July i8, 1895] 



NATURE 



27: 



= \. On the other hand, since the velocity of waves 

 travelling under the influence of capillarity alone is pro- 

 portional to the square root of the wave shortness or 

 reciprocal of the wave-lenj^th, the line that represents 

 their velocity is straight also, but slopes the other way 

 and to the same extent. Actually both causes are in 

 operation, but except over a range of wave-length of 

 about I to 100, the one influence so largely predominates 

 that the other is negligible. In the diagram this is made 

 evident on the velocity cur\'e which consists of two 

 straight branches joined by a cur\e, which runs into 

 them and is rapidly indistinguishable from them. The 

 dotted continuation of the branches shows what would 

 be the velocities under the influence of either cause 

 alone. Where the two lines cross, both gravity and 

 capillarity have equal influence, and the two together ] 



scale line, however, is much simpler, more convenient,, 

 and less confusing. In order to draw it, find a point 

 in either branch of the curve where the velocity reading 

 on the vertical scale of the chart is equal to the value 

 of T /) for the left, or of ^'' for the right branch. If within 

 the limits of the paper the branch of the curve does not 

 indicate a velocity, of which the value is T p or g, as the 

 case may be, take some whole power of lo or ^q as a 

 factor. P'or instance, though T 'p = 8i is within the limits 

 of the left branch, .^ = 98 ri is outside the paper on the 

 right, therefore find on the right branch ^^; 10 = gS'ii. 

 Now, in order to find some other point on the scale line, 

 imagine that each of these quantities is multiplied tenfold. 

 Tlie corresponding branch of each will be raised vertically 

 v'lo, or half a square. The new line so drawn will at some 

 point cut the vertical scale of the chart, in a line of which the 



produce a minimum effect. The actual curve may be 

 planted anywiiere on the chart: but in the diagram it is so 

 placed as to represent the facts with water for which T p = 8i 

 and willi ^ = 981-1. If other liquids are chosen, then, 

 since the gravitational branch of the curve is unaffected, 

 the curve, as a whole, must be made to slide along the 

 gravity branch on the right until the left branch assumes 

 its proper position. Similarly to represent the effect of 

 changes of g, the curve must be made to slide along 

 its capillary branch on the left until the gra\ity 1)ranch 

 on the right assumes its proper position. The proper 

 position in either case may be indicated bv ;i special 

 logarithmic scale ruled to half the scale adopted for the 

 squares of the chart, and placed upon the chart with its 

 length vertical and so that the branches of the curve 

 cut each scale, one at Si and the other at gSri. The 



NO. 1342, VOL. 52] 



value is ten times the reality, or is one square higher up 

 than the first point. Mark this point, and join it to 

 the first. The result is a sotlc line having the property 

 that wherever it is cut by the corresponding branch of 

 the curve the reading on the chart gives at once the 

 value of T p or of _^'', as the case may be, that is proper 

 to the new position of the curve, and conxersely in 

 order to fix the place of the curve for any value of 

 T por of_<;, it is merely necessary to find the desired values 

 of these quantities on the scale lines, and then to shift 

 the cur\e until its two branches or its two branches pro- 

 duced if necessary pass through the points on the scale 

 lines having the values sought. If the effect of a 

 variation of the constant upon the value indicated by 

 the curve line is one of simple proportion, the scale -line 

 will be vertical. If its power is less than one, it will be 



