312 Notices respecting New Books. 



that differential coefficient must be extremely large; as in the 

 rapid expansion of the tails of comets, and in explosions from 

 gaseous mixtures ; but it does not appear that there can be in 

 rerum naturd circumstances under which its value is absolutely 

 infinite. 



(2) The dilemma respecting the immobility of the stratum 

 immediately beneath the piston is fairly inferred, and demands 

 an explanation. I believe that in the work already cited I have 

 furnished the means of explaining it. One of the definitions of 

 a perfect fluid given in pp. 104 & 171 is, that its parts press 

 against each other and against any solid with which they are in 

 contact. Accordingly there is mutual pressure between a solid 

 and fluid in contact such as there is between contiguous parts of 

 the fluid, and pro tanto the solid may be considered a continua- 

 tion of the fluid. Now when any heavy mass is at rest, if we 

 conceive a horizontal plane to be drawn through it, the total up- 

 ward pressure in this plane must be equal to the weight of the part 

 of the mass above it, because this part is thereby just sustained. 

 Hence from the top to the bottom of the mass there will be a 

 gradual increment of pressure. If now another mass be placed 

 on the first, there will be a like increment of pressure from the 

 top of the upper to the bottom of the lower mass, and the pres- 

 sure and gradation of the pressure in the latter will not be the 

 same as before. Applying these considerations to the case of 

 the piston, it will be seen that before putting on the additional 

 weight there will be equality of pressure on the opposite sides of 

 the plane of contact of the fluid and the piston; but as soon as 

 the weight is added, there will be a tendency to an excess of 

 pressure on the upper side due to the disturbance of the pres- 

 sure in the solid piston ; but as no finite difference of pressure 

 can subsist, this tendency will give rise to a common acceleration 

 of the parts of the fluid and solid that are immediately conti- 

 guous to each other. Thus an acceleration would commence at 

 the upper surface of the stratum, and the equality of the pres- 

 sures at the upper and under surfaces would cease to exist. The 

 amount of the initial acceleration is determined by that of the 

 descending solid. 



Cambridge, September 22, 1873. J. Challis. 



XXXIX. Notices respecting New Books. 



The Moon, her Motions, Aspect, Scenery, and Physical Condition. 

 By Kichard A. Proctor, B.A. London : Longmans and Co. 



WE are somewhat disappointed in this work. Conceived on an 

 excellent plan, with abundant materials at hand for produ- 

 cing an exhaustive treatise on the moon, the author has failed to 



