THERMAL SURVEY. 245 



the method of least squares were performed by Dr. Barus and Mr. Reade.' 

 For the sake of comparison they also computed the observations made at 

 the Rose Bridge Colliery, and I add the Sperenberg observations with Mr 

 Heinrich's equation. The Sutro Tunnel data cannot be treated in the same 

 way, for they show an unmistakably curvilinear locus. A curve was drawn 

 empyrically through the plotted points, no weight being given to any pre- 

 conceived idea of the character of the law of increment. Subtangents were 

 constructed and found to be almost exactlj' equal; or, in other words, it 

 was found that the graphical approximation nearly coincided with the locus 

 of an exponential equation 



in which I denotes the horizontal distance from the Lode. 



The method of least squares is, of course, applicable to the computation 

 of an equation of this character, but the calculation is so serious an under- 

 taking as to be worth while only when a magnificent series of observations 

 is to be reduced. In the present case no exterpolation is desired, and a de- 

 termination of the character of the curve with an approximate knowledge 

 of the value of the constants is sufficient for the purposes of the discussion. 



' The method of least squares furnishes the formulas 



nSd^ — 2d . 2d ' 

 , _ n.2 dt—2d. 2t 

 n.2d^—2d.2d' 

 in which due preference is given to the temperatures corresponding to a greater depth. The observa- 

 tions become relatively more accurate as temperature and depth increase, and seem also to have been 

 m.ide with greater care. 



