332 Mr. W. Mathews on Canon Moseley's views 



or 



_ ^u* 



Inserting here for u 2 its value from (53) gives 



: = 2 ? r X /: 



Lastly, we will express the energy of our system. It is 



L = »M?i 1 <p(r) + -gi^-h y v\ 



m + m 1 



and consequently also 



mm l _. 



E = mm^(r) + i^q^ M 2 . 



The values from (52) and (53) inserted here give 



H = mm l l4>(p)+ip4>'(p)] (55) 



We have thus again arrived at a system of four equations — 

 (52), (53), (54), and (55) — by means of which we represent by 

 p the mean ergal, the mean vis viva, the period, and the energy ; 

 or else, after eliminating p, we can express the first three of these 

 quantities as functions of the energy, therefore as functions of a 

 quantity whose value can be given as soon as, for any distance of 

 the two points, their relative velocity is known. 



The four equations here found are of the same form as the 

 equations (19) to (22) — which might have been expected, since the 

 motion first considered is only a special case of the one last dis- 

 cussed — namely, the limiting case, which is arrived at by assu- 

 ming that one of the masses is so large in proportion to the other, 

 that during the motion round their common centre of gravity it 

 can be regarded as at rest. Hence it will not be necessary to 

 develope the special forms which the equations here found 

 assume when the force is proportional to a power of the distance, 

 because they perfectly correspond to the forms previously de- 

 veloped. 



XLI. On Canon Moseley's views upon Glacier -motion. 

 By William Mathews, President of the Alpine Club*. 



IN the Philosophical Magazine for August 1871 Canon 

 Moseley has criticised some remarks of mine upon the be- 

 haviour of ice-planks under strains produced by their own gravi- 

 tation. The remarks in question were contributed to the Alpine 

 * Communicated by the Author. 



