of the Rutherfurd Photographs. 223 



July 27, 1897. Temperature = 82.°i. 

 104.1532 mm. 

 525 

 505 

 53o 

 520 



495 

 5io 

 542 

 5io 

 522 

 548 

 525 



Mean, 104.1522^0.00031 

 Denoting by v as before the increase in the distance due to an in- 

 crease of i° in the temperature, and by L the distance between 

 the specks at the temperature 6o,.°6 we have the following four 

 observation equations : 



L — 104. 1543 = o weight 3 



L+ 1.4 »— 104.1537 = " 5 



L -\- 4..0V — 104.1536 = " 2 



I -f 12.5 « — 104.1522=0 " 5 



The weights are calculated from the probable errors given above, 

 the probable error of an equation of weight unity being 



± 0.00067 

 Solving by least squares we get 



v = — 0.00015 ± 0.000032 

 Taking into account the two previous series, the mean by weight is 



v = — 0.00019 mm - 

 which very probably does not differ from its true value hy as 

 much as 0.00005. 



Now the largest coordinate in the Prsesepe measures is less 

 than forty millimetres, and the greatest deviation for any single 

 day from the mean of the temperatures for the corresponding 

 plate is less than 5 ; consequently the largest correction which 

 it will ever be necessary to apply is 



0.00037 mm. 

 which corresponds to o/ r 02. As this is so small, even in the ex- 

 treme case, no appreciable error will be committed by neglecting 

 the correction altogether. We ma} r indeed conclude that for the 



