210 Instructions for the Scientific Expedition 



Again wait 20^, in which interval there is time for the entry, 

 &c. At 17"* 50^ remove the screen, or expose the instrument in 

 the sun ; at 5B^ begin to count beats ; and at the complete minute, 

 18™ OS read ofF(14°*8), and so on for several alternations, taking 

 care to begiti and end each series with a sun observation. If the in- 

 strument be held in the hand, care should be taken not to change 

 the inclination of its axis to the horizon between the readings, or the 

 compressibility of the liquid by its own weight will produce a very 

 appreciable amount of error. 



In the annexed form column 1. contains the times, initial and ter- 

 minal of each sun and shade observation. Column 2. expresses by 

 an appropriate mark, © and x , the exposure, whether in sun or 

 shade. Column 3. contains the readings, initial and terminal (A 

 and B). Column 4. gives the values of B — A, with its algebraical 

 sign expressing the rise and fall per minute. And here it may be 

 observed, that if by forgetfulness the exact minute be passed, the 

 reading off may be made at the next 10*^, and in that case the entry 

 in column 4; must be not the whole amount of B — A, but only |^ths 

 of that amount, so as to reduce it to an interval of 60^ precise. Co- 

 lumn 5. contains the radiations as derived from successive triplets, 

 OxO, xOx,0xO> &c. by the formula presently to be 

 stated ; and in column 6. are entered remarks, such as the state of 

 the sky, wind, &c. ; as also (when taken) the sun's altitude, baro- 

 meter, thermometer, and other readings, &c. 



The formula of reduction is as follows. Let O , x , ', X ', 

 O", x"} &c. represent the numbers in column 4, with their signs 

 in order, as they stand, or the values of B — A. Then will the 

 numbers in column 5 be respectively, 



+ 0' .. 



+ 



x+^L' + o' 



-h - X 



x'+x" + 0", 



2 

 and so on, the algebraic signs being carefully attended to. Thus 



34.75 = + 31 '3 + 33-4 ^ 2.4 

 2 



35-40 = + ?:i±J^ + 33-4, &c. 



2 



The mean of a series not exceeding three or four triplets may be 

 had by the formula 



+ 0^ + 0'^ + &c . _ X + x' + &c. ^ 

 n n — 1 



