DOUBLE INTEGRALS TO OPTICAL PROBLEMS. 
351 
§ 45. This expression as it stands is quite intractable. We are enabled, however, 
to make progress by means of tables which Ta it* gives in his paper on the kinetic 
theory. Our subject of integration is 
„-p 2 
sin 2/wP sin 2/wP 
P 3 e- 
P 2 
P <r p2 + (2P 2 + 1) 
i/P 
sin 2buP X 3 . „ , . 
-—— . — m i ait s notation. 
On marking out the graph of X 3 /X 3 by means of the values in column 6 of Tait’s 
table, it becomes obvious that the general outline of the function is very near to 
that of 
iP 2 e-^ 2 . 
To make the agreement as good as possible we choose /x so that the two curves 
may attain their maximum for the same value of P. 
Now the latter function has its maximum at P = - ; graphically we see that we 
must choose - = ‘9025 (about) ; = *81 . . . 
In the accompanying figure, I. (continuous curve) is X 3 /X 3 ; II. (dotted curve) is 
^P~e“ 1>v81 . The agreement is so good that the error in the integral through using II. 
instead of I. will be only about 1 per cent. But this is of the order of the errors 
in the observed visibilities, with which we propose to compare our results. 
