Equation to Uniform Motion of Water, 467 



APPENDIX. 



From the equation Q = AV (using Q and q for discharges per second, and A 

 and a for cross sections, and I and i for slopes), and from observation, I have 



1=a/ZT (2), and iU k/THL or * - a/ITS. .(3) 

 V V QI V V AVI V V AI 



from which I obtain a new equation to the flow of water in uniform con- 

 strained motion — that is, only when V = ?\ This is true for any slope with the 

 same material of channel, 



Then from (a), when T7 = 1 then A/ 1_ = A/ — or — =— . 



?_ _ Q ? ' 



Tlien from (3), when "v = 1 thenA/ JL= Aj or _f_== , 



v v A v i A i 



Then by compounding in the very general case when water is in uniform motion 

 we have the formula 



1_L(±+L) ( 4 ) 



i 2 \ A Q / 



It applies to water in canals in uniform motion, as in Figs. 6 and 7, page 

 446. Coefficients have to be used for each different material of channel, 

 which are here omitted. They are found by observation. 



The effect of motion in diminishing pressure is an important physical cause ; 

 this appears to have been overlooked. I quote some remarks on this subject 

 in relation to the barometer, because they have a general bearing on all physical 

 questions where pressure is modified by motion. 



From the Quarterly Journal of the Meteorological Society, _/br 

 yanuary, 1875. 



Mr. A. Tylor said he should like to offer some evidence to prove that the 

 barometer cannot be considered a correct instrument for registering the abso- 

 lute weight of the atmosphere, although it often indicates the relative weight 

 correctly. The absolute pressure on the cistern of the barometer varies much 

 more for horizontal motion of the air than it can for mere change of weight of 

 the atmosphere.* By analogical reasoning from his experiments on the Injector, 

 described page 215, Phil. Mag. September, 1874, he stated that the column of 

 mercury in the barometer shortens for motion instead of lengthening for 

 weight. There is a constant fall in the barometer during the formation of 

 clouds and condensation of vapour into rain in temperate climates, where the 

 rain-making process occurs in the lower strata of the atmosphere. The mixture 

 of dry air and vapour at 40 would cause a change only of 8 parts in a thousand 

 in volume, and yet would cause a considerable lateral and vertical displacement 

 and movement in the atmosphere. The change in absolute weight of the atmo- 

 sphere under these circumstances would be comparatively slight, and would not 

 account for a fall in the barometer of 0'3 in. or 0'4 in., or 3 per cent, (or 30 

 parts in a thousand), which is frequent in England during the process of rain- 



* Professor R. Tennant, of Glasgow, informs me he has read a paper recently at the Royal 

 Society of Edinburgh (which will appear in their Transactions), " On Meteorology," containing 

 a view of barometric action. From the abstract sent this appears to be similar to my own. 



