378 Mr. J. Prescott on the 



and 480 feet per second for Mark VII. In this case we 

 must use l Y instead of /. Then 



( ,_< )+% -^{_^| + (2+/) -*_ } 



" V 1 fr +l 7fc + ' ••••)• 



Now, r is such a large number that the first term in the 

 brackets is very much smaller than the third. Consequently, 

 the approximate results are 



—=( 2+ '>lf$$ ("7> 



y-^W <"« 



With the values of/ and c used in the last article, namely, 

 /=?4*2, c = 0'38 inch, the values of these angles for the 

 Mark VI. bullet, for which Z 1 = 6000, are 



;:;:«,} <-> 



The range corresponding to this drop of velocity is, by 

 equation (1<>), 



X = 2800 yards, approximately, 



and the whole angle, ex., through which the line of flight 

 turns in the 2800 yards range is 34°, obtained by adding 

 together the angles of elevation and arrival given in the 

 4 Musketry Regulations ' and allowing for the jump. The 

 angular deflexions of the axis from the line of flight are 

 therefore small compared with a. The lateral deflexion, 

 (y~~v)i ls t° the left for left-handed spin. It is remarkable 

 that this lateral deflexion, which is a consequence of the 

 lag of the line of flight behind the axis, is greater than the 

 lag in the plane of pursuit. 



85. When u = ui the values of (x — e) and {y — rj) given by 

 equation (116) are discontinuous because I must he used 

 when w> if, and Zj when u<u 1 . This does not mean that 

 the complete values of (x — e) and (y—rj) are discontinuous. 

 They must, of necessity, be continuous, and we can make 

 our values continuous by adding the complementary func- 

 tion in equation (73), with a proper choice of constants, to 

 the value of <f> given by equation (93). Our theory does, 



