58 BULLETIN OP THE UNIVERSITY OP WISCONSIN 



Zero at end. Zero in middle. 

 W. E. W. E. 



29.1 31.2 +64.0 +13.5 



35.4 24.9 - 10.1 - 60.7 



64.5 56.1 +77.5 



56.1 -70.8 



z 8.4 -4- 4 = 2.1 div. z= + 6.7 -=- 4 = + 1.675 div. 



A method of reduction which is the same for both types 

 of level, and which is in most cases more convenient than 

 the above, is as follows: In the square array of numbers 

 which constitute the observed readings of the level, take 

 the diagonal differences. The mean of the two diagonal 

 differences is the inclination of the line in half divisions of 

 the level. That end of the line is the higher which is ad- 

 jacent to the greatest single reading. If the level readings 

 have been correctly made the two diagonal differences will 

 be the same, and the reduction thus serves as a check upon 

 the accuracy of the record. 



Thus, from the readings given above, we see at a glance 

 that in the first case z = 4.2 half divisions and the readings 

 have been correctly made. In the second case 2 = 3.35 half 

 divisions and there is a discrepancy of 0.1 div. in the 

 readings. 



Although I cannot doubt that this simple mode of reduc- 

 ing level readings has been employed by others, I do not 

 find it in any of the treatises upon practical astronomy to 

 which I have access. 



To Focus a Telescope. Let the telescope be directed to a 

 circum-polar star near culmination and introduce between 

 the objective and the star an opaque screen pierced with a 

 circular aperture from 10 to 20 mm in diameter. As the 

 aperture is moved about in front of the objective an image 

 of the star will be formed by different parts of the objec- 

 tive, and if the telescope is not perfectly focused these im- 

 ages will fall at slightly different parts of the field; e. g., 

 let the aperture be held opposite the upper part of the 

 objective and the star's image be bisected with a horizontal 



