158 REPORT 1861. 



As to the confidence which may be placed in this formula, I think it clear 

 that, for the case in which the notch is so wide, or, what is the same, the slopes 

 of its edges are so slight, that the water may flow over each infinitely small 

 element of the length of its crest without being sensibly influenced in quan- 

 tity by lateral contraction arising from the inclination of the edges, the for- 

 mula may be relied on as having all the accuracy of the Lowell formula 

 from which it has been derived ; and I would suppose that when the notch is 

 of such width as to have slopes of about four or five to one, or when it is of 

 any greater width whatever, the deviation from accuracy in consequence of 

 lateral contraction might safely be neglected as being practically unimportant 

 or inappreciable. 



This formula for wide notches bears very satisfactorily a comparison with 

 the formulas obtained experimentally for narrower notches, as described in 



the foregoing Report. For slopes of one to one the formula was Q=*305 H'-*, 



and for slopes of two to one the formula was Q=*636 H*. To compare 

 these with the one now deduced for any very slight slopes, we may express 

 them thus : — 



For slopes of 1 to 1 Q=-305»tH^ 



And for slopes of 2 to 1 Q=-S18?wH^ 



While for any very slight slopes, or for any very 



wide notches, the formula now deduced from s 



the Lowell one is Q=-320mH. 



The very slight increase from '318 to '320 here shown in passing from 

 the experimental formula for notches with slopes of two to one, to notches 

 wider in any degree — that slight change, too, being in the right direction, 

 as is indicated by the increase from -305 to '318 in passing from slopes of 

 one to one, to slopes of two to one — gives a verification of the concluding 

 remarks in the foregoing Report ; and this may serve to induce confidence 

 in the application in practice of the formula now oflTered for wide notches. 



Report on Field Experiments and Laboratory Researches on the Con- 

 stituents of Manures essential to cultivated Crops. i?t/ Dr. Augustus 

 VoELCKER, Royal Agricultural College, Cirencester. 



In a Report read at the Aberdeen meeting, and subsequently printed in the 

 ' Transactions of the British As-sociation,' will be found recorded a number 

 of field experiments on turnips and on wheat. Siiflilar experiments upon 

 these two crops have since been continued from year to year, and a new 

 series of field experiments has been undertaken on the growth of barley. 



In connexion with these field trials I have made numerous laboratory 

 experiments on the solubility of the various forms and conditions in which 

 phosphate of lime is likely to be presented to growing plants, and have 

 likewise studied to some extent the influence of ammoniacal salts and a few 

 other saline combinations on the solubility of the various forms in which 

 phosphate of lime occurs in recent and fossil bones, in apatite, and other 

 phosphatic materials. 



The present Report will comprehend two sections. In the first I shall 

 give the results of my field experiments on turnips, wheat, and barley ; in 

 the second section reference will be made to the solubility of phosphatic 

 materials in various saline liquids. 



