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SPHEROMETERS

Page 2.

From the radii given and the leg center of his spherometer, I capculated the sagitta. These figures shall be used all through for reference.

 
"R"
"D"
"S"
  
Mirror
30.830
5.750"
0.13434"
  
Corrector
6.887"
5.750"
0.62879"
  
Now let us see how the 0.005" tolernce affects the Sagitta reading.
Mirror
30.835"
5.750"
0.13432"
 a difference of 0.00002"
Corrector
6.892"
5.750"
0.62829"
 a difference of 0.0005"
Now how 0.500" on the primary and 0.070" on the corrector.  
Mirror
31.330"
5.750"
0.13219"
 a difference of 0.00215"
Corrector
6.957"
5.750"
0.62184"
 a difference of 0.00695"

You will see that reasionable margin of error is allowable in taking the Sagitta reading.

Next is the effect of temperature. In Cairns the variation in Temperature at midday, winter to summer would be 7 Degrees Centigrade (12.6 Deg Fahrenheiit). As brass is eaiser to work with than steel we will see what effect the temperature has on readings.

Coefficent of Expansion for Brass
Coefficent of Expansion for Pyrex
Difference 		0.00000957" per Degree Fahrenheit
0.00000183" per Degree Fahrenheit
0.00000774" per Degree Fahrenheit

Expansion of "D"   =   5.76   x   0.00000774   x   12.6   =   0.00056"

 
"R"
"D"
"S"
  
Mirror
30.83698"
5.7506"
0.13434"
 A difference of 0.00698"
Corrector
6.6884"
5.7506"
0.62879"
 A difference of 0.0141"
 
Now let us see what effect errors of 0.001" in measuring the dimension "D" have.
         
Mirror
30.831"
5.750"
0.13434"
  
 
30.842"
5.751"
0.13434"
 A difference of 0.032"
 
30.852"
5.752"
0.13434"
 
30.853"
5.753"
0.13434"
  
         
Corrector
6.887"
5.750"
0.62879"
  
 
6.889"
5.751"
0.62879"
 A difference of 0.006"
 
6.892"
5.752"
0.62879"
 
6.894"
5.753"
0.62879"
  
         
Now let us see what effect errors of 0.0001" in measuring the dimension "S" have.
         
Mirror
30.831"
5.750"
0.13434"
  
 
30.808"
5.750"
0.13444"
 A difference of 0.069"
 
30.785"
5.750"
0.13454"
 
30.762"
5.750"
0.13464"
  
         
Corrector
6.887"
5.750"
0.62879"
  
 
6.886"
5.750"
0.62889"
 A difference of 0.003"
 
6.885"
5.750"
0.62899"
 
6.884"
5.750"
0.62909"
  

Now while the spacing "D" of the holes for the pins or balls nay not be critical as long as we can messure their centers, how critical is the centreing of the hole for the dial indicator or mictometer. I did a calculation. Suppose the drill ran whaen drilling the hole and it is out 3/32". I made a calulation on a radius on a 6" radius of curvature.

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