TRAKSACTIONS OI-' SECTION A. 039 



indicator at or near the maximum pressures, and thus obtaiaing an excellent 

 record of the rate of fdU of pressure in a closed vessel. 



Vieille has designed two instruments. 



In the first the record of a tuning-fork is inscrihed on a plate supported b}' 

 a stiff spring, which is bent by the pressure of the explosion. 



In the second the mo. ion of the spring itself is directly inscribed on a revolving 

 cylinder. 



The deflections in either case are very small, the records being read by means 

 of a microscope. 



In tbe instrument with which the present paper is more especially concerned 

 the spring of the indicator is replaced by a metal tube, the deflection corresponding 

 to the elastic compression of the material. 



The deflection is magnified by a very light lever, the curve being recorded 

 either photographically or stylographically on a revolving cylinder. 



The advantages of tbe instrument are twofold. 



1st. The time period is sufficiently short for an accurate record of the fastest 

 explosions to be obtained. 



:2nd. The records are of the dimensions of an ordinar}"^ steam-engine d'agram, 

 and can therefore be measured directly Avith sufficient accuracy. 



This instrument will give an accurate and easily read time-space curve. 



8. On an Improvement upon Huygem^ Construction. 

 By G. Johnstone Stoney, M.A., D.Sc, F.R.S. 



Tbe hypothesis that underlies Huygens' construction is that if S be a surface 

 with which the wave-fronts of an undulation come successively to coincide, and if 

 we call K and Q the spaces on either side of this surface, the direction of propaga- 

 tion being from K to Q, then, instead of the actual wave-motion in space Q, it is 

 permissible, as an hypf)the8is which is lea'itimate I'or some ])urposes, to substitute 

 the simultaneous advance into space Q of undulations of spherical wavelets which 

 have started simultaneously in the same phase from the several puncta (or physical 

 points) of surface S. 



The improvement consists in using, instead of the surface S, a stratum of a 

 wave-length in tliickness, and assuming that undulations of spherical wavelets of 

 equal intensity start simultaneously at the instant t = t from all the puncta of this 

 stratum in the phases in which the original undulation reaches those puncta at that 

 insta7it of time. 



This hypothesis can be justified as a simplification, which for almost all pur- 

 poses is legitimate, of the complete resolution into spherical Avavelets of which 

 use was made in a paper read by the present writer before the British Association 

 in 1859, and published in the ' Transactions ' of the Roval Irish Academy for 1860, 

 p. 37. 



While Huygens' more crude construction gives a correct result only in the 

 direction of propagation, furnishing results that deviate from the correct result in 

 inclined directions, and suggesting false results for backward directions, the 

 amended construction gives almost exactly correct results in all directions. 



Moreover, with the new construction it is legitimate to place the stratum S 

 oblique to the wave-front as well as coincident with it. When in the oblique 

 position the thickness of the stratum is to be X cos 0, 6 being the inclination of 8 to 

 the wave-front. 



9. Hoio to apply the Resolution of Light into Undulations of Flat Wavelets 

 to the Investigation of Optical Phenomena.^ ByG. Johnstone Stoney, 

 M.A., D.Sc, F.R.S. 



The light undulations that propagate themselves forward through a uniform 

 isotropic medium may be resolved in an infinity of different ways, and among 



' Phil. Mag., February 1903. 



