BAROMETRIC PRESSURES ON THE GREAT LAKES 31 



23, 29, and 30. The largest residual v for any one of these 8 days is +0. 079 

 foot on September 18. For that day the I term or observed rise (with the 

 small noted corrections) as expressed by the I term was +0.277 foot. In 

 other words, of the unusually large observed rise of 0. 280 foot (see table No. 

 4) from September 17 to September 18, 0.003 foot is accounted for by rain- 

 fall, inflow, and outflow, 0.198 foot is accounted for as barometric effects, and 

 only 0.079 foot, or only 28 per cent of the observed rise, is left unaccounted 



for. 



Substitution in Observation Equations for September 1910, at Milwaukee. 



The unit is 0.001 foot. 



Date BWO BWI Bw2 Bwz Bno Bni Bnz B n z I v 



31-1 -9 +122 +35 -8 +46 +20 -127 +6 - 9 = +76 



6 -4 +13 +26 +13 -12 +39 +171 -14 -213 = +19 



9 -5 +156 +18 -18 +10 -124 + 6 +18 + 21 = +82 



10 +11 -87 -32 -8 +2 +59 +25 -16 + 7= -39 



11 -20 -39 -9 +3 +8 -52 +25 -28 +45= -67 



12-13 - 5 +13 +73 - 4 +8 - 78 - 38 +18 + 44= +31 



14 -5 -17 +3 -4 +14 +59 +63 -8 -112= -7 



15 +2 -22 -9 -6 +20 -26+19 + 68 = +46 



16 -5 -30 +6 -9 +6 +19 -6 - 3 =-22 



18 -9 +43 +61 -17 +32 -131 -197 +20 +277 = +79 



19 +37 -82 +9 +3 -62 +65 +32 +16 35= -17 



20 +5 +13 +26 +4 +10 +52 +70 -18 -163= -1 



21 +16 +17 +3 -8 +22 -59 -89 +8 +118 = +28 



22 +2 -39 -47 -5 -28 +26 +32 +16 +68 = +25 



23 -28 -26 +53 +2 +10 +52 -101 -24 +110= +48 



27 -23 -56 +58 +13 -8-13 +171 -10 -92= +40 



29 -12 -43 -20 -2 +6 -78 +57 +2 +108= +18 



30 -12 - 9 -18 +9 +18 +7 +76-2 -113= -44 



THE FIVE FINAL SOLUTIONS FOR BAROMETRIC EFFECTS. 



The principal facts for each of the five least-square solutions which served 

 to give the adopted values for the quantities B u ^, B Wl , . . . B^, and B^ 

 expressing the barometric effects at the five stations, Buffalo, Cleveland, 

 Milwaukee, Harbor Beach, and Mackinaw, are here brought together for 

 convenient reference. 



Each of the five solutions was based upon 8 months of observation of 

 water elevations at the station named. At Buffalo and Cleveland, the 

 months were August to October, inclusive, 1909, and June to October, 

 inclusive, 1910. At Milwaukee, Harbor Beach, and Mackinaw, the months 

 were June to September, inclusive, in each of the two years 1910 and 1911. 



In table No. 6 the probable errors included in parentheses are estimated 

 on the basis of those which are not so marked. These latter were computed 

 rigorously from the residuals and the normal equations. 



The values of B^, B Wl , . . . B^ and B ni as given in table No. 6 

 correspond to the units arbitrarily adopted for convenience in the obser- 

 vation equations that is, if b wo , b Wl , ... 6^ and b n3 are expressed in 

 units of 0.01 inch and the above values for B u , , B Wl , . . . B H2 and B U3 are 

 used, the resulting products b u ^ B Wa , b Wl B Wl ...&, Bn, and 6 nj B nt are 

 barometric effects expressed in units of 0.001 foot. 



