April i8, 191 8] 



NATURE 



12^ 



^^^^ Commons, the first on the occasion of pre- 

 H^ting^ the Education Estimates in April, 

 ^^■7, and the second on the introduction of the 

 ^^Ht Education Bill in the following August. He 

 ^^K accompanied the publication by a highly 

 ■Bbminating preface of sixteen pages, in which 

 B resumed all the more important features of 

 the revised draft of the Education Bill of 1918, 

 iand of the chief points of his many speeches in 

 support of his reforms, characterised by a felicity 

 of phrase and diction which will go far to hearten 

 supporters of the measure and even to conciliate 

 and win opponents. Mr. Fisher's addresses are 

 instinct with a broad humanity and a spirit of real 

 elpfulness. He is a man consumed with the idea 

 that the welfare of the child is the nation's most 

 vital concern, and his arguments and pleadings 

 est " upon the right of human beings to be con- 

 sidered as ends in themselves, and to be entitled, 

 so far as our imperfect social arrangements may 

 rmit, to know and enjoy all the best that life 

 Can offer in the sphere of knowledge, emotion, 

 and hope." In this faith he goes forward on his 

 high mission, confident that he will win the sup- 

 port of all who desire the highest well-being of 

 the nation. 



Microscopic Examination of Steel, By Dr. Henry 

 Fay. Pp. iv+i8+Fig. i + photographs 55. 

 (New York : John Wiley and Sons, Inc. ; Lon- 

 don : Chapman and Hall, Ltd., 1917.) Price 

 6s. net. 



fulness of metallographic methods in the control 

 of material, although a considerable amount of 

 experience is required before it is possible to inter- 

 pret aright the indications of the microscope. For 

 the purpose of acquiring such experience, the 

 reader is recommended to examine a number of 

 steel specimens, the heat treatment of which is 

 definitely known, before attempting the study of 

 abnormalities. C. H. D. 



LETTERS TO THE EDITOR. 

 [The Editor does not hold himself responsible for 

 opinions expressed by his correspondents. Neither 

 can he undertake to return, or to correspond with 

 the writers of, rejected manuscripts intended for. 

 this or any other part of Nature. No notice is 

 taken of anonymous communications.] 



Long-range Guns. 



Several correspondents have rightly pointed out 

 that the ranges given in my short article on this sub- 

 ject in Nature of April 4 are twice as great as wouW 

 be given by the stated initial velocities. The heading 

 of the velocity column should have been " Horizontal 

 Component of Initial Velocity," not "Initial Velocity." 

 The horizontal component, where there is no resist- 

 ance, is constant for the whole range. 



At the end of the article I referred to the elliptic orbit 

 of the projectile. The elements of the ellipse are easilv 

 found. Since, at the vertex of the trajectory, the weight 

 of the projectile is just balanced by centrifugal force, 

 and since the radius of curvature of an ellipse at the 

 end of the major axis is b=*/a, b'/a = v^/g', where v is 

 the velocity in apogee and g' the earth's attraction at 

 that distance; also, since b^ = a^(i — e^*), it follows that 

 e = i-v^/R'g', where R' is the apogee distance of the 

 projectile from the centre of the earth, and 



R'./Llf. 



V i+g 



A short table of v and b is appended. 



If R' = R + H, R being the earth's radius and H the 

 greatest height of the trajectory above the earth's sur- 

 face, and if, also, 6 is the angular distance between 

 the major axis of the ellipse and point where the orbit 

 cuts the surface of the earth, the range is 2R sin 6, 6 

 being determined by the equation 



cos 6- 



M--^; 



The Motion of the Perihelion of Mercury. 



I AM obligtKl to Mr. Harold Jeffreys for his friendly 

 criticism (Nature, April 11, p. 103), but my suggestion 

 was not one of a resisting medium pure and simple, 

 but of a resistance greater at perihelion than aphelion, 

 and therefore synchronous with the planet's orbital 



