358 Mr. J. Prescott on the 



the shape and composition of the bullet to calculate the 

 precise moments of inertia B and A. To get approximate 

 values we will assume something reasonably near the truth, 

 namely, that the bullet is a homogeneous cylinder 1*2 inches 

 long with the actual diameter of the bullet. Also, the 

 length c, which is the distance from the centre of mass 

 of the bullet to the point where the line of resistance meets 

 the axis, cannot possibly be greater than 0*7 of an inch, and 

 is very likely less than 0*4 of an inch. We will assume the 

 value 0'4 for this at present. Of course it is a very un- 

 certain quantity, and it is quite possible that its value is not 

 more than 0*15 inch. However, taking the value 0*4, which 

 is very likely too great, 



Bco Id* 



CO CO 



2A 2(^ 2 + tV 2 ) 4 pV + l 



m 2 = 990200, 



Wcl cl 



= 995-1, 



K59) 



9 A -^tf + Js* 



= 80170. 



All that we know about /is that it is sure to be a small 

 number greater than unity. It might be 2 or 3, it might 

 conceivably be 5 or 6, but it could not be much greater, 

 nor is it likely to be less than 2. Thus rf is very uncertain 

 on account of both c and f, and reasonable guesses at its 

 value might range between 60,000 and 600,000. 



52. When u < 1063 feet per second we must use l± 

 instead of I, so that, writing r x for the new r, 



4840 

 n = 80170x|^g =184770. 



Also 



T=- or \ 



u u 



which is as small as f when u = 2800 feet per second, and 

 as large as 12 when w = 403. 



53. Without substituting the preceding numerical values 

 in the expression for cr, it is clear that this is a very large 

 number. It is equally clear that the term Hf 2 — 1), which is 

 part of the coefficient of T" 2 in the expression for a, is 

 insignificant compared with the part rf We may, there- 

 fore, drop altogether the former part. 



54. Let us now return to equation (57). Since we re- 

 placed one variable % by two variables p and fi, we are at 



