202 Suggestiotisfor rendering a Meridian marie visible at NighU 

 and the equation (1.) becomes after reduction 



9(S)-'p(|-^)=o, 



which is rendered identical by putting (p(d) equal to any arbi- 

 trary function of sin 2d, as F(sin 2fl). 



Hence the most general solution of equation (1.) is 



(/(6)}2=:cos2fi+(cos9-sina)F(sin29). . . (2.) 



In the application of this formula to the Parallelogram of 

 Forces, we must make use of some condition that the function 

 F may be determined ; as mechanical experience shows it 

 cannot remain arbitrary. Such a condition is the following : 

 that if fi be increased by tt, the resultant will obviously be the 

 same as before in magnitude, but opposite in sign : this will 

 therefore be the Ciise with/(fl). 



Put, therefore, 7r + 6 for 9 in (2.), and equate the two values 

 of the square of the function (as they must be the same), and 

 reduce, and we have 



cos2d+(cos5-sind)F(sin2d) = cos2d-(co5 9-sinfl)F(sin29); 



.-. F(sin25)=0 



for all values of fl. 



Hence in the case of the Parallelogram of Forces, 



/(6) = cos5 or — cos 9 J 



the latter is excluded, because when 9 = 0, the resultant is the 

 force itself, or/(0)=l. 



Hence/'(9) = cos d is the complete solution. 

 I am. Gentlemen, 



Your obedient Servant, 

 Bombay, Dec. 14, 1848. T. H. PllATT. 



XXVII. Suggestions for rendering a Meridian mark visible at 

 Night. By N. S. Heineken, Esq. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, Sidmouth, Feb. 14,1849. 



SHOULD you deem the following suggestions likely to be 

 of service, 1 shall be glad if you will give them a place in 

 the Philosophical Magazine. 



I am. Gentlemen, 



Respectfully yours, 



N. S. Heineken. 



It occurred to me eleven years since, that platinum wire, 

 rendered incandescent by the galvanic battery, might be ap- 



