868 



SCIENCE 



[N. S. Vol. XXXI. No. 805 



in the second case if he is to be any arbitrary 

 displacement comparable to hV above, § 1. 



If aa' are chosen cotemporaneous, since both 

 motions are continuous, the rate at which the 

 interval vpill grow from nothing at a to U 

 at c, dt second later is 



and the distance passed along the curve in 

 this time excess, 



d 



is therefore 



dl 



M ■ dl 



(i'-y 



as the figure shows. Hence obviously aa 

 before 



Sx+{x + Si)dt + xj6t ■ dt = xdt + (!i:-|- ^(!x ■ dt, 



Jt'^ = '' + 4t"- (2) 



It is also obvious that if we sum up the 



increments vectorially, from a to c in the two 



directions the same proposition will hold with 



regard to s; 



3. The important transformation 



— (xfix) = jife + i — rfa; 



by which one passes from D'Alembert to 

 Hamilton or to least action, respectively (see 

 Webster's " Dynamics," which, by the way 

 should be the text-book of every American 

 university, patriotic or not), is a mere inter- 

 pretation of the last term by the aid of equa- 

 tion (1) in the first case, of equation (2) in 

 the second. 



Finally with regard to variations in gen- 

 eral it is clear that if (f> is to have but one 

 value at each point in space and is to vary 

 at a single definite rate in each direction 

 from that point, it is immaterial whether 

 one uses the differentials, dx, dy, dz, meaning 

 thereby that in a complete differentiation we 

 must get back to the initial surface or region 

 ^ = c; or the variations Zx, Sy, 8z, meaning 



that, in general, our progress may terminate 

 in any infinitely near region ^^d, at pleas- 

 ure, the same differential coefficients must be 

 used. For along x, ^ can not vary in any 

 other way than at a rate, dtf>/dx, whether our 

 absolute progress is to be dx or 8x. 



All this is simple enough, but with my stu- 

 dents it has made the difference between the 

 spiritless acceptation of what somebody else 

 is supposed to understand and the satisfaction 

 of an actual grasp of the subject. 



C. Barus 

 Beown Univeesitt, 

 Peovidence, R. I. 



• MOSQUITO HABITS AND MOSQUITO CONTROL 



Until recently it was the general impres- 

 sion that all mosquitoes are blood-suckers and 

 essentially alike in habits. Since the discov- 

 ery of their relation to disease mosquitoes 

 have been extensively studied, both systemat- 

 ically and biologically. While the study of 

 mosquito biology has not by any means kept 

 pace with the systematic work, a great deal 

 has been learned about mosquito habits and 

 it is now clear that there is great diversity of 

 habits within the group. 



To any one who has followed the literature, 

 or become directly acquainted with the re- 

 markable specializations in mosquito habits, 

 it must be obvious that no contr-ol work can 

 be carried out successfully and economically 

 without intimate knowledge of the habits of 

 these insects. Many persons, however, who 

 are concerned with mosquitoes in a practical 

 way, either directly in control work or as its 

 advocates, have failed to appreciate this and 

 hold the antiquated ideas. Work done on 

 such a shallow basis must in many cases end 

 in failure and disappointment. 



Two striking examples, which have recently 

 come to my notice, illustrate very well how 

 such shortcomings lead to error. Sir Hubert 

 W. Boyce, dean of the Liverpool School of 

 Tropical Medicine, is the author of an inter- 

 esting and excellent work which appeared 

 recently under the title " Mosquito or Man ?" 

 While the book is written on broad lines it 

 nevertheless contains specific statements, and 



