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The superiority of the Jackson crossed cylinder technic in determining the exact axis of astigmatism has been adequately stressed and demonstrated photographically, mathematically and practically. Not much is said about its advantages in determining the exact amount of cylinder required in any given case. I believe this is due to the fact that as one makes the series of indicated changes in the cylindric lens in the trial frame, one must be continually altering the amount of the spherical component of the combination in order to keep the general visual acuity up to a sufficiently high level for fine differences to be perceptible.
If the accommodation has been paralyzed in a case of compound hyperopic astigmatism, the visual acuity will be increased by the addition of plus spheres up to a figure that corresponds to the spherical error plus one half of the cylindric error, provided proper test objects are
Smart FP. SOME OBSERVATIONS ON CROSSED CYLINDERS. Arch Ophthalmol. 1940;24(5):999–1000. doi:10.1001/archopht.1940.00870050149014
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