180 
MINUTES OF PROCEEDINGS OF 
Ex.—Suppose tlie angle of elevation 5°, and the position of the point 
to be required where the inclination is 4°. Suppose “y” to be *7. 
Refer to p. 71, Table VI., where y = *7. Instead of 4 X. 7 5 being given, 
we have the values of X from 0 up to 4° or 5°, &c. 
_ V (4X/<) = — U J- (-07366 - -09348) = -01982 . u -i-=x. 
9 9 9 
Similarly for “y 33 and “ t” 
2 bu 3 
it Q can be determined from equation (2), and thence y — —°- is also 
9 
known. 
Thus the reader has the materials for calculating trajectories, and it 
only remains to point out the system of work to be adopted—which is, 
it must be confessed, slightly tedious. A few preliminary remarks will 
be useful. 
• 12. Remarks on “ u q ” “2b, 33 “ K” &c. 
If the reader will carefully study Art. 71, which gives the actual 
calculation of a trajectory, he will find several values for u 0} namely— 
f.s. 
p. 60. 
?i 0 = 1025’5 
p. 61. 
« 0 = 1024-1 
1025-3 
p. 62. 
**0= 1027-1 
u 0 = 1031*9 (the calculated velocity at vertex), 
w 0 = 1026-4 
u 0 - 1021-8 
all the values being obtained in the same example. 
The explanation is this :—- 
See §11. In the consideration of each section of the trajectory, “u 0 ” enters 
p. 177. into all the calculations; but this “ tc 0 33 is not the real velocity at the 
vertex, but what it would be if the coefficient of the resistance of the 
air remained constant up to the vertex, at the value adopted for the 
section. 
Eq n (2). In the equation — = — (Sp +p s ), the value obtained for u 0 
u u o 9 w 
§ 9. evidently depends on the value given to 2 b, or to K — (1000) 3 2 b ^ the 
tabulated form. 
Equation (2) may be written 
/loooy __ /loooy 
\ u ) "" \ u 0 ) 
Kd* 
9 w 
(3p +/); 
