450 Mr. J. J. Sylvester on Projectiles. 



It is perhaps unnecessary to point out the advantages of this 

 mode of observation. These are the complete elimination of the 

 effects of the star's diurnal motion, and of x-efraction, advantages 

 which it shares in common with Fraunhofer's method. It pos- 

 sesses, moreover, the additional recommendations of requiring 

 only one observer, and of dispensing with the necessity of illu- 

 minating either the field or the wires of the telescope. Those 

 who have had any experience of the difficulty attending observa- 

 tions of faint spectra will appreciate the value of this last pro- 

 perty. 



4 Duke Street, Edinburgh, 

 May 17, 1856. 



LVIII. A Trifle on Projectiles. 5y J. J. Sylvester, Professor 

 of Mathematics at the Royal Military Academy*. 



T N teaching the subject of projectiles in vacuo, the following 

 solution has presented itself to me of a question not wholly 

 without practical interest, viz. of determining the angle of projec- 

 tion to give the best range in the most general case, viz. when a 

 gun is fired upon a slope at a given vertical height above the slope. 

 The solution is not wholly either without theoretical interest in 

 point of method, as leading to a result of some little complexity 

 in maxima and minima by very simple calculations, and without 

 the aid of the differential calculus. Therefore I venture to sub- 

 mit it to the readers of the Philosophical Magazine. In the 

 next Number of the Magazine I hope to have leisure to lay 

 before them a subject of much greater interest, also belonging 

 to the theory of projectiles, showing how, by the oblique action 

 of gravity combined with the earth's rotation, a pendulum suit- 

 ably adjusted may be caused to advance in a westerly direction, 

 and so the earth be made the means of impelling a light carriage 

 without any \asible motive force, or any influence of magnetism. 



To this pendulum I give, for reasons which will be apparent 

 when the matter is more clearly set forth, and in contradistinc- 

 tion to the ordinary fixed or circular pendulum on the one hand, 

 and to Foucault's free or spherical pendulum on the other, the 

 name of the Cylindrical or Travelling Pendulum. But to resume 

 the business of this present communication : let us begin with 

 determining the angle of projection to give the maximum range 

 when a gun is fired from a point in a plane sloping at an angle 

 i from the horizon. 



This question is most simply solved (the result itself is of 

 course familiar to all who will read this paper) by resolving the 



* Communicated by the Author. 



