TABLE FOR FORMING THE PRODUCTS OF GIVEN NUMBERS BY THE 

 SINE OR COSINE OF A GIVEN ANGLE. 



THIS table is formed for the especial purpose of facilitating the formation of the 

 products (r.x.3) sin !ty, (<:<:'l) cos 3y, etc., (().*. 1) sin//, (p.c.l) cos g, for entire degrees 

 < f ij. It is so arranged that the required products can be taken out at sight. 

 Supposing the number to be given in seconds and decimal fractions of a second, 

 we first seek tin- given angle at the top or bottom of the pnge, and then enter one 

 of the first nine lines of the table with the fraction part of the second, interpolating 

 lor the hundrcdths. We then add the result mentally to the number corresponding 

 to the entire seconds. The algebraic signs at the sides of the angles are those of 

 the sines or cosines corresponding to the angle and to the column above or below. 

 If the number does not exceed 3" we can enter the table as if it were ten times 

 greater, and remove the decimal point one place to the left in the result. 



For example, to find the value of 



2l".67 sin 280 -f 2*.25 cos 280 



we find the angle 280 at the bottom of a pair of columns, the right hand one being 

 the sine column. Entering this column with 0.67 as the argument, we find O.tiG. 

 Kntering with 2.1, we find 20.68, to which adding 0.66, we have 21".34 as the 

 sine product. Entering the other column with 22.5, and moving the decimal point, 

 we find 0*.39 for the cosine product. Noticing the algebraic signs on each side 

 of 280, we find the result to be 21".34 + 0".39 = 20".95. 



( 279 ) 



