P E R 



Lat. Seconds gained. 



For the ellipticity of the earth as deduced from these experiments 



see Earth, figure -of. 



The following Table shews tine seconds gained in one day by a pendulum 

 vibrating seconds at the Equator., in different latitudes, when it remains 

 of the same length. ( Vince.) 



Lat. Seconds gained. 

 50 ......... 134",0 



153,2 

 171,2 

 187,5 

 201,6 

 213,0 

 221,4- 

 226,5 



40 

 15 



20 

 25 , 

 30 < 

 35 

 40 , 

 45 , 



. 6,9 



, 15,3 



. 26,7 



, 40,8 



, 57,1 



, 75,1 



, 94,3 



, 114,1 



55 

 -() 

 65 

 70 

 75 

 80 

 35 

 90 



228,3 



PERCUSSION, Centre of. See Centre. 

 PERMUTATIONS and Combinations. 



Permutations. 



1. The number of permutations that can be formed out of n quantities, 

 Taken 2 and 2 together ... ....... = n. (n- 1.) 



Taken 3 and 3 together ......... = n. (w-.l.) (ra-2.) 



&c. &c. 



Taken r and r together ......... = n. (n- 1.) (n - 2) ... (n - r + 1.) 



Thus the number of changes that can be made with 3 bells out of 8 = 

 8.7. 6. = 336. 



If n r Le. if the permutations respect all the quantities at once, then. 

 (since n-r 0} the number will be n. (n - 1.) (n - 2) ...... 3. 2. 1. Thus 



the number of permutations which can be formed ont of the letters com- 

 posing the word virtue, are 6. 5. 4. 3. 2. 1 720. 



2. The number of permutations that can be made out of w things where 

 there are p of one kind, r of another, q of another, &c, 



n. (n - 1.) (n - 2.) (n - 3) ......... 2. 1 



~~ F. 2. 3...p X 172.3 ...... r X 1. 2. 3 ... q ' 



Thus the number of permutations that can be made of the letters ill the 

 s.vord Bacchanalia (since a occurs four times, c twice) 



11.10.9. 8. 7.6.4.3.2.1 



1. 2. 3. 4 X 1. 2 



203 



