis, 1 of Orion, 

 means the first which comes on the me- 

 ridian, of all the stars in Orion which 

 Flamsteed observed and recorded ; 7 

 Leonis, 7 of Leo, is the star of this con- 

 stellation which comes seventh on the 

 meridian. So long as a star has either 

 Bayer's letter (See Letters for Stars) or 

 Flamsteed's number, both are used indif- 

 ferently and perfectly understood ; nor is 

 it expected that there will be any con- 

 nexion between the letter, which refers, 

 or was supposed to refer, to the bright- 

 ness of the star, and the number, which 

 is derived from its position. Thus 1 Vir- 

 ginis happens to have w for its letter; it 

 is only of the sixth magnitude, though it 

 comes early to the meridian ; but a Vir- 

 ginis, a splendid star, is Q7 Virginis in 

 Flamsteed. 



NUMERATION (wMwert/*, anumber>. 

 A method of calculating numbers by 

 means of ten signs, viz a cipher and 

 nine digits. Higher numbers are sig- 

 nified by placing these signs by the side 

 of one another, and agreeing that the 

 first figure on the right hand shall retain 



