34 MR J. Y. BUCHANAN ON THE 



the times at which the hydrometer is immersed and removed, while the temperatures 

 of the water at these times are given in lines e and j, with their mean, T, in line k ; 

 the range of temperature over which the series of observations was carried out is 

 shown in line /. Although it is intended that the temperature shall be uniform 

 during an experiment, it sometimes happens that it varies, and this has to be 

 provided for in the table. Line f^ gives the headings iv, the weights used to sink 

 the hydrometer in the liquid, and R, the reading on the scale of the instrument 

 corresponding to these weights. 



Lines f-^ to f^ give, under w, the values of the weights, and under R, the 

 corresponding scale readings, obtained during the series of observations. The value 

 of the mean added weight, w, is given in line g, while the mean reading, R, is 

 shown in line h. 



The departure of the mean reading from 50 mm., 50 — R, is entered in line m ; it is 

 given in the headings as dr. In line n we have the weight which is equivalent to df, 

 expressed as dw^ (see § 15). 



The weight required to immerse the hydrometer to the 50-mm. mark, w-\-dWr, 

 irrespective of temperature corrections, is shown in line o, being that weight which 

 would cause the instrument to float with the scale division at 50 mm. in the plane of 

 the surface of the liquid, at the mean temperature, T. The difi"erence of the mean 

 temperature, T, from the standard temperature, T, is given in the line p, and is 

 expressed as T — T = c?i ; the weight corresponding to the difference dt is entered in 

 line q; it is expressed as dwt (see § 16). 



The total corrected added weight required to immerse the hydrometer to the 

 50-mm. mark at the standard temperature, T, is w + dwr-'r dwt, and is given in 

 line r. 



The total weight of liquid displaced by the hydrometer when floating in the 

 liquid at the 50-mm. mark at the standard temperature, T, is entered in line s, and 

 is equal to the weight of the instrument in vacuo plus w + dwr + diVf 



Having explained the meaning of the lines, we will proceed to inspect the results 

 of the observations in Table A^. 



After preliminary trial, the first weight added to the hydrometer at the commence- 

 ment of a series of observations is chosen so that the mean of the nine series of 

 immersions or scale readings produced by successive added weights, each increasing 

 by O'l gram, shall approximate closely to 50 mm. It is evident that the initial, or 

 first, added weight might be different for each series of observations. In the ten series 

 of observations detailed in Table Aj, however, the first added weight in each case 

 was 0'525 gram, and therefore the nine added weights are given only once, under w, 

 in lines /^ to /g of the first column. Each of the ten succeeding columns contains a 

 complete series of observations of the immersions produced by the nine added weights, 

 and the steps in the calculation of the total weight of the hydrometer when floating 

 at the 50-mm. mark at the standard temperature. 



