Surface- Loading on the Flexure of Beams. 489 



In order to establish the hyperbolic law with greater 

 certainty, experiments were made enabling as many as seven 

 points on the curve to be obtained within 3' 5 millim. of the 

 point of contact, the highest point being about '5 millim. 

 from the top of the beam. 



Within this range the effect due to the steel frame may 

 with accuracy be neglected. 



Experiment 2. A beam of annealed glass, 61 millim. x 6*5 

 millim. x 20 millim. deep, was placed in the steel straining- 

 frame, on a piece of thick paper, and loaded as before with the 

 steel roller 2 millim. in diameter. 



Nicols crossed and at 45° to the axis of the beam. 



The screw load was applied until six interference-fringes 

 appeared under the roller ; these were examined through a 

 microscope with a micrometer-eyepiece divided to thousandths 

 of an inch. Light from a sodium-flame was used, and the 

 distance between the point of contact and the intersection of 

 each fringe with the normal was measured in micrometer- 

 divisions. 



I. Distances in micrometer-divisions to successive fringes : 



11-0 13-5 17-0 23-0 35-0 7-1-5, 



but the shears are as 6.5.4.3.2.1, since there is a difference 

 of phase of only -J a wave-length required to produce a fringe, 

 hence taking the products of distances into shears we get 



66-0 67-5 68-0 69'0 70-0 71'5. 



But we have so far neglected the value of 0, the distance of 

 the axis of shears from the point of contact. 



By taking the two most reliable observations, where the 

 distance from the point of contact is large and yet where the 

 fringes are well defined, we should have, if the law is 

 hyperbolic, 



3(23 + 0) =4(17 + 0), 

 or 



0=1*. 



Correcting the original readings by adding 6 to each, we get 



12 14-5 18 24 36 72-5, 



and the products become 



72 72-5 72 72 72 72'5. 



II. Same beam, &c, as before, roller and load readjusted. 

 Distance to successive fringes : — 



11-5 14-25 17-75 24-0 36'0 75*0 



* One micrometer-division = 0-044 millim. 



