428 Mr. W. H. Preece on the Parallelogram of Forces. 



hibiting a great number of fissures in nearly equal directions. A 

 similar but by far smaller portion appears in a rounded section, 

 0*6 millim. in breadth, occupying one-half of the whole diameter, 

 and bordered on both sides by granular aggregations of the 

 transparent mineral. 



The metallic iron, like the two other opaque minerals, generally 

 appears interspersed in proportionally minute particles. In some 

 few cases (see fig. 7) particles of iron, of 06 to 0*8 millim., in- 

 clude granules of the transparent silicate, with some few black 

 granules in its interior, and others at the external margin of the 

 central granule and of the iron. 



Small fragments acted on by the blowpipe-flame are locally 

 covered with a black glossy enamel. The grey powder of the 

 meteorite, brought into contact with curcuma-paper moistened by 

 distilled water, offers a distinct and sometimes intense alkaline 

 reaction ; it is partly soluble in hydrochloric acid, emitting sul- 

 phuretted hydrogen and leaving gelatinous silica. 



XLTX. The Parallelogram of Forces. 

 By William Henry Preece, Assoc. Inst. C.E. §-c* 



IT is said that there are twenty-seven known proofs of the pa- 

 rallelogram of forces. Any attempt to add to this number 

 appears to be a needless undertaking ; but the proofs usually 

 inserted in elementary works are generally so laboured, that 

 beginners rarelysucceed in mastering them fullyin their first jour- 

 ney through statics. Indeed it appears to me that the proof that 

 the resultant is represented in magnitude as well as in direction 

 by the diagonal, as usually given, is defective ; for we are required 

 to draw a line equal to an unknown quantity, and then to show 

 that another line is equal to this line without obtaining the un- 

 known quantity. 



I have therefore ventured to arrange another proof based 

 upon the principle of couples, which not only attempts to re- 

 move this defect, but to free the usual proofs from the necessity 

 of subdividing the proposition into the two cases of commensu- 

 rable and incommensurable forces — a veritable pons asinorum to 

 all students. 



Definitions. 



(1) A couple is a system of two equal forces acting in dissi- 

 milar directions in parallel lines. 



(2) The arm of a couple is the perpendicular distance between 

 the lines of direction of the two forces. 



* Communicated bv the Author. 



