ANN 



8. The following experiments by Peron, with Regnier'3 dynamometer. 

 shew that the strength of men depends considerably on the climate. 

 English ............... 71,4 Van Diemen's Land 51,8 



French ........... .... 69,2 New Holland ......... 50,6 



Timor ............... 58,7 (Ency. Brit Supplt) 



ANNUAL Equation. See Moon. 

 ANNUITIES. 



1. Annuities at Simple Interest. 



1. Let A be the annuity, r the interest of 1. for one year, M the 

 amount of the annuity for n years, then 



M n A + n. ^ . r A. 



2. Let P be the present value of an annuity to continue for n years ; 

 the rest as before, then 



n A + n. n "* 1 . r A. 



~ 



\ ^f. n r 



In these Equations any one of the quantities may be found, the rest be- 

 ing given. 



Annuities at Compound Interest. 

 3. Let R rz 1. and its interest for one year, the rest as before, then 



X A 



which gives the value of a freehold estate, A being the annual rent. 



4. The present value of an annuity to commence at the expiration of p 

 years, and to continue g years, is the difference between its present value 

 for p -f- g years, and its present value for p years, 



= /_! i ^ x _A_. 



If the annuity, instead of being payable annually, be made payable 

 half-yearly, quarterly, or at any other given interval, the above formu- 

 lae are still applicable, by calling R 1. and it* interest for -the tfivn hi- 

 t t-rval, and n the number of those interval*. 



10 



