412 



NATURE 



\Marck 6, 1890 



perimeter was very rough. This change in the variation 

 of c with relation to the s lope was found to depend upon 

 the hydraulic radius.being greater or less than 3'28i feet ; 

 so that c becomes independent of the change in slope 

 when R approximates to this value, though the actual 

 value of R at which the modification occurs varies with 

 the degree of roughness of the channel. This result is 

 attributed to the conflicting currents and eddies in large 

 rivers having irregular beds, or in small channels with 

 very rough beds, which are intensified by an increase in 

 the slope ; whereas, in small streams flowing in confined 

 channels with smooth beds, an increased velocity tends to 

 dissipate retarding lateral movements. A preliminary 



/ 



a + 



form adopted for the value of c was 



1 + 



an 



where 



a-\- - replaces y in the original formula, and an = x, or 

 n 



X = ny — /, in which a'ls a. constant with value 41 '66 in 

 English measures; /is another constant, equal to a/R 

 when R has the special value 3*281 referred to above, 

 and therefore I'Sii ; and n is the coefficient of rough- 

 ness, varying, according to the state of the channel, from 

 0*009 to 0*040. The above value of c suffices for the flow 

 in pipes and other small channels with steep slopes, 

 owing to the small influence of a variation of slope on the 

 coefficient c in such cases ; but for ordinary channels 

 allowance has to be made for variations in slope, necessi- 

 tating the introduction of another variable factor into the 

 expression for c. The final shape given to the value of c 

 by Messrs. Ganguillet and Kutter, in their general 



formula, was 



, / .in 

 n o 

 m\ n 



where ni = 0*0028075, 



i-H a + 



S/VR 



for English measures, is a constant of a hyperbola em- 

 ployed in constructing the formula. The general formula, 

 accordingly, became, for English measures— 



rSii 



+ 41*6 + 



V 



0*00281 

 S 



I ( .,.c, t 0*0028l\ t, 



n 



Vrs, 



where V is the mean velocity in feet per second, which 

 multiplied by the cross-section would give the discharge 

 in cubic feet per second, and S is the actual slope. 



The main interest of the book consists in the clear 

 exposition of the several steps by which the formula was 

 reached ; and even if at some future time, by the aid of 

 fresh observations and more accurate experiments, the 

 formula should be superseded by a more comprehensive 

 and exact one, the merit of this work as an elaborate 

 scientific investigation for a general empirical formula 

 must always remain ; and the book would deserve to be 

 consulted on this ground alone. The formula depends 

 entirely upon the exactness of the observations upon 

 which it has been based. Mr. Rdvy has questioned the ac- 

 curacy of the Mississippi experiments, owing to the use of 

 double floats ; and if fresh investigations should establish 

 the inaccuracy of any of the observations made use of, or 

 if further experiments should extend the scope of the 

 inquiry, or bring new facts to light, a modified formula 



will be required. The authors, however, of the formula 

 do not regard it as final or complete, nor do they claim 

 for it any mathematical precision ; they only consider 

 that it agrees more closely than any previous formula 

 with the results of recorded observations. The formula 

 has naturally been objected to on account of its com- 

 plicated appearance ; but the variation due to change of 

 slope renders this inevitable ; and it has been seen that 

 a simpler formula may be adopted for pipes, and small ' 

 channels with steep slopes ; and, moreover, graphical 

 methods and tables might simplify the calculations. At 

 the close of last year, Mr. Robert Manning, Engineer to 

 the Board of Works in Dublin, presented a new formula 

 to the Institution of Civil Engineers of Ireland, which, in 

 its general form, is hardly less complicated than that of 

 Messrs. Ganguillet and Kutter. This formula is 



i 0*22/ 



V 



VS^|Ri + 



i(R 



0*1 5 ;« 



)}• 



where n is the coefficient of roughness, g the force 

 gravity, and m the height of the barometric column of 

 mercury. Mr. Manning puts it forward as simpler and 

 better than the other, and claims for it, in a simplified 

 form, a closer approximation to the mean of the results 

 of seven of the best known formulae than any other. 

 Actual observations, however, form a surer basis upon 

 which to establish a general formula than the results of 

 previous formulse ; and it is upon a close concordance with 

 very varied and accurate observations that any general 

 formula must claim acceptance. Whatever position may 

 in the future be assigned to the formula of Messrs. Gan- 

 guillet and Kutter, their work marks a notable step in 

 advance, and must rank with the researches of Messrs. 

 Darcy and Bazin, and Messrs. Humphreys and Abbot, as 

 a record of important hydraulic investigations ; and the 

 translators have performed a valuable service in placing 

 clearly before English readers the successive steps by 

 which this general formula has been established. 



THE COMPASS ON BOARD. 



Der Kompass an Bord : Ein Handbuch fiir Fiihrer von 

 eisernen Schiffen. Herausgegeben von der Direktion 

 der Deutschen Seewarte. (Hamburg: L. Friederichsen 

 and Co., 1889.) 



THE important subject of the magnetism of iron ships 

 and the resulting deviations of their compassesr 

 has, during the last fifty years, received marked attention 

 in England from eminent men of science, attended with 

 most valuable results for the safe navigation of our Royal 

 and mercantile navies. 



During the last thirteen years this same subject has 

 been one of continuous inquiry at the German Naval 

 Observatory in Hamburg, and papers have been published 

 from time to time in the annual report of that institutionr 

 showing what had been accomplished. Combining the 

 results of this work with those obtained from the extensive 

 literature chiefly produced in England, Dr. Neumayer,. 

 the Director of the Observatory, has compiled the present 

 work for the use of officers commanding the iron ships of 

 the German mercantile navy. 



Of the six chapters into which the work is divided, the 

 first is devoted to information on the magnetism of iron 



