The Rev. R. Murphy on Rectangular Forces 105 



than the anterior extremity, and is thickly clail with hair; its colour is 

 grayish brown, with a faint tinge oi' olive, a broad, obscure, dentated band 

 of a lighter hue, which terminates in three points, extending from the 

 anterior part, along the middle, nearly one half its length, and a series 

 of pale, transverse, curved lines, somewhat enlarged at their extremities, 

 and diminishing in length as they approach the spinners, occupying the 

 space between the ternn'nation of the band and the extremity of the abdo- 

 men : the underside is of a yellow brown colour. 



Length, from the anterior part of the cephalothorax to the extremity of 

 the abdomen, ^ths of an inch ; length of the cephalothorax ^V; breadth 

 4i^; breadth of the abdomen, -^l; length of a posterior leg 1 inch; length 

 of a leg of the third pair |ths. 



The male resembles the female, but is rather ligliter-coloured, and more 

 distinctly marked. Though somewhat less, its legs are longer, a posterior 

 one measuring 1 inch and 1*^. The fourth joint of the palpi is a little 

 longer than the third ; the fifth is of an oblong oval form, and is thinly 

 covered with dull brown hair ; underneath, at the upper extremity, is a 

 sniall aperture containing the palpal organs, which are neither highly de- 

 veloped, nor complicated in structure, and are of a dark red-brown co- 

 lour. 



I discovered males, females, and young of this species in May, 1836, 

 among water-worn stones and fragments of rock, on the banks of the river 

 Llugwy, near Capel Curig, Caernarvonshire. 



Crumpsall Hall, Nov. 9, 1836. 



XXIII. On the Composition of two Rectangular Forces acting 

 on a Point, By the Rev. R. Murphy, M.A,*^ 



T ET two forces, X, Y, act upon a point, which we may sup- 

 -" pose the origin of coordinates, and let their directions be 

 those of the axes of x and y respectively. 



If the forces X, Y be doubled, trebled, &c., the resultant 

 would then be the sum of the resultants of two or three, &c. 

 systems of forces similar to X and Y; that is, it would be ac- 

 cordingly doubled, trebled, &c., in magnitude, without any 

 change of direction. 



Now as X and Y may be regarded as the multiples of very 



Y 



small forces, it follows that the ratio -^ remaining constant, 



the ratio -^ (R being the resultant) and the inclination of R 



to the axis of x will also remain invariable. 



The equation to the line in which Uie resultant acts is there- 

 fore 



^=/(x)--^ • • • • ('•) 



the form of the function^ being at present unknown. 



* Communicated by the Author. 

 ThirdSeries. Vol. 10. No. 59. Feb. 1837. P 



