304 [Dec. 11, 



II. "On the Strains in the Interior of Beams." By GEORGE 

 BIDDELL AIRY, F.R.S., Astronomer Royal. Received No- 

 vember 6, 1862. 



(Abstract.) 



The author states that he had long desired to possess a theory 

 which should enable him to compute numerically the strains on 

 every point in the interior of a beam or girder, but that no memoirs 

 or treatises had given him the least assistance. He had therefore 

 constructed a theory, which solves completely the problems for 

 which he wanted it, and which appears to admit of application at 

 least to all ordinary cases. 



The theory contemplates forces acting in one plane. A beam, 

 therefore, is considered as a lamina in a vertical plane, the same 

 considerations applying to every vertical lamina of which a beam 

 may be conceived to be composed. 



The author remarks that it is unnecessary to recognize every 

 possible strain in a beam. Metallic masses are usually in a state of 

 strain from circumstances occurring in their formation; but such 

 strains are not the subject of the present investigation, which is 

 intended to ascertain only those strains which are created by the 

 weight of the beam and its loads. The algebraical interpretation of 

 this remark is, that it is not necessary to retain general solutions of 

 the equations which will result from the investigation, but only such 

 solutions as will satisfy the equations. 



After denning the unit of force as the weight of a square unit of 

 the lamina, and the measure of compression-thrust or extension-pull 

 as the length of the ribbon of lamina whose breadth is the length of 

 the line which is subject to the transverse action of the compression 

 or tension, and whose weight is equal to that compression or tension, 

 the author considers the effect of tension, &c., estimated in a direction 

 inclined to the real direction of the tension, and shows that it is 

 proportional to the square of the cosine of inclination. f He then 

 considers the effect of compounding any number of strains of 

 compression or tension which may act simultaneously on the same 

 part of a lamina, and shows that their compound effect may, in every 

 case, be replaced by the compound effect of two forces at right 

 angles to each other, the two forces being both compressions, or 



