Intelligence and Miscellaneous Articles. 



479 



one spot to another. But these variations being now materially re- 

 duced in the firing of projectiles by rifled cannon, the influence of 

 the rotation of the earth should be taken into account. This is what 

 I shall show by comparing the deviation due to this motion with the 

 total deviation given by experiment. 



As the calculation of the deviation due to the rotation of the 

 earth at any latitude by Poisson's method is very tedious and there- 

 fore unpractical, I have used another, which is very expeditious and 

 is virtually as exact as the preceding, as a comparison of the results 

 obtained by each will show. 



This method consists simply : — 



(1) In calculating the azimuthal angle 6, described by the plane 

 of firing about the vertical passing through the mouth of the piece, 

 during the passage of the projectile. 



This is performed by M. Foucault's formula, 



0=£ io sin A, (1) 



in which w is the velocity of rotation of the earth about its axis of 

 figure, X the latitude of the place of experiment, both known quan- 

 tities. 



(2) In multiplying the range given by experiment by sin Q. 



So that the deviation A due to the rotation of the earth is given 

 by the formula 



A=E sin 0=E sin (tw sin X)* (a) 



The formulae of Poisson and this formula give the following results 

 for the firing of mortars of 27 centims. at 1200 metres, and of 

 32 centims. at 4000 metres, in our latitude : — 



Mortars. 



of 0»-27. of 0^-32. 

 Deviation according to Poisson . . l m, 20 7 m, 00 

 formula (a) . l m -27 6 m -98 

 The agreement of these results confirms the accuracy of the 

 formula (a). 



Applying this latter to the firing of projectiles from rifled cannon, 

 we obtain, for the 



FRENCH CANNON. 



0, angle of firing 



E, range 



t, time of flight 



D, lateral deflection t to the right 

 A, deviation due to the rotation"! 

 of the earth j 



Ratio ^ . . . 



Projectiles of 



4kil. 2kil. 12kil* 50kil. 80 Ml 



17° 



3200 m 



17* 

 198 m 



2 m -90 



1 

 395 



14° 



1400 m 

 12' 

 46 m 



l m -67 

 1_ 

 70 



45° 



2800 m 



30 3 



310 m 



4m-50 



1 



72 



45° 



3496 m 



31 s 

 494m 



5 m -80 

 _1_ 



85 



50° 

 3700 m 



38 s 

 870 m 



7 m -10 

 J_ 

 79 



* For latitude 49°, which is virtually that of Paris, we get 0=10", 98 t. 

 t The term deflection is applied to the lateral departure of the point at 



