Page:Proceedings of the Royal Society of London Vol 69.djvu/102

94

When the contractions are plotted out in terms of percentages, the former as ordinates and the latter as abscissae upon a scale of 1 mm. for 10~ 4 c.c. and 10" 1 percentage, there is in each case an ascending and a descending branch. The maximum corresponds to a percentage 54 per cent., a result which is in accordance with the former observa- tion of Kolb, who found a constant maximum from 52-33 per cent, to 54 per cent. The value calculated from this observer's density at 15 for 53 per cent, (corrected to 14'2) expressed in the terms herein adopted by us is 6968 x 10~ 5, whereas that found by us at 52'87 per cent, is 7025 x 10~ 5 or a difference of 57 x 10~ 5 , a difference readily explained, having regard to the somewhat crude analytical methods adopted by Kolb.

Further, both the ascending and descending branches consist of a series of straight lines with the exception of the portion between 95 to 100 per cent., which is markedly curved.

The Ascending Branch consists in all three cases examined of four segments, namely, (i) a steep portion from to 19 per cent, with a slight variation at about 4 per cent., (ii) a less steep portion from 19 to 33 per cent., (iii) a flatter portion from 33 to 42 per cent, and an almost horizontal portion at 42 to 53 per cent. ; in all cases the percentages are given in round figures.

The equations for the several straight lines* have been put into the form Ci = C a (-^j), wherein Ci is the contraction to be calculated, C the contraction at the selected origin of the co-ordinates, a a constant and &p the difference of percentage. The value of C was determined graphically, being the point of intersection of the two several branches.

The values for n are summarised for the purpose of convenience in the following table :

Percentage.

At 4.

At 14 -2.

At 24 -2.

I

r o 4

+ 210

+ 197

+ 190

420

+ 200

+ 190

+ 182

II

2033

+ 155

+ 152

+ 145 Ill

33 42

+ 115

+ 100

+ 100

IV

4254

+ 30

+ 30

+ 45

ruler with bevelled edge has been found convenient and more expeditious than the common forms of opaque rulers.
 * For drawing mean straight lines for a number of observations a flat glaSs